Research ArticleSelf-Interference Cancellation-Based Mutual-Coupling Modelfor Full-Duplex Single-Channel MIMO Systems

Pawinee Meerasri Peerapong Uthansakul and Monthippa Uthansakul

School of Telecommunication Engineering Suranaree University of Technology Muang Nakhon Ratchasima 30000 Thailand

Correspondence should be addressed to Peerapong Uthansakul uthansakulsutacth

Received 26 July 2013 Revised 1 December 2013 Accepted 2 December 2013 Published 16 January 2014

Academic Editor Hon Tat Hui

Copyright copy 2014 Pawinee Meerasri et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The challenge of a full-duplex single-channel system is the method to transmit and receive signals simultaneously at the same timeand on the same frequency Consequently a critical issue involved in such an operation is the resulting self-interference Moreoverfor MIMO system the full-duplex single-channel system is subjected to the very strong self-interference signals due to multipletransmitting and receiving antennas So far in the pieces of literature there have not been any suitable techniques presented toreduce the self-interference for full-duplex single-channel MIMO systems This paper initially proposes the method to cancel theself-interference by utilizing the mutual-coupling model for self-interference cancellation The interference can be eliminated byusing a preknown interference that is the mutual-coupling signals The results indicate that the channel capacity performance ofthe proposed technique can significantly be improved due to the reduction of the self-interference powerThemeasurement resultsindicate that the proposed MIMO system can suppress the self-interference and mutual-interference signals with the reduction of31 dB received power

1 Introduction

Nowadays multiple-input multiple-output (MIMO) systemis the promising technology for the next generation of wire-less communication systems as MIMO system can providea wide coverage area a high spectral efficiency and anincreased system capacity The MIMO system employs themultiple antennas to transmit signals on the same frequencywhich cause the strong interference signals at the receivingantennas on the same side These interferences are morepronounced when operating the full-duplex single-channelMIMO system

The full-duplex single-channel system is one of the mostinteresting technologies for future wireless communicationsbecause it can offer double throughput from any conventionalsystem without paying any expenses of spectrum This isbecause the system is able to receive and transmit simultane-ously within a single channel In the literature the problemof full-duplex interference has been addressed on the specificconfiguration of MIMO relay nodes The self-interferencecancellation is introduced to be used at only relaying node

[1ndash3] So far there have not been any techniques proposedfor source or destination In this light the authors proposethe new technique to suppress the self-interference for full-duplex single-channelMIMO systems From the literature onRF interference cancellation thework in [4ndash9] presents a full-duplex wireless system that can transmit and receive signalsat the same time and on the same frequency band since itrequires at least two antennas having one for transmitter (Tx)and one for receiver (Rx)The key challenge in realizing sucha system lies in addressing the self-interference generatedby the Tx antenna at the Rx antenna For example onecan implement the above self-interference cancellation ideacompletely in analog domain using noise cancellation circuitsreported by Radunovic et al [5] But the practical noisecancellation circuits can only handle a dynamic range ofat most sim30 dB Another technique in [6] employs theantenna cancellation by using three antennas to create a beamforming nullThis method cancels the self-interference at thereceiver antenna by using antenna placement as an additionalcancellation technique or antenna cancellation The antennacancellation requires two asymmetrically placed transmitting

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 405487 10 pageshttpdxdoiorg1011552014405487

2 International Journal of Antennas and Propagation

antennas and one receiving antenna This three-antennasystem can remove sim60 dB reduction of self-interferencepower for a802154 system Although it looks promising theantenna cancellation-based designs have two major limita-tions The first is that they require three antennas havingtwo transmitting antennas and one receiving antenna whichare very sensitive to the relative location of antennas andany material around them It is a fact that the full-duplexsystem can have double throughput but with three antennasaMIMO system can have triple throughput Hence the use ofmultiple antennas for only full-duplex purpose is not worthThe second limitation is a bandwidth constraint a theoreticallimit which prevents supporting wideband signal such asWiFi

TheMIMO techniques for wireless communications havebeen studied extensively over the past decade as a means ofachieving significant capacity gains needed for supportinghigh-rate wireless broadband applications [10] A criticalfactor in the design and analysis of MIMO systems is the the-oretical models which are used for representing the MIMOtransceiver as well as the wireless fading channel So far inthe literature the factor on realistic channel configuration hasgained a lot of attention such as spatial correlation (see eg[11 12] and many others) One issue which has received lessattention in comparison is that ofmutual coupling [10 13ndash15]which occurs due to electromagnetic interactions betweenthe antennas in both transmitter and receiver This effectas well as spatial correlation is particularly significant forapplications with compact antennas such as cellular mobilein which the available space for placing the antennas is highlyrestrictive

In this paper we will investigate the effect of antennamutual coupling (MC) on the full-duplex single-channelMIMO system with the aim of self-interference eliminationsBased on the mutual-coupling model the signals with self-interference can be preknown As a result it is possible toeliminate all self-interference signals by subtracting frompreknown signals The concept of transmitting and receivingmutual impedances is employed to incorporate the antennaMC effect into the correlated channel model [16] This modelis applied towork out the suppression technique to reduce theself-interference performed by subtracting the interferencesignals from the transmitting signals that are suitably tunedaccording to the interaction between multiple antennas Thisis because the self-interference signals do not depend onthe environments Then the proposed technique can bedone on the manufacturing process The paper presents thecomparison between the MC full-duplex single-channel sys-tems with and without the proposed technique The channelcapacity performance is the key performance used to indicatethe merit of proposed technique The results show that theproposed technique is not only to suppress the interferencebut also to improve the system performance capacity

2 Problem Formulation

This paper focuses on the full-duplex wireless communica-tions operating on the same frequency and at the same time

The simultaneous transmitting and receiving signals can beachieved via the cancellation of the self-interference signalHowever the problem is that the self-interference is billions oftimes stronger (60ndash90 dB) than a received signal for examplefor WiFi the self-interference would be nearly up to 80 dBstronger Hence the main key success is to eliminate the self-interference as much as possible In this section the overviewof full-duplex system is presented in order to be the basicknowledge before getting to the main problem of this workNext the survey of RF interference cancellation techniques isdetailed

21 Full-Duplex Wireless Communication Currently full-duplex wireless systems achieve the isolation requiredbetween the two directions of communication using inde-pendence in either time or frequency Accordingly theseduplexings are called time division duplexing (TDD) andfrequency division duplexing (FDD) The TDD system isthe system that divides the access of each node in timeTDD is also commonly known as half-duplexing Other full-duplex wireless systems separate the Tx and Rx functionsin the frequency domain the so-called FDD and mayoperate using two different carrier frequencies for carryingtransmissions In this case nodes 1 and 2 can send data toeach other at the same time although using two differentfrequencies The use of different frequencies prevents thetwo signals from interfering with each other even thoughthe two transmissions occur at the same time Time divisionduplexing exacerbates the inconsistency in the channel viewsacross nodes Since only one node among a pair of com-municating nodes can transmit at a given time the wirelesschannel around the transmitting node may look occupiedwhile the wireless channel around the receiving node maylook unoccupied Such inconsistencies are the root cause ofmany of the problems with time division duplexing wirelessnetworks such as packet losses due to hidden terminal effectsOn the other hand frequency division duplexing requiresa wireless node to use twice the frequency bandwidth forsending and receiving signals of a given bandwidth In somecases this is expensive and infeasible The key challenge inimplementing a full-duplex wireless system where a devicecan simultaneously transmit and receive signals over-the-airat the same time and in the same frequency band is the largepower differential between the self-interference from a nodersquosown transmission and the signal of interest coming from adistant source

22 Single-Channel Full-DuplexWireless Communications Abasic perception of wireless communication is that a radiocannot transmit and receive on the same frequency and at thesame time Aswireless signals attenuate quickly over distancethe signal from a local transmitting antenna is hundreds ofthousands of times stronger than transmissions from othernodes Figure 1 shows an example where nodes 1 and 2 aretrying to send data to each other simultaneously using thesame frequency Node 1 own transmission is much strongerat its receiving antenna compared to the signal it receivesfrom node 2 With such strong self-interference the receiver

International Journal of Antennas and Propagation 3

Tx Rx

Rx Tx

Node 1 Node 2

Self-interference

Figure 1 Self-interference in the single-channel full-duplex wirelesscommunications using one transmitting antenna and one receivingantenna

of node 1 is unable to decode any signals that node 2 istrying to send to node 1 This example shows that the biggestchallenge in designing single-channel full-duplex wirelesscommunications is to eliminate the self-interference signalfrom the receiver of the wireless node In theory this problemshould be easy to solve For a system with antennas each fortransmitting and receiving since the system knows the signalof transmitting antenna it can subtract this from the signal ofreceiving antenna and decode the remainder

23 Self-Interference Cancellation Thework in [17] proposedthe design of full-duplex system that requires only oneantenna using circulator to share the same antenna for trans-mitting and receiving paths as shown in Figure 2 The self-interference cancellation (SIC) uses the knowledge of trans-mission to cancel self-interference in the RF signal beforeit is digitized In an ideal analog cancellation scenario theamplitudes from the two paths would be perfectly matchedat the receiver and phase of the two signals would differby exact 120587 To cancel self-interference the best performingprior design is obtained The authors gain the inverse of thetransmitted signal using a phase shifter with attenuator Theattenuator and phase shifter allow a modulator to control theangle and amplitude of a feed signal

3 System Model

31 MIMO Model In this section the capacity formula ofMIMO systems is briefly given We assume an indepen-dent and identically distributed (iid) Rayleigh flat-fadingchannel in rich scattering environments and the channelis unknown at the transmitter and perfectly known at thereceiver The basic MIMO structure is depicted in Figure 3Let the number of transmitting and receiving antennas be119873

119879

and119872119877 respectively We denote this MIMO communication

link as (119873119879119872

119877) The119872

119877times 1 received signal vector y can be

written as

y = Hx + n (1)

Tx data

Rx data

Antenna

Leakage

f1

f1

Figure 2 Self-interference in the single-channel full-duplex single-antenna wireless communications

Tx Rx

Figure 3 Basic structure of MIMO system

with this notation channel output sequence that can bewritten in matrix form as

[

[

[

[

[

119910

1

119910

2

119910

119872119877

]

]

]

]

]

=

[

[

[

[

[

ℎ

11ℎ

12ℎ

1119873119879

ℎ

21ℎ

22sdot sdot sdot ℎ

2119873119879

d

ℎ

1198721198771ℎ

1198721198772sdot sdot sdot ℎ

119872119877119873119879

]

]

]

]

]

[

[

[

[

[

119909

1

119909

2

119909

119873119879

]

]

]

]

]

+

[

[

[

[

[

119899

1

119899

2

119899

119872119877

]

]

]

]

]

(2)

where H is 119872119877times 119873

119879channel matrix with the entry ℎ

119894119895

describing the channel gain between the 119895th transmittingantenna and the 119894th receiving antenna x is119873

119879times1 transmitted

signal vector with independent symbols and n is 119872119877times 1

additive white Gaussian noise (AWGN) vectorThe AWGN vector n satisfies 119864nn119867 = I

119872119877in which n119867

denotes the conjugate transpose of n and I119872119877

denotes119872119877times

119872

119877identity matrixAs the channel is unknown at the transmitter equal power

is allocated to each of the transmitting antennas Then theMIMO capacity in bits per second per Hertz (bpsHz) isderived as

