Spatial Modulation - A New Low ComplexitySpectral Efficiency Enhancing Technique

R. Mesleh, and H. HaasSchool of Engineering and ScienceInternational University Bremen

28759 Bremen, Germany{r.mesleh & h.haas}@iu-bremen.de

Abstract- The multiplexing gain of multiple antenna transmis-sion strongly depends on transmit and receive antenna spacing,transmit antenna synchronization, and the algorithm used toeliminate interchannel interference (ICI) at the receiver. In thispaper, a new transmission approach, called spatial modulation,that entirely avoids ICI and requires no synchronization betweenthe transmitting antennas while maintaining high spectral effi-ciency is presented. A block of information bits is mapped into aconstellation point in the signal and the spatial domain, i.e. intothe location of a particular antenna. The receiver estimates thetransmitted signal and the transmit antenna number and usesthe two information to de-map the block of information bits.For this purpose, a novel transmit antenna number detectionalgorithm called iterative-maximum ratio combining (i-MRC) ispresented. Spatial modulation is used to transmit differentnumber of information bits and i-MRC is used to estimate boththe transmitted signal and the transmit antenna number. Theresults are compared to ideal V-BLAST (Vertical-Bell Lab Lay-ered Space-Time) and to MRC. Spatial modulation outperformsMRC. The (bit-error-ratio) BER performance and the achievedspectral efficiency is comparable to V-BLAST. However, spatialmodulation results in a vast reduction in receiver complexity.

I. INTRODUCTION

The need to improve the spectral efficiency and reliabilityof radio communication is driven by the ever increasingrequirement for higher data rates and improved QoS (Qualityof Service) across wireless links. Higher data rate and bet-ter spectral efficiency are of paramount importance in nextgeneration cellular communication. MIMO (multiple inputmultiple output) technology is one solution to attain this bytransmitting multiple data streams from multiple antennas [1].However, the capacity gain results from MIMO transmissiondepends strongly on transmit and receive antenna spacing [2],[3], transmit antenna synchronization [4], [5], and the usedalgorithm to reduce the interchannel interference (ICI) at thereceiver input. Copious ICI reduction algorithms are reportedin literature. The proposed Bell Labs Layered Space-TimeArchitecture (BLAST) [6] is one of the most promising MIMOdetection algorithms. In its most basic form known as vertical(V)-BLAST [7], multiple transmitted data streams are sepa-rated and detected successively using a combination of arrayprocessing (nulling) and interference cancellation techniques.It was demonstrated that with the V-BLAST algorithm spectral1-4244-0463-0/06/$20.00 ©2006 IEEE

Chang Wook Ahn, and Sangboh YunC & N Lab., Samsung AIT11-4, Nongseo-ri, Youngln-si

Kyeonggi-Do, KOREAcwan.ahngsamsung.com

efficiencies of 20 -40 bps/Hz can be achieved in an indoorrich scattering propagation environment assuming a practicalSNR range, and bit-error performance respectively [7]. Thehigh spectral efficiencies stem from parallel signal transmis-sion resulting in a multiplexing gain. Other multiple antennatechniques employ, for example, space-time coding (STC)techniques in order to increase the SNR at the receiver byexploitation of spatial diversity [8]. In this case the systemimprovement results from a diversity gain.An alternative transmission approach that entirely avoids

ICI at the receiver input was proposed in [9], [10] forBPSK and QPSK transmission respectively. The idea is tocompress a block of Nt symbols into a single symbol priorto transmission, where Nt indicates the number of transmitantennas. Information is retained by an algorithm that mapsthis single symbol to one, and only one, of the Nt antennas.The task of the receiver is twofold: First, to estimate thesingle symbol, and second, to detect the respective antennanumber from which the symbol is transmitted. By combiningboth information and by carrying out the inverse encodingoperation, the receiver is able to retrieve the entire block ofNt symbols. Thereby, multiplexing gain is achieved, but ICIin the MIMO transmission is completely avoided. However,the scheme in [10] suffers from a loss in spectral efficiencyas compared to V-BLAST due to the use of parity symbols.Moreover, a general solution for different modulation schemesis not provided in [10].

The proposed concept solves this problem in a novelfashion. Traditionally, modulation techniques such as BPSK(binary phase shift keying), QPSK (quadrature phase shiftkeying), 8PSK, 16QAM (quadrature amplitude modulation),etc. map a fixed number of information bits into one symbol.Each symbol represents a constellation point in the complex,two dimensional signal plane. In the following this is referredto as signal modulation. In this paper, a novel approach isproposed in which this two dimensional plane is extended toa third dimension - the spatial dimension. In the following thisis referred to as spatial modulation. It is demonstrated that thisnew approach will result in a very flexible mechanism which isable to achieve high spectral efficiency and very low receivercomplexity, and that is ideally suited for high speed uplinktransmission.

The idea of using the transmit antenna number as anadditional source of information is utilized in spatial modula-tion. The number of information bits that can be transmittedusing spatial modulation depends on the used constellationdiagram and the given number of transmit antennas. Forinstance, six information bits can be mapped into 32QAMand two transmit antennas. Alternatively, if the channel andinterference environment do not allow the use of 32QAM, thesame spectral efficiency can be achieved with 16QAM andfour transmit antennas, etc..