119862 = log2det(I

119872119877+

120588

119873

119879

HH119867) (3)

where 120588 is the average received signal to noise ratio (SNR)His normalized channel matrix [18]

32 Mutual-Coupling Effects on MIMO In this section inorder to support parallel signal transmission in a MIMOsystem the antennas at transmitter and receiver have to beproperly coupled to the modes offered by the wireless com-munication channel Hence in Figure 4 the array elements

4 International Journal of Antennas and Propagation

Transmitter Channel Receiver

Vs1

Vs2

VsN

Is1

Is2

IsN

Zs

Vt1

Vt2

VtN

ZT ZR

Vr1

Vr2

VrM

ZL

H

Figure 4 An 119872119877times 119873

119879MIMO system based on mutual-coupling

model

location (including spacing and orientation) with respect tothe scatterers is of paramount importance in the operationof the MIMO system The interactions between the entireset of antennas and scatterers are initially described bythe impedance matrix Z For dipoles however the mutualimpedance can easily be calculated using classical inducedelectromagnetic force (EMF) method [19] The value of themutual impedance between the 119898th and 119899th dipoles 119885

119898119899is

given by [20]

119885

119898119899=

30 [05772 + ln (120573119889lam) minus 119862119894 (120573119889lam)]+119895 [30119878

119894(120573119889lam)] 119898 = 119899

30 [2119862

119894(119906

0) minus 119862

119894(119906

1) minus 119862

119894(119906

2)]

minus119895 [30 (2119878

119894(119906

0) minus 119878

119894(119906

1) minus 119878

119894(119906

2))] 119898 = 119899

(4)

where 120573 = 2120587119889lam is the wave number 119889lam2 is the dipolelength and the constants are given by [20]

119906

0= 120573119889

ℎ

119906

1= 120573(

radic119889

2

ℎ+ (119889lam2)

2+ (119889lam2))

119906

2= 120573(

radic119889

2

ℎ+ (119889lam2)

2minus (119889lam2))

(5)

where 119889ℎis the horizontal distance between the two dipole

antennas and119862119894(119906) and 119878

119894(119906) are the cosine and sine integrals

respectively

119862

119894 (119906) = int

119906

infin

cos (119909)119909

119889119909 119878

119894 (119906) = int

119906

0

sin (119909)119909

119889119909 (6)

It has to be noted that while calculating119885119898119899 we assume that

the 119899th dipole is excited with current while all the remainingdipoles are open circuited

In general mutual coupling can be characterized bynumerical modelling techniques [19] However for dipoleswe can use analytical mutual coupling into theMIMO systemmodelThe couplingmatrix of transmitting antenna arrayC

119879

can bewritten using fundamental electromagnetic and circuittheory [19] C

119879has the meaning of transfer function matrix

for the transmitting array and is given as

C119879= (119885

119860+ 119885

119879) (Z + 119885

119879I119873119879)

minus1

(7)

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4

Tx1

Rx1Tx2

Rx2

Tx3

Rx3Tx4

Rx4S X

HLI

HLI

HLI

HLI

HNI

H1

Figure 5 Model of full-duplex single-channel 4 times 4MIMO system

where119885119860is the elementrsquos impedance in isolationThe element

119885

119898119899of matrix Z is defined by using the EMF method

as described in (4) Also the coupling matrix of receivingantenna array C

119877can be determined in a similar manner C

119877

has the meaning of transfer function matrix for the receivingarray and is given as

C119877= (119885

119860+ 119885

119879) (Z + 119885

119879I119872119877)

minus1

(8)

4 Proposed Self-Interference Cancellation

In this section we consider a generic MIMO radio unitequipped with 119872

119877RF receivers antennas and 119873

119879RF signal

generatorstransmitters Among all generators there are119873119904=

119873

119879minus119872

119877primary generators and 119872

119877auxiliary generators

The primary generators are used to transmit up to 119873

119878

independent streams of data The auxiliary generators areused to generate RF waveforms for SIC at the RF frontendof the receivers on the same frequency See Figure 5

Furthermore we index the receiver by 119896 = 1 119872

119877

and the transmitter by 119896 = 119872

119877+ 1 119873

119879 Then for each

transmitted data packet subject to linear modulation a RFsignal stream transmitted from the 119896th generator ideally canbe expressed by 119909

119896(119905) = Re119909

119896(119905) exp(1198952120587119891

119888119905) where119891

119888is the

carrier frequency and

119909

119896 (119905) =

119868

sum

119894=1

119892

(119894)

119896(119905) lowast

119873minus1

sum

119899=minus119871

119904

(119894)

119899119901 (119905 minus 119899119879) (9)

where 119909119896(119905) is the complex baseband form (also called 119868119876

waveform) of 119909119896(119905) Here 119892(119894)

119896(119905) is the complex impulse

response of the 119896th transmission for data stream 119894 (of total 119868streams) 119904(119894)

119899is the complex symbol sequence for data stream

119894 119873 + 119871 is the number of complex symbols per stream(including the 119871 prefixed symbols as used in OFDM system)and 119901(119905) is the fundamental pulse waveform used for linearpulse modulation which has the double-sided bandwidth119882and the effective duration 119879 For high spectral efficiency it istypical that 119879 is equal to or only slightly larger than 1119882 Theoperator lowast denotes convolution

International Journal of Antennas and Propagation 5

Tx1

Tx2

Tx3

Tx4

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4 Rx4

Rx3

Rx2

Rx1

ZS ZT ZR ZL

S X

H1

H2

Figure 6 4 times 4MIMO system with mutual-coupling model

TheRF self-interference received by the by the 119897th receiveris 119910119897(119905) = Re119910

119897(119905) exp(1198952120587119891

119888119905) where 119897 = 1 119872

119877 and

119910

119897(119905) = sum

119873119879

119896=1ℎmc119897119896(119905)lowast119909119896(119905) = sum

119868

119894=1([sum

119873119879

119896=1ℎmc119897119896(119905)lowast119892

(119894)

119896(119905)]lowast

sum

119873minus1

119899=0119904

(119894)

119899119905(119905 minus 119899119879)) is the 119868119876 waveform of 119910

119897(119905) In Figure 6

when the mutual coupling is presented ℎ119897119896(119905) is the complex

baseband channel impulse response from the 119896th generator tothe 119897th receiver on the same radio Hence the channel matrixℎ

119897119896(119905) obtained from the case that this effect is absent has to be

pre- and postmultiplied by coupling matrices C119877and C

119879 As

a result the new channel matrix is given by Hmc = C119877HC119879

To cancel the RF self-interference 119910119897(119905) for all 119897 and 119905 it is

necessary to find 119892(119894)119896(119905) for all 119896 and 119894 such that 119910

119897(119905) = 0 for

all 119897 or equivalently sum119873119879119896=1

ℎmc119897119896(119905) lowast 119892(119894)

119896(119905) = 0 for all 119897 and 119894

The matrix form of this condition is

[

[

[

ℎmc11 (119905) sdot sdot sdot ℎmc1119873119879(119905)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

ℎmc1198721198771(119905) sdot sdot sdot ℎmc119872119877119873119879

(119905)

]

]

]

lowast

[

[

[

119892

(119894)

1(119905)

sdot sdot sdot

119892

(119894)

119873119879(119905)

]

]

]

= 0 (10)

or equivalently in more compact form

Hmc (119905) lowast g(119894) (119905) = 0 (11)

Although given in baseband (11) ensures SIC even at the RFfrontend Also note that when all elements in a row ofHmc(119905)are corrupted by a common scalar due to receiver phase noisethe solution g(119894)(119905) to (11) is not affected

To find the solution to (10) we need to apply a knownnotion of vector space in the field of functions of timeThe rank 119903H(119905) of the matrix Hmc(119905) that are convolutelyindependent It follows that 119903H(119905) le min119872

119877 119873

119879 = 119872

119877

The dimension of the solution space of (10) which is alsocalled the dimension of the (right) null space ofHmc(119905) is thenumber of convolutely independent solutions to (10) whichis 119889null = 119873

119879minus 119903H(119905) ge 119873

119904 If 119889null = 119873

119904 we call it a typical

case (very likely in practice) or otherwise if 119889null gt 119873

119904 we

call it atypical case (not very likely in practice) The number119868 of the data streams in (9) must be no larger than 119889null

In general for119872119877ge 1 and 119873

119904ge 1 the 119894th in a set of 119873

119904

convolutely independent solutions to (12) can be written as

g(119894) (119905) =

[

[

[

[

[

[

[

[

[

[

[

g(119894) (119905)

0119894minus11

119892

(119894)

0(119905)

0119868minus11

]

]

]

]

]

]

]

]

]

]

]

(12)

where 01198981

is the 119898 times 1 zero vector and g(119894)(119905) and 119892(119894)0(119905) are

a solution to A(119905) lowast g(119894)(119905) + b119894(119905) lowast 119892

(119894)

0(119905) = 0 where A(119905) is

a square matrix equal to Hmc(119905) without its last 119873119904 columnsand b

119894(119905) is the (119872

119877+ 119894)th column of Hmc(119905) Furthermore

we can choose the solution

g(119894) (119905) = minusadj A (119905) lowast b119894 (119905) (13)

and 119892

(119894)

0(119905) = detA(119905) Both the adjoint adjA(119905)and the

determinant detA(119905) can be obtained analytically in thesame way as those of a matrix of numbers as shown in[21] except that all multiplications should be substituted byconvolutions It is important to note that expression (13) doesnot involve any division but only convolutions and sums

The solutions shown in (12) are valid for arbitraryHmc(119905)as long as detA(119905) = 0This condition can bemet if ℎ

119896119896(119905) for

119896 = 1 119872

119877have the largest norms among ℎ

119897119896(119905) for all 119897

and 119896 To ensure that we can either place the 119872119877auxiliary

transmitting antennas close enough to the 119872

119877receiving

antennas or directly couple the119872119877auxiliary generators to the

119872

119877receivers at the RF frontendIn this section the proposed system is designed to

formulate the self-interference based on mutual-couplingmodel These self-interference signals are caused by multipleantennasTheproposed system for full-duplex single-channelMIMO system is illustrated in Figure 7 As shown in Figure 7the self-interference based on mutual-coupling Hmc119868 can bewritten as

Hmc119868s = HLIs +HNIC119877s (14)

where s isin 119862

119904times1 is the transmitted signal HLI isin 119862

119904times119904 is adiagonal matrix that represents the self-interference signalsand HNI isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

Next the proposed method to suppress the interferencesignals is performed as shown in Figure 7 The transmittedsignals are coupled to matrix 119882 in order to perform thenegative self-interference and mutual-interference signals asclosely as possible Inside matrix 119882 the attenuation andphase shifter are employed to adjust the preknown signalsfor compensating the self-interference signals and mutual-interference signals The compensation matrix W is givenby

Ws = T119909C119879s + Gs (15)

where T119909isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

2 International Journal of Antennas and Propagation

antennas and one receiving antenna This three-antennasystem can remove sim60 dB reduction of self-interferencepower for a802154 system Although it looks promising theantenna cancellation-based designs have two major limita-tions The first is that they require three antennas havingtwo transmitting antennas and one receiving antenna whichare very sensitive to the relative location of antennas andany material around them It is a fact that the full-duplexsystem can have double throughput but with three antennasaMIMO system can have triple throughput Hence the use ofmultiple antennas for only full-duplex purpose is not worthThe second limitation is a bandwidth constraint a theoreticallimit which prevents supporting wideband signal such asWiFi

TheMIMO techniques for wireless communications havebeen studied extensively over the past decade as a means ofachieving significant capacity gains needed for supportinghigh-rate wireless broadband applications [10] A criticalfactor in the design and analysis of MIMO systems is the the-oretical models which are used for representing the MIMOtransceiver as well as the wireless fading channel So far inthe literature the factor on realistic channel configuration hasgained a lot of attention such as spatial correlation (see eg[11 12] and many others) One issue which has received lessattention in comparison is that ofmutual coupling [10 13ndash15]which occurs due to electromagnetic interactions betweenthe antennas in both transmitter and receiver This effectas well as spatial correlation is particularly significant forapplications with compact antennas such as cellular mobilein which the available space for placing the antennas is highlyrestrictive

In this paper we will investigate the effect of antennamutual coupling (MC) on the full-duplex single-channelMIMO system with the aim of self-interference eliminationsBased on the mutual-coupling model the signals with self-interference can be preknown As a result it is possible toeliminate all self-interference signals by subtracting frompreknown signals The concept of transmitting and receivingmutual impedances is employed to incorporate the antennaMC effect into the correlated channel model [16] This modelis applied towork out the suppression technique to reduce theself-interference performed by subtracting the interferencesignals from the transmitting signals that are suitably tunedaccording to the interaction between multiple antennas Thisis because the self-interference signals do not depend onthe environments Then the proposed technique can bedone on the manufacturing process The paper presents thecomparison between the MC full-duplex single-channel sys-tems with and without the proposed technique The channelcapacity performance is the key performance used to indicatethe merit of proposed technique The results show that theproposed technique is not only to suppress the interferencebut also to improve the system performance capacity

2 Problem Formulation

This paper focuses on the full-duplex wireless communica-tions operating on the same frequency and at the same time

The simultaneous transmitting and receiving signals can beachieved via the cancellation of the self-interference signalHowever the problem is that the self-interference is billions oftimes stronger (60ndash90 dB) than a received signal for examplefor WiFi the self-interference would be nearly up to 80 dBstronger Hence the main key success is to eliminate the self-interference as much as possible In this section the overviewof full-duplex system is presented in order to be the basicknowledge before getting to the main problem of this workNext the survey of RF interference cancellation techniques isdetailed

21 Full-Duplex Wireless Communication Currently full-duplex wireless systems achieve the isolation requiredbetween the two directions of communication using inde-pendence in either time or frequency Accordingly theseduplexings are called time division duplexing (TDD) andfrequency division duplexing (FDD) The TDD system isthe system that divides the access of each node in timeTDD is also commonly known as half-duplexing Other full-duplex wireless systems separate the Tx and Rx functionsin the frequency domain the so-called FDD and mayoperate using two different carrier frequencies for carryingtransmissions In this case nodes 1 and 2 can send data toeach other at the same time although using two differentfrequencies The use of different frequencies prevents thetwo signals from interfering with each other even thoughthe two transmissions occur at the same time Time divisionduplexing exacerbates the inconsistency in the channel viewsacross nodes Since only one node among a pair of com-municating nodes can transmit at a given time the wirelesschannel around the transmitting node may look occupiedwhile the wireless channel around the receiving node maylook unoccupied Such inconsistencies are the root cause ofmany of the problems with time division duplexing wirelessnetworks such as packet losses due to hidden terminal effectsOn the other hand frequency division duplexing requiresa wireless node to use twice the frequency bandwidth forsending and receiving signals of a given bandwidth In somecases this is expensive and infeasible The key challenge inimplementing a full-duplex wireless system where a devicecan simultaneously transmit and receive signals over-the-airat the same time and in the same frequency band is the largepower differential between the self-interference from a nodersquosown transmission and the signal of interest coming from adistant source

22 Single-Channel Full-DuplexWireless Communications Abasic perception of wireless communication is that a radiocannot transmit and receive on the same frequency and at thesame time Aswireless signals attenuate quickly over distancethe signal from a local transmitting antenna is hundreds ofthousands of times stronger than transmissions from othernodes Figure 1 shows an example where nodes 1 and 2 aretrying to send data to each other simultaneously using thesame frequency Node 1 own transmission is much strongerat its receiving antenna compared to the signal it receivesfrom node 2 With such strong self-interference the receiver

International Journal of Antennas and Propagation 3

Tx Rx

Rx Tx

Node 1 Node 2

Self-interference

Figure 1 Self-interference in the single-channel full-duplex wirelesscommunications using one transmitting antenna and one receivingantenna

of node 1 is unable to decode any signals that node 2 istrying to send to node 1 This example shows that the biggestchallenge in designing single-channel full-duplex wirelesscommunications is to eliminate the self-interference signalfrom the receiver of the wireless node In theory this problemshould be easy to solve For a system with antennas each fortransmitting and receiving since the system knows the signalof transmitting antenna it can subtract this from the signal ofreceiving antenna and decode the remainder

23 Self-Interference Cancellation Thework in [17] proposedthe design of full-duplex system that requires only oneantenna using circulator to share the same antenna for trans-mitting and receiving paths as shown in Figure 2 The self-interference cancellation (SIC) uses the knowledge of trans-mission to cancel self-interference in the RF signal beforeit is digitized In an ideal analog cancellation scenario theamplitudes from the two paths would be perfectly matchedat the receiver and phase of the two signals would differby exact 120587 To cancel self-interference the best performingprior design is obtained The authors gain the inverse of thetransmitted signal using a phase shifter with attenuator Theattenuator and phase shifter allow a modulator to control theangle and amplitude of a feed signal

3 System Model

31 MIMO Model In this section the capacity formula ofMIMO systems is briefly given We assume an indepen-dent and identically distributed (iid) Rayleigh flat-fadingchannel in rich scattering environments and the channelis unknown at the transmitter and perfectly known at thereceiver The basic MIMO structure is depicted in Figure 3Let the number of transmitting and receiving antennas be119873

119879

and119872119877 respectively We denote this MIMO communication

link as (119873119879119872

119877) The119872

119877times 1 received signal vector y can be

written as

y = Hx + n (1)

Tx data

Rx data

Antenna

Leakage

f1

f1

Figure 2 Self-interference in the single-channel full-duplex single-antenna wireless communications

Tx Rx

Figure 3 Basic structure of MIMO system

with this notation channel output sequence that can bewritten in matrix form as

[

[

[

[

[

119910

1

119910

2

119910

119872119877

]

]

]

]

]

=

[

[

[

[

[

ℎ

11ℎ

12ℎ

1119873119879

ℎ

21ℎ

22sdot sdot sdot ℎ

2119873119879

d

ℎ

1198721198771ℎ

1198721198772sdot sdot sdot ℎ

119872119877119873119879

]

]

]

]

]

[

[

[

[

[

119909

1

119909

2

119909

119873119879

]

]

]

]

]

+

[

[

[

[

[

119899

1

119899

2

119899

119872119877

]

]

]

]

]

(2)

where H is 119872119877times 119873

119879channel matrix with the entry ℎ

119894119895

describing the channel gain between the 119895th transmittingantenna and the 119894th receiving antenna x is119873

119879times1 transmitted

signal vector with independent symbols and n is 119872119877times 1

additive white Gaussian noise (AWGN) vectorThe AWGN vector n satisfies 119864nn119867 = I

119872119877in which n119867

denotes the conjugate transpose of n and I119872119877

denotes119872119877times

119872

119877identity matrixAs the channel is unknown at the transmitter equal power

is allocated to each of the transmitting antennas Then theMIMO capacity in bits per second per Hertz (bpsHz) isderived as

119862 = log2det(I

119872119877+

120588

119873

119879

HH119867) (3)

where 120588 is the average received signal to noise ratio (SNR)His normalized channel matrix [18]

32 Mutual-Coupling Effects on MIMO In this section inorder to support parallel signal transmission in a MIMOsystem the antennas at transmitter and receiver have to beproperly coupled to the modes offered by the wireless com-munication channel Hence in Figure 4 the array elements

4 International Journal of Antennas and Propagation

Transmitter Channel Receiver

Vs1

Vs2

VsN

Is1

Is2

IsN

Zs

Vt1

Vt2

VtN

ZT ZR

Vr1

Vr2

VrM

ZL

H

Figure 4 An 119872119877times 119873

119879MIMO system based on mutual-coupling

model

location (including spacing and orientation) with respect tothe scatterers is of paramount importance in the operationof the MIMO system The interactions between the entireset of antennas and scatterers are initially described bythe impedance matrix Z For dipoles however the mutualimpedance can easily be calculated using classical inducedelectromagnetic force (EMF) method [19] The value of themutual impedance between the 119898th and 119899th dipoles 119885

119898119899is

given by [20]

119885

119898119899=

30 [05772 + ln (120573119889lam) minus 119862119894 (120573119889lam)]+119895 [30119878

119894(120573119889lam)] 119898 = 119899

30 [2119862

119894(119906

0) minus 119862

119894(119906

1) minus 119862

119894(119906

2)]

minus119895 [30 (2119878

119894(119906

0) minus 119878

119894(119906

1) minus 119878

119894(119906

2))] 119898 = 119899

(4)

where 120573 = 2120587119889lam is the wave number 119889lam2 is the dipolelength and the constants are given by [20]

119906

0= 120573119889

ℎ

119906

1= 120573(

radic119889

2

ℎ+ (119889lam2)

2+ (119889lam2))

119906

2= 120573(

radic119889

2

ℎ+ (119889lam2)

2minus (119889lam2))

(5)

where 119889ℎis the horizontal distance between the two dipole

antennas and119862119894(119906) and 119878

119894(119906) are the cosine and sine integrals

respectively

119862

119894 (119906) = int

119906

infin

cos (119909)119909

119889119909 119878

119894 (119906) = int

119906

0

sin (119909)119909

119889119909 (6)

It has to be noted that while calculating119885119898119899 we assume that

the 119899th dipole is excited with current while all the remainingdipoles are open circuited

In general mutual coupling can be characterized bynumerical modelling techniques [19] However for dipoleswe can use analytical mutual coupling into theMIMO systemmodelThe couplingmatrix of transmitting antenna arrayC

119879

can bewritten using fundamental electromagnetic and circuittheory [19] C

119879has the meaning of transfer function matrix

for the transmitting array and is given as

C119879= (119885

119860+ 119885

119879) (Z + 119885

119879I119873119879)

minus1

(7)

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4

Tx1

Rx1Tx2

Rx2

Tx3

Rx3Tx4

Rx4S X

HLI

HLI

HLI

HLI

HNI

H1

Figure 5 Model of full-duplex single-channel 4 times 4MIMO system

where119885119860is the elementrsquos impedance in isolationThe element

119885

119898119899of matrix Z is defined by using the EMF method

as described in (4) Also the coupling matrix of receivingantenna array C

119877can be determined in a similar manner C

119877

has the meaning of transfer function matrix for the receivingarray and is given as

C119877= (119885

119860+ 119885

119879) (Z + 119885

119879I119872119877)

minus1

(8)

4 Proposed Self-Interference Cancellation

In this section we consider a generic MIMO radio unitequipped with 119872

119877RF receivers antennas and 119873

119879RF signal

generatorstransmitters Among all generators there are119873119904=

119873

119879minus119872

119877primary generators and 119872

119877auxiliary generators

The primary generators are used to transmit up to 119873

119878

independent streams of data The auxiliary generators areused to generate RF waveforms for SIC at the RF frontendof the receivers on the same frequency See Figure 5

Furthermore we index the receiver by 119896 = 1 119872

119877

and the transmitter by 119896 = 119872

119877+ 1 119873

119879 Then for each

transmitted data packet subject to linear modulation a RFsignal stream transmitted from the 119896th generator ideally canbe expressed by 119909

119896(119905) = Re119909

119896(119905) exp(1198952120587119891

119888119905) where119891

119888is the

carrier frequency and

119909

119896 (119905) =

119868

sum

119894=1

119892

(119894)

119896(119905) lowast

119873minus1

sum

119899=minus119871

119904

(119894)

119899119901 (119905 minus 119899119879) (9)

where 119909119896(119905) is the complex baseband form (also called 119868119876

waveform) of 119909119896(119905) Here 119892(119894)

119896(119905) is the complex impulse

response of the 119896th transmission for data stream 119894 (of total 119868streams) 119904(119894)

119899is the complex symbol sequence for data stream

119894 119873 + 119871 is the number of complex symbols per stream(including the 119871 prefixed symbols as used in OFDM system)and 119901(119905) is the fundamental pulse waveform used for linearpulse modulation which has the double-sided bandwidth119882and the effective duration 119879 For high spectral efficiency it istypical that 119879 is equal to or only slightly larger than 1119882 Theoperator lowast denotes convolution

International Journal of Antennas and Propagation 5

Tx1

Tx2

Tx3

Tx4

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4 Rx4

Rx3

Rx2

Rx1

ZS ZT ZR ZL

S X

H1

H2

Figure 6 4 times 4MIMO system with mutual-coupling model

TheRF self-interference received by the by the 119897th receiveris 119910119897(119905) = Re119910

119897(119905) exp(1198952120587119891

119888119905) where 119897 = 1 119872

119877 and

119910

119897(119905) = sum

119873119879

119896=1ℎmc119897119896(119905)lowast119909119896(119905) = sum

119868

119894=1([sum

119873119879

119896=1ℎmc119897119896(119905)lowast119892

(119894)

119896(119905)]lowast

sum

119873minus1

119899=0119904

(119894)

119899119905(119905 minus 119899119879)) is the 119868119876 waveform of 119910

119897(119905) In Figure 6

when the mutual coupling is presented ℎ119897119896(119905) is the complex

baseband channel impulse response from the 119896th generator tothe 119897th receiver on the same radio Hence the channel matrixℎ

119897119896(119905) obtained from the case that this effect is absent has to be

pre- and postmultiplied by coupling matrices C119877and C

119879 As

a result the new channel matrix is given by Hmc = C119877HC119879

To cancel the RF self-interference 119910119897(119905) for all 119897 and 119905 it is

necessary to find 119892(119894)119896(119905) for all 119896 and 119894 such that 119910

119897(119905) = 0 for

all 119897 or equivalently sum119873119879119896=1

ℎmc119897119896(119905) lowast 119892(119894)

119896(119905) = 0 for all 119897 and 119894

The matrix form of this condition is

[

[

[

ℎmc11 (119905) sdot sdot sdot ℎmc1119873119879(119905)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

ℎmc1198721198771(119905) sdot sdot sdot ℎmc119872119877119873119879

(119905)

]

]

]

lowast

[

[

[

119892

(119894)

1(119905)

sdot sdot sdot

119892

(119894)

119873119879(119905)

]

]

]

= 0 (10)

or equivalently in more compact form

Hmc (119905) lowast g(119894) (119905) = 0 (11)

Although given in baseband (11) ensures SIC even at the RFfrontend Also note that when all elements in a row ofHmc(119905)are corrupted by a common scalar due to receiver phase noisethe solution g(119894)(119905) to (11) is not affected

To find the solution to (10) we need to apply a knownnotion of vector space in the field of functions of timeThe rank 119903H(119905) of the matrix Hmc(119905) that are convolutelyindependent It follows that 119903H(119905) le min119872

119877 119873

119879 = 119872

119877

The dimension of the solution space of (10) which is alsocalled the dimension of the (right) null space ofHmc(119905) is thenumber of convolutely independent solutions to (10) whichis 119889null = 119873

119879minus 119903H(119905) ge 119873

119904 If 119889null = 119873

119904 we call it a typical

case (very likely in practice) or otherwise if 119889null gt 119873

119904 we

call it atypical case (not very likely in practice) The number119868 of the data streams in (9) must be no larger than 119889null

In general for119872119877ge 1 and 119873

119904ge 1 the 119894th in a set of 119873

119904

convolutely independent solutions to (12) can be written as

g(119894) (119905) =

[

[

[

[

[

[

[

[

[

[

[

g(119894) (119905)

0119894minus11

119892

(119894)

0(119905)

0119868minus11

]

]

]

]

]

]

]

]

]

]

]

(12)

where 01198981

is the 119898 times 1 zero vector and g(119894)(119905) and 119892(119894)0(119905) are

a solution to A(119905) lowast g(119894)(119905) + b119894(119905) lowast 119892

(119894)

0(119905) = 0 where A(119905) is

a square matrix equal to Hmc(119905) without its last 119873119904 columnsand b

119894(119905) is the (119872

119877+ 119894)th column of Hmc(119905) Furthermore

we can choose the solution

g(119894) (119905) = minusadj A (119905) lowast b119894 (119905) (13)

and 119892

(119894)

0(119905) = detA(119905) Both the adjoint adjA(119905)and the

determinant detA(119905) can be obtained analytically in thesame way as those of a matrix of numbers as shown in[21] except that all multiplications should be substituted byconvolutions It is important to note that expression (13) doesnot involve any division but only convolutions and sums

The solutions shown in (12) are valid for arbitraryHmc(119905)as long as detA(119905) = 0This condition can bemet if ℎ

119896119896(119905) for

119896 = 1 119872

119877have the largest norms among ℎ

119897119896(119905) for all 119897

and 119896 To ensure that we can either place the 119872119877auxiliary

transmitting antennas close enough to the 119872

119877receiving

antennas or directly couple the119872119877auxiliary generators to the

119872

119877receivers at the RF frontendIn this section the proposed system is designed to

formulate the self-interference based on mutual-couplingmodel These self-interference signals are caused by multipleantennasTheproposed system for full-duplex single-channelMIMO system is illustrated in Figure 7 As shown in Figure 7the self-interference based on mutual-coupling Hmc119868 can bewritten as

Hmc119868s = HLIs +HNIC119877s (14)

where s isin 119862

119904times1 is the transmitted signal HLI isin 119862

119904times119904 is adiagonal matrix that represents the self-interference signalsand HNI isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

Next the proposed method to suppress the interferencesignals is performed as shown in Figure 7 The transmittedsignals are coupled to matrix 119882 in order to perform thenegative self-interference and mutual-interference signals asclosely as possible Inside matrix 119882 the attenuation andphase shifter are employed to adjust the preknown signalsfor compensating the self-interference signals and mutual-interference signals The compensation matrix W is givenby

Ws = T119909C119879s + Gs (15)

where T119909isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

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International Journal of

International Journal of Antennas and Propagation 3

Tx Rx

Rx Tx

Node 1 Node 2

Self-interference

Figure 1 Self-interference in the single-channel full-duplex wirelesscommunications using one transmitting antenna and one receivingantenna

of node 1 is unable to decode any signals that node 2 istrying to send to node 1 This example shows that the biggestchallenge in designing single-channel full-duplex wirelesscommunications is to eliminate the self-interference signalfrom the receiver of the wireless node In theory this problemshould be easy to solve For a system with antennas each fortransmitting and receiving since the system knows the signalof transmitting antenna it can subtract this from the signal ofreceiving antenna and decode the remainder

23 Self-Interference Cancellation Thework in [17] proposedthe design of full-duplex system that requires only oneantenna using circulator to share the same antenna for trans-mitting and receiving paths as shown in Figure 2 The self-interference cancellation (SIC) uses the knowledge of trans-mission to cancel self-interference in the RF signal beforeit is digitized In an ideal analog cancellation scenario theamplitudes from the two paths would be perfectly matchedat the receiver and phase of the two signals would differby exact 120587 To cancel self-interference the best performingprior design is obtained The authors gain the inverse of thetransmitted signal using a phase shifter with attenuator Theattenuator and phase shifter allow a modulator to control theangle and amplitude of a feed signal

3 System Model

31 MIMO Model In this section the capacity formula ofMIMO systems is briefly given We assume an indepen-dent and identically distributed (iid) Rayleigh flat-fadingchannel in rich scattering environments and the channelis unknown at the transmitter and perfectly known at thereceiver The basic MIMO structure is depicted in Figure 3Let the number of transmitting and receiving antennas be119873

119879

and119872119877 respectively We denote this MIMO communication

link as (119873119879119872

119877) The119872

119877times 1 received signal vector y can be

written as

y = Hx + n (1)

Tx data

Rx data

Antenna

Leakage

f1

f1

Figure 2 Self-interference in the single-channel full-duplex single-antenna wireless communications

Tx Rx

Figure 3 Basic structure of MIMO system

with this notation channel output sequence that can bewritten in matrix form as

[

[

[

[

[

119910

1

119910

2

119910

119872119877

]

]

]

]

]

=

[

[

[

[

[

ℎ

11ℎ

12ℎ

1119873119879

ℎ

21ℎ

22sdot sdot sdot ℎ

2119873119879

d

ℎ

1198721198771ℎ

1198721198772sdot sdot sdot ℎ

119872119877119873119879

]

]

]

]

]

[

[

[

[

[

119909

1

119909

2

119909

119873119879

]

]

]

]

]

+

[

[

[

[

[

119899

1

119899

2

119899

119872119877

]

]

]

]

]

(2)

where H is 119872119877times 119873

119879channel matrix with the entry ℎ

119894119895

describing the channel gain between the 119895th transmittingantenna and the 119894th receiving antenna x is119873

119879times1 transmitted

signal vector with independent symbols and n is 119872119877times 1

additive white Gaussian noise (AWGN) vectorThe AWGN vector n satisfies 119864nn119867 = I

119872119877in which n119867

denotes the conjugate transpose of n and I119872119877

denotes119872119877times

119872

119877identity matrixAs the channel is unknown at the transmitter equal power

is allocated to each of the transmitting antennas Then theMIMO capacity in bits per second per Hertz (bpsHz) isderived as

119862 = log2det(I

119872119877+

120588

119873

119879

HH119867) (3)

where 120588 is the average received signal to noise ratio (SNR)His normalized channel matrix [18]

32 Mutual-Coupling Effects on MIMO In this section inorder to support parallel signal transmission in a MIMOsystem the antennas at transmitter and receiver have to beproperly coupled to the modes offered by the wireless com-munication channel Hence in Figure 4 the array elements

4 International Journal of Antennas and Propagation

Transmitter Channel Receiver

Vs1

Vs2

VsN

Is1

Is2

IsN

Zs

Vt1

Vt2

VtN

ZT ZR

Vr1

Vr2

VrM

ZL

H

Figure 4 An 119872119877times 119873

119879MIMO system based on mutual-coupling

model

location (including spacing and orientation) with respect tothe scatterers is of paramount importance in the operationof the MIMO system The interactions between the entireset of antennas and scatterers are initially described bythe impedance matrix Z For dipoles however the mutualimpedance can easily be calculated using classical inducedelectromagnetic force (EMF) method [19] The value of themutual impedance between the 119898th and 119899th dipoles 119885

119898119899is

given by [20]

119885

119898119899=

30 [05772 + ln (120573119889lam) minus 119862119894 (120573119889lam)]+119895 [30119878

119894(120573119889lam)] 119898 = 119899

30 [2119862

119894(119906

0) minus 119862

119894(119906

1) minus 119862

119894(119906

2)]

minus119895 [30 (2119878

119894(119906

0) minus 119878

119894(119906

1) minus 119878

119894(119906

2))] 119898 = 119899

(4)

where 120573 = 2120587119889lam is the wave number 119889lam2 is the dipolelength and the constants are given by [20]

119906

0= 120573119889

ℎ

119906

1= 120573(

radic119889

2

ℎ+ (119889lam2)

2+ (119889lam2))

119906

2= 120573(

radic119889

2

ℎ+ (119889lam2)

2minus (119889lam2))

(5)

where 119889ℎis the horizontal distance between the two dipole

antennas and119862119894(119906) and 119878

119894(119906) are the cosine and sine integrals

respectively

119862

119894 (119906) = int

119906

infin

cos (119909)119909

119889119909 119878

119894 (119906) = int

119906

0

sin (119909)119909

119889119909 (6)

It has to be noted that while calculating119885119898119899 we assume that

the 119899th dipole is excited with current while all the remainingdipoles are open circuited

In general mutual coupling can be characterized bynumerical modelling techniques [19] However for dipoleswe can use analytical mutual coupling into theMIMO systemmodelThe couplingmatrix of transmitting antenna arrayC

119879

can bewritten using fundamental electromagnetic and circuittheory [19] C

119879has the meaning of transfer function matrix

for the transmitting array and is given as

C119879= (119885

119860+ 119885

119879) (Z + 119885

119879I119873119879)

minus1

(7)

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4

Tx1

Rx1Tx2

Rx2

Tx3

Rx3Tx4

Rx4S X

HLI

HLI

HLI

HLI

HNI

H1

Figure 5 Model of full-duplex single-channel 4 times 4MIMO system

where119885119860is the elementrsquos impedance in isolationThe element

119885

119898119899of matrix Z is defined by using the EMF method

as described in (4) Also the coupling matrix of receivingantenna array C

119877can be determined in a similar manner C

119877

has the meaning of transfer function matrix for the receivingarray and is given as

C119877= (119885

119860+ 119885

119879) (Z + 119885

119879I119872119877)

minus1

(8)

4 Proposed Self-Interference Cancellation

In this section we consider a generic MIMO radio unitequipped with 119872

119877RF receivers antennas and 119873

119879RF signal

generatorstransmitters Among all generators there are119873119904=

119873

119879minus119872

119877primary generators and 119872

119877auxiliary generators

The primary generators are used to transmit up to 119873

119878

independent streams of data The auxiliary generators areused to generate RF waveforms for SIC at the RF frontendof the receivers on the same frequency See Figure 5

Furthermore we index the receiver by 119896 = 1 119872

119877

and the transmitter by 119896 = 119872

119877+ 1 119873

119879 Then for each

transmitted data packet subject to linear modulation a RFsignal stream transmitted from the 119896th generator ideally canbe expressed by 119909

119896(119905) = Re119909

119896(119905) exp(1198952120587119891

119888119905) where119891

119888is the

carrier frequency and

119909

119896 (119905) =

119868

sum

119894=1

119892

(119894)

119896(119905) lowast

119873minus1

sum

119899=minus119871

119904

(119894)

119899119901 (119905 minus 119899119879) (9)

where 119909119896(119905) is the complex baseband form (also called 119868119876

waveform) of 119909119896(119905) Here 119892(119894)

119896(119905) is the complex impulse

response of the 119896th transmission for data stream 119894 (of total 119868streams) 119904(119894)

119899is the complex symbol sequence for data stream

119894 119873 + 119871 is the number of complex symbols per stream(including the 119871 prefixed symbols as used in OFDM system)and 119901(119905) is the fundamental pulse waveform used for linearpulse modulation which has the double-sided bandwidth119882and the effective duration 119879 For high spectral efficiency it istypical that 119879 is equal to or only slightly larger than 1119882 Theoperator lowast denotes convolution

International Journal of Antennas and Propagation 5

Tx1

Tx2

Tx3

Tx4

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4 Rx4

Rx3

Rx2

Rx1

ZS ZT ZR ZL

S X

H1

H2

Figure 6 4 times 4MIMO system with mutual-coupling model

TheRF self-interference received by the by the 119897th receiveris 119910119897(119905) = Re119910

119897(119905) exp(1198952120587119891

119888119905) where 119897 = 1 119872

119877 and

119910

119897(119905) = sum

119873119879

119896=1ℎmc119897119896(119905)lowast119909119896(119905) = sum

119868

119894=1([sum

119873119879

119896=1ℎmc119897119896(119905)lowast119892

(119894)

119896(119905)]lowast

sum

119873minus1

119899=0119904

(119894)

119899119905(119905 minus 119899119879)) is the 119868119876 waveform of 119910

119897(119905) In Figure 6

when the mutual coupling is presented ℎ119897119896(119905) is the complex

baseband channel impulse response from the 119896th generator tothe 119897th receiver on the same radio Hence the channel matrixℎ

119897119896(119905) obtained from the case that this effect is absent has to be

pre- and postmultiplied by coupling matrices C119877and C

119879 As

a result the new channel matrix is given by Hmc = C119877HC119879

To cancel the RF self-interference 119910119897(119905) for all 119897 and 119905 it is

necessary to find 119892(119894)119896(119905) for all 119896 and 119894 such that 119910

119897(119905) = 0 for

all 119897 or equivalently sum119873119879119896=1

ℎmc119897119896(119905) lowast 119892(119894)

119896(119905) = 0 for all 119897 and 119894

The matrix form of this condition is

[

[

[

ℎmc11 (119905) sdot sdot sdot ℎmc1119873119879(119905)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

ℎmc1198721198771(119905) sdot sdot sdot ℎmc119872119877119873119879

(119905)

]

]

]

lowast

[

[

[

119892

(119894)

1(119905)

sdot sdot sdot

119892

(119894)

119873119879(119905)

]

]

]

= 0 (10)

or equivalently in more compact form

Hmc (119905) lowast g(119894) (119905) = 0 (11)

Although given in baseband (11) ensures SIC even at the RFfrontend Also note that when all elements in a row ofHmc(119905)are corrupted by a common scalar due to receiver phase noisethe solution g(119894)(119905) to (11) is not affected

To find the solution to (10) we need to apply a knownnotion of vector space in the field of functions of timeThe rank 119903H(119905) of the matrix Hmc(119905) that are convolutelyindependent It follows that 119903H(119905) le min119872

119877 119873

119879 = 119872

119877

The dimension of the solution space of (10) which is alsocalled the dimension of the (right) null space ofHmc(119905) is thenumber of convolutely independent solutions to (10) whichis 119889null = 119873

119879minus 119903H(119905) ge 119873

119904 If 119889null = 119873

119904 we call it a typical

case (very likely in practice) or otherwise if 119889null gt 119873

119904 we

call it atypical case (not very likely in practice) The number119868 of the data streams in (9) must be no larger than 119889null

In general for119872119877ge 1 and 119873

119904ge 1 the 119894th in a set of 119873

119904

convolutely independent solutions to (12) can be written as

g(119894) (119905) =

[

[

[

[

[

[

[

[

[

[

[

g(119894) (119905)

0119894minus11

119892

(119894)

0(119905)

0119868minus11

]

]

]

]

]

]

]

]

]

]

]

(12)

where 01198981

is the 119898 times 1 zero vector and g(119894)(119905) and 119892(119894)0(119905) are

a solution to A(119905) lowast g(119894)(119905) + b119894(119905) lowast 119892

(119894)

0(119905) = 0 where A(119905) is

a square matrix equal to Hmc(119905) without its last 119873119904 columnsand b

119894(119905) is the (119872

119877+ 119894)th column of Hmc(119905) Furthermore

we can choose the solution

g(119894) (119905) = minusadj A (119905) lowast b119894 (119905) (13)

and 119892

(119894)

0(119905) = detA(119905) Both the adjoint adjA(119905)and the

determinant detA(119905) can be obtained analytically in thesame way as those of a matrix of numbers as shown in[21] except that all multiplications should be substituted byconvolutions It is important to note that expression (13) doesnot involve any division but only convolutions and sums

The solutions shown in (12) are valid for arbitraryHmc(119905)as long as detA(119905) = 0This condition can bemet if ℎ

119896119896(119905) for

119896 = 1 119872

119877have the largest norms among ℎ

119897119896(119905) for all 119897

and 119896 To ensure that we can either place the 119872119877auxiliary

transmitting antennas close enough to the 119872

119877receiving

antennas or directly couple the119872119877auxiliary generators to the

119872

119877receivers at the RF frontendIn this section the proposed system is designed to

formulate the self-interference based on mutual-couplingmodel These self-interference signals are caused by multipleantennasTheproposed system for full-duplex single-channelMIMO system is illustrated in Figure 7 As shown in Figure 7the self-interference based on mutual-coupling Hmc119868 can bewritten as

Hmc119868s = HLIs +HNIC119877s (14)

where s isin 119862

119904times1 is the transmitted signal HLI isin 119862

119904times119904 is adiagonal matrix that represents the self-interference signalsand HNI isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

Next the proposed method to suppress the interferencesignals is performed as shown in Figure 7 The transmittedsignals are coupled to matrix 119882 in order to perform thenegative self-interference and mutual-interference signals asclosely as possible Inside matrix 119882 the attenuation andphase shifter are employed to adjust the preknown signalsfor compensating the self-interference signals and mutual-interference signals The compensation matrix W is givenby

Ws = T119909C119879s + Gs (15)

where T119909isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

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DistributedSensor Networks

International Journal of

4 International Journal of Antennas and Propagation

Transmitter Channel Receiver

Vs1

Vs2

VsN

Is1

Is2

IsN

Zs

Vt1

Vt2

VtN

ZT ZR

Vr1

Vr2

VrM

ZL

H

Figure 4 An 119872119877times 119873

119879MIMO system based on mutual-coupling

model

location (including spacing and orientation) with respect tothe scatterers is of paramount importance in the operationof the MIMO system The interactions between the entireset of antennas and scatterers are initially described bythe impedance matrix Z For dipoles however the mutualimpedance can easily be calculated using classical inducedelectromagnetic force (EMF) method [19] The value of themutual impedance between the 119898th and 119899th dipoles 119885

119898119899is

given by [20]

119885

119898119899=

30 [05772 + ln (120573119889lam) minus 119862119894 (120573119889lam)]+119895 [30119878

119894(120573119889lam)] 119898 = 119899

30 [2119862

119894(119906

0) minus 119862

119894(119906

1) minus 119862

119894(119906

2)]

minus119895 [30 (2119878

119894(119906

0) minus 119878

119894(119906

1) minus 119878

119894(119906

2))] 119898 = 119899

(4)

where 120573 = 2120587119889lam is the wave number 119889lam2 is the dipolelength and the constants are given by [20]

119906

0= 120573119889

ℎ

119906

1= 120573(

radic119889

2

ℎ+ (119889lam2)

2+ (119889lam2))

119906

2= 120573(

radic119889

2

ℎ+ (119889lam2)

2minus (119889lam2))

(5)

where 119889ℎis the horizontal distance between the two dipole

antennas and119862119894(119906) and 119878

119894(119906) are the cosine and sine integrals

respectively

119862

119894 (119906) = int

119906

infin

cos (119909)119909

119889119909 119878

119894 (119906) = int

119906

0

sin (119909)119909

119889119909 (6)

It has to be noted that while calculating119885119898119899 we assume that

the 119899th dipole is excited with current while all the remainingdipoles are open circuited

In general mutual coupling can be characterized bynumerical modelling techniques [19] However for dipoleswe can use analytical mutual coupling into theMIMO systemmodelThe couplingmatrix of transmitting antenna arrayC

119879

can bewritten using fundamental electromagnetic and circuittheory [19] C

119879has the meaning of transfer function matrix

for the transmitting array and is given as

C119879= (119885

119860+ 119885

119879) (Z + 119885

119879I119873119879)

minus1

(7)

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4

Tx1

Rx1Tx2

Rx2

Tx3

Rx3Tx4

Rx4S X

HLI

HLI

HLI

HLI

HNI

H1

Figure 5 Model of full-duplex single-channel 4 times 4MIMO system

where119885119860is the elementrsquos impedance in isolationThe element

119885

119898119899of matrix Z is defined by using the EMF method

as described in (4) Also the coupling matrix of receivingantenna array C

119877can be determined in a similar manner C

119877

has the meaning of transfer function matrix for the receivingarray and is given as

C119877= (119885

119860+ 119885

119879) (Z + 119885

119879I119872119877)

minus1

(8)

4 Proposed Self-Interference Cancellation

In this section we consider a generic MIMO radio unitequipped with 119872

119877RF receivers antennas and 119873

119879RF signal

generatorstransmitters Among all generators there are119873119904=

119873

119879minus119872

119877primary generators and 119872

119877auxiliary generators

The primary generators are used to transmit up to 119873

119878

independent streams of data The auxiliary generators areused to generate RF waveforms for SIC at the RF frontendof the receivers on the same frequency See Figure 5

Furthermore we index the receiver by 119896 = 1 119872

119877

and the transmitter by 119896 = 119872

119877+ 1 119873

119879 Then for each

transmitted data packet subject to linear modulation a RFsignal stream transmitted from the 119896th generator ideally canbe expressed by 119909

119896(119905) = Re119909

119896(119905) exp(1198952120587119891

119888119905) where119891

119888is the

carrier frequency and

119909

119896 (119905) =

119868

sum

119894=1

119892

(119894)

119896(119905) lowast

119873minus1

sum

119899=minus119871

119904

(119894)

119899119901 (119905 minus 119899119879) (9)

where 119909119896(119905) is the complex baseband form (also called 119868119876

waveform) of 119909119896(119905) Here 119892(119894)

119896(119905) is the complex impulse

response of the 119896th transmission for data stream 119894 (of total 119868streams) 119904(119894)

119899is the complex symbol sequence for data stream

119894 119873 + 119871 is the number of complex symbols per stream(including the 119871 prefixed symbols as used in OFDM system)and 119901(119905) is the fundamental pulse waveform used for linearpulse modulation which has the double-sided bandwidth119882and the effective duration 119879 For high spectral efficiency it istypical that 119879 is equal to or only slightly larger than 1119882 Theoperator lowast denotes convolution

International Journal of Antennas and Propagation 5

Tx1

Tx2

Tx3

Tx4

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4 Rx4

Rx3

Rx2

Rx1

ZS ZT ZR ZL

S X

H1

H2

Figure 6 4 times 4MIMO system with mutual-coupling model

TheRF self-interference received by the by the 119897th receiveris 119910119897(119905) = Re119910

119897(119905) exp(1198952120587119891

119888119905) where 119897 = 1 119872

119877 and

119910

119897(119905) = sum

119873119879

119896=1ℎmc119897119896(119905)lowast119909119896(119905) = sum

119868

119894=1([sum

119873119879

119896=1ℎmc119897119896(119905)lowast119892

(119894)

119896(119905)]lowast

sum

119873minus1

119899=0119904

(119894)

119899119905(119905 minus 119899119879)) is the 119868119876 waveform of 119910

119897(119905) In Figure 6

when the mutual coupling is presented ℎ119897119896(119905) is the complex

baseband channel impulse response from the 119896th generator tothe 119897th receiver on the same radio Hence the channel matrixℎ

119897119896(119905) obtained from the case that this effect is absent has to be

pre- and postmultiplied by coupling matrices C119877and C

119879 As

a result the new channel matrix is given by Hmc = C119877HC119879

To cancel the RF self-interference 119910119897(119905) for all 119897 and 119905 it is

necessary to find 119892(119894)119896(119905) for all 119896 and 119894 such that 119910

119897(119905) = 0 for

all 119897 or equivalently sum119873119879119896=1

ℎmc119897119896(119905) lowast 119892(119894)

119896(119905) = 0 for all 119897 and 119894

The matrix form of this condition is

[

[

[

ℎmc11 (119905) sdot sdot sdot ℎmc1119873119879(119905)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

ℎmc1198721198771(119905) sdot sdot sdot ℎmc119872119877119873119879

(119905)

]

]

]

lowast

[

[

[

119892

(119894)

1(119905)

sdot sdot sdot

119892

(119894)

119873119879(119905)

]

]

]

= 0 (10)

or equivalently in more compact form

Hmc (119905) lowast g(119894) (119905) = 0 (11)

Although given in baseband (11) ensures SIC even at the RFfrontend Also note that when all elements in a row ofHmc(119905)are corrupted by a common scalar due to receiver phase noisethe solution g(119894)(119905) to (11) is not affected

To find the solution to (10) we need to apply a knownnotion of vector space in the field of functions of timeThe rank 119903H(119905) of the matrix Hmc(119905) that are convolutelyindependent It follows that 119903H(119905) le min119872

119877 119873

119879 = 119872

119877

The dimension of the solution space of (10) which is alsocalled the dimension of the (right) null space ofHmc(119905) is thenumber of convolutely independent solutions to (10) whichis 119889null = 119873

119879minus 119903H(119905) ge 119873

119904 If 119889null = 119873

119904 we call it a typical

case (very likely in practice) or otherwise if 119889null gt 119873

119904 we

call it atypical case (not very likely in practice) The number119868 of the data streams in (9) must be no larger than 119889null

In general for119872119877ge 1 and 119873

119904ge 1 the 119894th in a set of 119873

119904

convolutely independent solutions to (12) can be written as

g(119894) (119905) =

[

[

[

[

[

[

[

[

[

[

[

g(119894) (119905)

0119894minus11

119892

(119894)

0(119905)

0119868minus11

]

]

]

]

]

]

]

]

]

]

]

(12)

where 01198981

is the 119898 times 1 zero vector and g(119894)(119905) and 119892(119894)0(119905) are

a solution to A(119905) lowast g(119894)(119905) + b119894(119905) lowast 119892

(119894)

0(119905) = 0 where A(119905) is

a square matrix equal to Hmc(119905) without its last 119873119904 columnsand b

119894(119905) is the (119872

119877+ 119894)th column of Hmc(119905) Furthermore

we can choose the solution

g(119894) (119905) = minusadj A (119905) lowast b119894 (119905) (13)

and 119892

(119894)

0(119905) = detA(119905) Both the adjoint adjA(119905)and the

determinant detA(119905) can be obtained analytically in thesame way as those of a matrix of numbers as shown in[21] except that all multiplications should be substituted byconvolutions It is important to note that expression (13) doesnot involve any division but only convolutions and sums

The solutions shown in (12) are valid for arbitraryHmc(119905)as long as detA(119905) = 0This condition can bemet if ℎ

119896119896(119905) for

119896 = 1 119872

119877have the largest norms among ℎ

119897119896(119905) for all 119897

and 119896 To ensure that we can either place the 119872119877auxiliary

transmitting antennas close enough to the 119872

119877receiving

antennas or directly couple the119872119877auxiliary generators to the

119872

119877receivers at the RF frontendIn this section the proposed system is designed to

formulate the self-interference based on mutual-couplingmodel These self-interference signals are caused by multipleantennasTheproposed system for full-duplex single-channelMIMO system is illustrated in Figure 7 As shown in Figure 7the self-interference based on mutual-coupling Hmc119868 can bewritten as

Hmc119868s = HLIs +HNIC119877s (14)

where s isin 119862

119904times1 is the transmitted signal HLI isin 119862

119904times119904 is adiagonal matrix that represents the self-interference signalsand HNI isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

Next the proposed method to suppress the interferencesignals is performed as shown in Figure 7 The transmittedsignals are coupled to matrix 119882 in order to perform thenegative self-interference and mutual-interference signals asclosely as possible Inside matrix 119882 the attenuation andphase shifter are employed to adjust the preknown signalsfor compensating the self-interference signals and mutual-interference signals The compensation matrix W is givenby

Ws = T119909C119879s + Gs (15)

where T119909isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 5

Tx1

Tx2

Tx3

Tx4

Tx1

Tx2

Tx3

Tx4

Rx1

Rx2

Rx3

Rx4 Rx4

Rx3

Rx2

Rx1

ZS ZT ZR ZL

S X

H1

H2

Figure 6 4 times 4MIMO system with mutual-coupling model

TheRF self-interference received by the by the 119897th receiveris 119910119897(119905) = Re119910

119897(119905) exp(1198952120587119891

119888119905) where 119897 = 1 119872

119877 and

119910

119897(119905) = sum

119873119879

119896=1ℎmc119897119896(119905)lowast119909119896(119905) = sum

119868

119894=1([sum

119873119879

119896=1ℎmc119897119896(119905)lowast119892

(119894)

119896(119905)]lowast

sum

119873minus1

119899=0119904

(119894)

119899119905(119905 minus 119899119879)) is the 119868119876 waveform of 119910

119897(119905) In Figure 6

when the mutual coupling is presented ℎ119897119896(119905) is the complex

baseband channel impulse response from the 119896th generator tothe 119897th receiver on the same radio Hence the channel matrixℎ

119897119896(119905) obtained from the case that this effect is absent has to be

pre- and postmultiplied by coupling matrices C119877and C

119879 As

a result the new channel matrix is given by Hmc = C119877HC119879

To cancel the RF self-interference 119910119897(119905) for all 119897 and 119905 it is

necessary to find 119892(119894)119896(119905) for all 119896 and 119894 such that 119910

119897(119905) = 0 for

all 119897 or equivalently sum119873119879119896=1

ℎmc119897119896(119905) lowast 119892(119894)

119896(119905) = 0 for all 119897 and 119894

The matrix form of this condition is

[

[

[

ℎmc11 (119905) sdot sdot sdot ℎmc1119873119879(119905)

sdot sdot sdot sdot sdot sdot sdot sdot sdot

ℎmc1198721198771(119905) sdot sdot sdot ℎmc119872119877119873119879

(119905)

]

]

]

lowast

[

[

[

119892

(119894)

1(119905)

sdot sdot sdot

119892

(119894)

119873119879(119905)

]

]

]

= 0 (10)

or equivalently in more compact form

Hmc (119905) lowast g(119894) (119905) = 0 (11)

Although given in baseband (11) ensures SIC even at the RFfrontend Also note that when all elements in a row ofHmc(119905)are corrupted by a common scalar due to receiver phase noisethe solution g(119894)(119905) to (11) is not affected

To find the solution to (10) we need to apply a knownnotion of vector space in the field of functions of timeThe rank 119903H(119905) of the matrix Hmc(119905) that are convolutelyindependent It follows that 119903H(119905) le min119872

119877 119873

119879 = 119872

119877

The dimension of the solution space of (10) which is alsocalled the dimension of the (right) null space ofHmc(119905) is thenumber of convolutely independent solutions to (10) whichis 119889null = 119873

119879minus 119903H(119905) ge 119873

119904 If 119889null = 119873

119904 we call it a typical

case (very likely in practice) or otherwise if 119889null gt 119873

119904 we

call it atypical case (not very likely in practice) The number119868 of the data streams in (9) must be no larger than 119889null

In general for119872119877ge 1 and 119873

119904ge 1 the 119894th in a set of 119873

119904

convolutely independent solutions to (12) can be written as

g(119894) (119905) =

[

[

[

[

[

[

[

[

[

[

[

g(119894) (119905)

0119894minus11

119892

(119894)

0(119905)

0119868minus11

]

]

]

]

]

]

]

]

]

]

]

(12)

where 01198981

is the 119898 times 1 zero vector and g(119894)(119905) and 119892(119894)0(119905) are

a solution to A(119905) lowast g(119894)(119905) + b119894(119905) lowast 119892

(119894)

0(119905) = 0 where A(119905) is

a square matrix equal to Hmc(119905) without its last 119873119904 columnsand b

119894(119905) is the (119872

119877+ 119894)th column of Hmc(119905) Furthermore

we can choose the solution

g(119894) (119905) = minusadj A (119905) lowast b119894 (119905) (13)

and 119892

(119894)

0(119905) = detA(119905) Both the adjoint adjA(119905)and the

determinant detA(119905) can be obtained analytically in thesame way as those of a matrix of numbers as shown in[21] except that all multiplications should be substituted byconvolutions It is important to note that expression (13) doesnot involve any division but only convolutions and sums

The solutions shown in (12) are valid for arbitraryHmc(119905)as long as detA(119905) = 0This condition can bemet if ℎ

119896119896(119905) for

119896 = 1 119872

119877have the largest norms among ℎ

119897119896(119905) for all 119897

and 119896 To ensure that we can either place the 119872119877auxiliary

transmitting antennas close enough to the 119872

119877receiving

antennas or directly couple the119872119877auxiliary generators to the

119872

119877receivers at the RF frontendIn this section the proposed system is designed to

formulate the self-interference based on mutual-couplingmodel These self-interference signals are caused by multipleantennasTheproposed system for full-duplex single-channelMIMO system is illustrated in Figure 7 As shown in Figure 7the self-interference based on mutual-coupling Hmc119868 can bewritten as

Hmc119868s = HLIs +HNIC119877s (14)

where s isin 119862

119904times1 is the transmitted signal HLI isin 119862

119904times119904 is adiagonal matrix that represents the self-interference signalsand HNI isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

Next the proposed method to suppress the interferencesignals is performed as shown in Figure 7 The transmittedsignals are coupled to matrix 119882 in order to perform thenegative self-interference and mutual-interference signals asclosely as possible Inside matrix 119882 the attenuation andphase shifter are employed to adjust the preknown signalsfor compensating the self-interference signals and mutual-interference signals The compensation matrix W is givenby

Ws = T119909C119879s + Gs (15)

where T119909isin 119862

119904times119904 is a symmetric matrix that represents themutual-interference signals caused by the other antennas

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Antennas and Propagation

Tx1

Rx1

Coupling

Combiner

Tx2

Rx2

Coupling

Combiner

Tx3

Rx3

Coupling

Combiner

Tx4

Rx4

Coupling

Combiner

ZS ZTW

HLI

HLI

HLI

HLI

CR

CR

CR

CR

Figure 7 Proposed self-interference cancellation for full-duplexsingle-channel 4 times 4MIMO system based on mutual-couplingmodel

G isin 119862

119904times119904 is a diagonal matrix that represents the self-interfer-ence signals

Then the received signal at the destination with the pro-posed compensation matrix for the interference suppressioncan be rewritten as

y = Hmcx +Hmc119868s minusWs + N (16)

where N sim CN(0 1205902119889I119904) is the AWGN contribution at the

destination

5 Results and Discussion

51 Channel Capacity In order to investigate the effect ofmutual coupling on MIMO capacity in this section thechannel capacity for our 4 times 4MIMO system can be given by(17) [2]This capacity denotes the average of channel capacityin bpsHz Also we assume the uniform transmitting powerfor each antenna (119864xx119867 = (119875

0119873

119904)I119909) Consider

119862 = log2det [I

119904+

119875

0

119873

119904

HmcH119867

mc

times(120590

2

119868H1015840mc119868H

1015840119867

mc119868 + 1205902

119889I119904)

minus1

]

(17)

We assume that 1198750is the maximum available power at the

source and119873119904is the power of the self-interference signals

The performance of channel capacity is presented byconsidering four cases The first case is that there is neitherself-interference nor mutual-coupling effect (called withoutinterference and MC) in the system In the second casethere is no interference but including mutual-coupling effect(called without interference and with MC) The third case isthe case that the system uses the self-interference cancellationand there is a mutual-coupling effect in the systems (called

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40

45

50

SNR (dB)

Without interference and MC

Capa

city

(bps

Hz)

Without interference and With MCProposedWith interference and MC

Figure 8 Channel capacity versus SNR for 80 interference reduc-tion

proposed) For the last case the system experiences bothinterference and mutual-coupling effect but no any cancella-tion technique is applied (called with interference and MC)

The simulation produced byMATLAB programming canbe described as follows The source and the destination areequipped with four transmitting and four receiving antennasthat is 119904 = 119909 = 4 We assume that the source-destinationchannels experience Rayleigh fading Hence the new channelmatrixHmc is an independentmatrix containing independentidentically distributed (iid) entries in which the randomdistribution is explained byCN(0 1) For the self-interferencechannels they also experience Rayleigh fading Hence theself-interference channel matrices HLI and HNI are indepen-dent matrices containing independent identically distributed(iid) entries distributed as CN(0 1) For simplicity weassume that the noise variances are equal in each antenna120590

2Figure 8 shows the channel capacity versus SNR for 80

interference reduction when the MIMO system is affectedby mutual coupling It can be noticed that the proposedtechnique lies between with and without the interferencesuppression The channel capacity of the proposed system isabout 070 bpsHz (at SNR = 20 dB) higher than the systemwith self-interference and the system with mutual couplingIn Figure 9 the relation between capacity and the percentageof interference reduction is presented It can be noticed thatthe channel capacity of the proposed system requires only90 interference reduction to achieve the capacity close tothe system without any interference

52 Self-Interference Reduction The work in [6 8 17 22ndash25]shows that a single-channel full-duplex system can beworkedby using the method of self-interference cancellation Twokey techniques are RF interference cancellation (RFIC) and

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 7

0 10 20 30 40 50 60 70 80 90 100

16

17

18

19

Interference reduction ()

Capa

city

(bps

Hz)

Without interference and MCWithout interference and With MCProposedWith interference and MC

155

165

175

185

Figure 9 Relation between channel capacity and interference re-duction for SNR = 20 dB

digital interference cancellation (DIC) which utilize the sig-nals fromboth the transmitting and receiving paths Figure 10presents the signal diagram of self-interference cancellationconsisting of both RFIC and DIC RFIC uses the knowledgeof transmitting signals to cancel the self-interference in theRF signal before it is digitized For analog cancellation theamplitudes from two paths have to be perfectly matched atthe receiver Then the phase of the two signals would beideally differed by the exact 120587 To cancel self-interferencethe best performing prior design is obtained The authorsgain the inverse of the transmitted signal using phase shifterand attenuator dynamically adjusting the attenuation andphase of the inverse signal to match the self-interferenceleaking from circulator After combining both inverse andleak signals the received signal can be passed through theprocessing unit with the minimum effect of self-interference

In measurement the operating frequency band is on245GHz in order to match with a practical wireless channelas IEEE 80211 The measurement has been performed toinvestigate the concept of a single-channel full-duplex wire-less system The results show that the system can reducethe self-interference about minus75 dB This reduction is goodenough to investigate the concept of a single-channel full-duplex wireless system The results show that the system canreduce the self-interference about minus75 dB This reduction isgood enough to transmit and receive on the same frequencyat the same time However we have proposed the self-interference suppression for MIMO system in which theself-interference signals are caused by mutual coupling Theproposed suppression technique can also be applied to theMIMO system by separating the multiple antennas intoindividualmeasurement In this paper the RFIC is performedaccording to the diagram shown in Figure 10 Then theDIC is performed inside USRP (Universal Software RadioPeripheral) processors

TX

RX

DAC

ADC

Adaptive filter

Antenna

Coupler

Phase shift

Attenuator

Combiner

Feedback

Digital interferencecancellation

RF interference cancellation

R

+minus+minus

Figure 10 Block diagram of the proposed system in practice

Signal generator Power supply

CirculatorPhase shifter

USRP

Figure 11 Photograph of experimental scenario

The Universal Software Radio Peripheral (USRP) is aplatform developed by Ettus Research LLC Inside the USRPthere are two main components The first component is amother board containing an Altera Cyclone EP1C12 FieldProgrammableGateArray (FPGA) It has 4ADCswith 12 bitsper sample and 4 DACs with 14 bits per sample The secondcomponent is a daughter board that all working processes arein a field of RF-Front End This paper employs XCVR2450daughter board which responses to radio frequency in dualband both 24GHz and 59GHz All components are assem-bled in one USRP box using 3A-6V power supply USRP isconnected to the host PC via USB 20 (Universal Serial Bus20)

The digital interference cancellation technique in ourdesign employs a finite impulse response (FIR) filter tocancel the remainder of the self-interference signals after RFinterference cancellationThe transmitted digital samples arepassed through the FIR filter to create digital interferencecancellation samples which are subtracted from the receivedsamples to further clean interference from the received signal

Figure 11 shows the photograph of the experimentalscenario for measuring the self-interference signalThe blockdiagram of each antenna with both RFIC and DIC is shownin Figure 10

Figure 12 shows the measured spectrum of self-inter-ference signal In Figure 12(a) the spectrum of the self-interference leakage without any cancellation is notice-ably high In Figure 12(b) the measured spectrum of self-interference signal with RF interference cancellation isreduced by 58 dB In Figure 12(c) the measured spectrum of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Antennas and Propagation

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(a)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(b)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

minus80

minus90

Am

plitu

de (d

B)

2449 24495 245 24505 2451

Frequency (GHz)

(c)

Figure 12 Measured spectrum of the self-interference signal (a)without any cancellations (b) with RF interference cancellation butwithout digital interference cancellation and (c) with both RF anddigital interference cancellations

self-interference signals with both RF and digital cancella-tions is very low and close to the noise floor level with thereduction of 75 dB At this stage the self-interference signalis low enough to provide a little impact on the desirablyreceived signals It means that the full-duplex system can beoperated on the same channel at the same time because theself-interference is treated to be a noise for both forward andreserve links Consequently the throughput can be doubledby using our proposed method

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Control voltage (V)

Rece

ived

sign

al p

ower

(dBm

)

Self-interference signals (TX1 only)Self- and mutual-interference signalsProposed

minus60

minus55

minus50

minus45

minus40

minus35

minus30

minus25

minus20

Figure 13 The received signal power of interference signals at Rx1

53 Mutual-Interference Reduction In the previous sectionthe reduction of self-interference power is observed How-ever in MIMO system there are other interference signalscalled mutual-interference signals The proposed work alsoconsiders the reduction of mutual interference as well Byusing the samemeasurement as previous section but increas-ing all sets for 4times4MIMOoperation themutual-interferencepower can be observed The operating frequency band is on245GHz for all transmitting antennas The attenuations andphase shifters are employed to perform the suitable matrixW which is illustrated in Figure 7 The power inputs of Tx1Tx2 Tx3 and Tx4 are equal Figure 13 shows the measuredpowers from Rx1 output There are three curves presented inFigure 13The first curve is named as self-interference signalsbecause the signal is sent by only Tx1 while there is no inputpower for Tx2 Tx3 and Tx4 This is the same situation asin the previous section except that it might be the effect ofmutual coupling from the neighbour antenna For the secondcurve named as self- and mutual-interference signals thereare equal powers for Tx1 Tx2 Tx3 and Tx4 but there is nomatrix W in the system It can be observed that the totalpower of this curve is higher than the first curve In thethird curve named as proposed the matrix W is performedto suppress both self-interference and mutual-interferencesignals In this measurement there is no signal coming fromthe other side Hence Rx1 should not receive any power ifmatrix 119882 works very well In our measurement it can benoticed that the received power of the proposedmethod is theleast The self-interference and mutual-interference signalscan be reduced by adjusting the suitable voltage control forphase shifter Actually there are four phase shifters related tothis curve and all are needed to be properly adjusted at thesame time To explain the mechanism of phase adjustmentonly one voltage control has been presented in Figure 13 Itcan be clearly seen that the right voltage offers the maximumreduction of interference signals At control voltage 4-5V

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Antennas and Propagation 9

0 5 10 15 20 25 30

BER

Without interference and MC

ProposedWith interference and MC

10minus4

10minus3

10minus2

10minus1

100

EbNo (dB)

Figure 14 BER performance for 4 times 4MIMO system

the received power of self-interference and mutual-interfer-ence signals is reduced by 31 dB

54 Performance of ProposedMIMOSystem After getting thesuitable matrix 119882 the other side of communication sendsthe data signal through the wireless 4 times 4 channel It is afact that the channel capacity is a theoretical quantity whichcannot be directly measured In practice throughput and biterror rate (BER) are two indicators to judge the merit ofsystem In this paper BER can be obtained by using the zeroforcing technique to decode the data All signals are sent withQPSKmodulation Figure 14 shows BER performance for 4times4MIMOsystem It is clearly seen that the proposed techniquecan provide a similar BER to the system without interferencewhen EbNo is less than 15 dB Even though EbNo is morethan 15 dB the proposed system still significantly improvesthe BER performance in comparison with the system withinterference

Note that even the BER of proposed system is nearlythe same as that of the system without interference but thethroughput of proposed system is a double of that of normalfull-duplex system This is because the proposed MIMOsystem can transmit and receive at the same time and on thesame frequency

6 Conclusions

In this paper we proposed the method of self-interferencecancellation for full-duplex single-channel MIMO systembased on mutual-coupling model The performance of pro-posed technique can suppress the self-interference signalsby using the preknown interferences which are affected bymutual coupling between antennas Simulation results illus-trate that the proposed system outperforms the system withinterference This implies the success of using the proposed

concept for full-duplex single-channel MIMO system Inaddition the measurement results indicate that the self-interference and mutual-interference reductions are goodenough to successfully transmit and receive on the samefrequency at the same time in practice As a result theproposed throughput can be actually twice the conventionalsystem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors got a financial support from Thailand ResearchFund through the Royal Golden Jubilee PhD Program(Grant no PHD00762554)

References

[1] T Riihonen SWerner and RWichman ldquoSpatial loop interfer-ence suppression in full-duplex MIMO relaysrdquo in Proceedingsof the 43rd Asilomar Conference on Signals Systems and Com-puters (Asilomar rsquo09) pp 1508ndash1512 Pacific Grove Calif USANovember 2009

[2] Y Y Kang and J H Cho ldquoCapacity of MIMO wireless channelwith full-duplex amplify-and-forward relayrdquo in Proceedings ofthe IEEE 20th Personal Indoor and Mobile Radio Commu-nications Symposium (PIMRC rsquo09) pp 117ndash121 Tokyo JapanSeptember 2009

[3] P Larsson and M Prytz ldquoMIMO on-frequency repeater withself-interference cancellation and mitigationrdquo in Proceedings ofthe IEEE 69th Vehicular Technology Conference (VTC rsquo09) pp1ndash5 Bercelona Spain April 2009

[4] A GoldsmithWireless Communications CambridgeUniversityPress Cambridge UK 2005

[5] B Radunovic D Gunawardena P Key et al ldquoRethinkingindoor wireless mesh design low power low frequency full-duplexrdquo in Proceedings of the 5th Annual IEEE Workshop onWireless Mesh Networks (WiMesh rsquo10) pp 25ndash30 Boston MassUSA June 2010

[6] J Choi II M Jain K Srinivasan P Levis and S Katti ldquoAchiev-ing single channel full duplex wireless communicationrdquo inProceedings of the 16th Annual Conference onMobile Computingand Networking (MobiCom rsquo10) pp 1ndash12 Chicago Ill USASeptember 2010

[7] N Singh D Gunawardena A Proutiere B Radunovic HV Balan and P Key ldquoEfficient and fair MAC for wirelessnetworks with self-interference cancellationrdquo in Proceedings ofthe International Symposium of on Modeling and Optimizationin Mobile Ad Hoc and Wireless Networks (WiOpt rsquo11) pp 94ndash101 Princeton NJ USA May 2011

[8] M Jain J I Choi T Kim et al ldquoPractical real-time fullduplex wirelessrdquo in Proceedings of the 17th Annual InternationalConference on Mobile Computing and Networking (MobiComrsquo11) pp 301ndash312 Las Vegas Nev USA September 2011

[9] M A Khojastepour K Sundaresan S Rangarajan X Zhangand S Barghi ldquoThe case for antenna cancellation for scalablefull-duplex wireless communicationsrdquo in Proceedings of the

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Antennas and Propagation

10th ACM SIGCOMM Workshop on Hot Topics in Networks(HotNets-X rsquo11) article 17 Cambridge Mass USA November2011

[10] L Sun P LiM RMcKay andRDMurch ldquoCapacity ofMIMOsystems with mutual coupling transmitter optimization withdual power constraintsrdquo IEEE Transactions on Signal Processingvol 60 no 2 pp 848ndash861 2012

[11] T Nguyen W Meng and H Wang ldquoChannel capacity analysison cooperative MIMO with antenna spatial correlation andmulti-pathrdquo in Proceedings of the 6th International ICST Con-ference on Communications and Networking in China (CHINA-COM rsquo11) pp 181ndash185 Harbin China August 2011

[12] R M Legnain R H M Hafez I D Marsland and A MLegnain ldquoA novel spatial modulation using MIMO spatialmultiplexingrdquo in Proceedings of the 1st International Conferenceon Communications Signal Processing and their Applications(ICCSPA rsquo13) pp 1ndash4 Sharjah United Arab Emirates February2013

[13] P Li L Sun M R McKay and R D Murch ldquoTransmitteroptimization for MIMO systems with mutual coupling at highSNRrdquo in Proceedings of the 45th Asilomar Conference on SignalSystems and Computers (ASILOMAR rsquo11) pp 1058ndash1588 PacificGrove Calif USA November 2011

[14] H-B Shi S Gong and T-C Zheng ldquoThe effect of mutual cou-pling on the channel performance of MIMO communicationsystemrdquo in Proceedings of the 10th International Symposium onAntennas Propagation amp EM Theory (ISAPE rsquo12) pp 335ndash339Xian China October 2012

[15] S Lu H T Hui and M Bialkowski ldquoOptimizing MIMOchannel capacities under the influence of antenna mutualcouplingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 287ndash290 2008

[16] P UthansakulAdaptive MIMO Systems Explorations for IndoorWireless Communications VDM Berlin Germany 2009

[17] N Phungamngern P Uthansakul and M Uthansakul ldquoDigitaland RF interference cancellation for single-channel full-duplextransceiver using a single antennardquo in Proceedings of the 10thInternational Conference on Electrical EngineeringElectronicsComputer Telecommunications and Information Technology(ECTI-CON rsquo13) pp 1ndash5 Krabi Thailand May 2013

[18] E Telatar ldquoCapacity of multi-antenna Gaussian channelsrdquoEuropean Transactions on Telecommunications vol 10 no 6 pp585ndash595 1999

[19] C A BalanisAntenaTheory JohnWiley amp Sons Hoboken NJUSA 3rd edition 2005

[20] S Durrani and M E Bialkowski ldquoEffect of mutual couplingon the interference rejection capabilities of linear and circulararrays in CDMA systemsrdquo IEEE Transactions on Antennas andPropagation vol 52 no 4 pp 1130ndash1134 2004

[21] H Lutkepohl Handbook of Matrices John Wiley amp Sons NewYork NY USA 1996

[22] M Duarte and A Sabharwal ldquoFull-duplex wireless communi-cations using off-the-shelf radios feasibility and first resultsrdquo inProceedings of the 44th Asilomar Conference on Signals Systemsand Computers (ASILOMAR rsquo10) pp 1558ndash1562 Pacific GroveCalif USA November 2010

[23] M A Khojastepour and S Rangarajan ldquoWideband digitalcancellation for full-duplex communicationsrdquo in Proceedings ofthe 46th Asilomar Conference on Signals Systems andComputers(ASILOMAR rsquo12) pp 1300ndash1304 Pacific Grove Calif USANovember 2012

[24] M Duarte C Dick and A Sabharwal ldquoExperiment-drivencharacterization of full-duplex wireless systemsrdquo IEEE Transac-tions onWireless Communications vol 11 no 12 pp 4296ndash43072012

[25] N Li W Zhu and H Han ldquoDigital interference cancellationin single channel full duplex wireless communicationrdquo inProceedings of the 8th International Conference on WirelessCommunications Networking and Mobile Computing (WiCOMrsquo12) pp 1ndash4 Shanghai China September 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of