In view of the fact that information is not only included inthe transmitted symbol but also in the actual physical locationof the antenna, estimation of the transmit antenna numberis of key importance. In this paper, an innovative transmitantenna number detection algorithm, called iterative-maximumratio combining (i-MRC) is presented. The i-MRC algorithm isbased on the fact that only one antenna transmit at a time. Theantenna number may change at the subsequent transmissioninstants, but at any given time only a single transmit antennais transmitting. The channel vectors between each transmitantenna and the number of receive antennas are consideredseparately at the receiver. The receiver iteratively computesthe MRC results between the channel paths from each transmitantenna to the corresponding receive antennas. Assuming fullknowledge of the channel at the receiver, the receiver choosesthe transmit antenna number which gives highest correlation.

In addition to eliminating ICI at the receiver, spatial modu-lation produces no correlation between the transmit antennasand it requires no synchronization between them. In general,1/2 wavelength spacing can achieve uncorrelated fading butthis is affected by factors such as the proximity to thehuman body and other objects. On the other hand, lack ofsynchronization is shown to have a major effect on systemperformance [4], [5]. Furthermore, in spatial modulation, thesymbol duration is unchanged while the transmitted symbolcarries a higher number of information bits (note that thedistance between the signal constellation points is not altered)due to the novel extension of modulation to the spatial domain.As a consequence, an improvement in spectrum efficiency isobtained.

The rest of the paper is organized as follows: In Sec-tion II, the spatial modulation system model is presented. InSection III, the i-MRC antenna number detection algorithmis presented. Simulation results and a receiver complexitycomparison are shown in Section IV. Finally, conclusions areprovided in Section V.

modulation, m = log2 (M) is the number of bits/symbol. Thespatial modulation system model is shown in Fig. 1. q(k)is a vector of n bits to be transmitted. The binary vector ismapped into another vector x(k) of size Nt such that only oneelement in the resulting vector is different from zero. Symbolnumber f in the resulting vector x(k) is xe, where f is themapped transmit antenna number f C [1: Nt]. The symbolx. is transmitted from the antenna number f over the MIMOchannel, H(k). H(k) can be written as a set of vectors whereeach vector corresponds to the channel path gains betweentransmit antenna v and the receive antennas as follows:

H = [h1 h2 ... hN, ] (1)

where:(2)

The received vector is then given by y(k) = h(= )xf +w(k);where w(k) is the additive white Gaussian noise vector.

The number of transmitted information bits, n, can beadjusted in two different and independent ways - either bychanging the signal modulation and/or changing the spatialmodulation. For example, three bits per symbol could be sendfrom four transmit antennas using BPSK modulation as shownin Fig. 2. Alternatively, using two transmit antennas instead offour, three bits could be send if the modulation technique ischanged to 4QAM as shown in Fig. 2. Similarly, in order totransmit four bits, BPSK modulation and eight antennas canbe used or 4QAM modulation and four transmit antennas. Thesame spectral efficiency can be achieve if two antennas and8QAM are used.

In general, the number of bits that can be transmitted usingspatial modulation is given as follows:

n = log2(Nt) +m (3)

III. TRANSMIT ANTENNA NUMBER ESTIMATION

With spatial modulation data is encoded in an informationsymbol and an antenna number. Hence, estimation of thetransmit antenna number is an important task. In the following,a novel antenna number detection algorithm is presented.

The received vector y(k) is iteratively multiplied by thechannel path gains, which are assumed to be known at thereceiver, in order to estimate both: the transmitted symbol andthe transmit antenna number:

II. SYSTEM MODEL

Throughout the paper, the following notations and assump-tions are used. Bold and small letters 'a' denote vectors.Bold and capital letters 'A' denote matrices. The notations,( *, (.)+, (.)H* and (.)T denote conjugate, pseudoinverse,Hermitian, and transpose, of a matrix or a vector respectively,and () -1 denotes the inverse of a matrix. hV, T is the channelgain between transmit antenna T and receive antenna v.Nr is the number of receive antennas. Finally, for MQAM

hjHy, Forj=:Ntg = [91 92 9Ntl]£ = argmax*g

i'zf = Q(g(j=i))

(4)(5)(6)

(7)

where Q(.) is the constellation quantization (slicing) function.Assuming correct estimates for £ and x., the receiver can

straightforwardly de-map the original information bits.

hv = [hi, 1, h2,z, ... hN,, Ij

Modulation

q(k)= [O I ..]q(k) x(k)= [0 x, ... 0]

Nt symbols

=[O 1 ...I

n bits

Ihl hl2

Hk=h2l h22

-hNrl hNr2

Fig. 1. Spatial Modulation System Model

a nt' ant:±a , / 4to o antt, % o-1 f 0 O 0 ant'1 0 Symbol.4

0 1/arn' W f(antl~ 1 6 A

a n t it0 _ 2an /M......a t4t1 ant lan>t

an antatnFg2.Satial1odulation: 2bistansissonsinBPKadfurranmitantnna,o,4AM ndworanm

/ 2

Fg2.SataMouainnbt rnmsinuigBS n ortasi ant nnas or1QM n w tasiatna

A. Example: 3 bits spatial modulation transmission and detec-tion using 2x4 antenna configuration and 4QAM transmission

The mapping table for 3 bits transmission using 4QAMsignal modulation and 2x4 MIMO antenna configuration isshown in Fig. 2.Assume the following sequence of bits to be transmitted,

q(k) = [0, 1, 1]. Mapping this to a 4QAM symbol and twotransmit antennas results in x(k) [1i,0]T where iis the imaginary number, i 11. The vector x(k) istransmitted over the 2x4 MIMO channel H(k). Note that onlyantenna number one will be transmitting the symbol x. andantenna number two will be transmitting zero energy. Forexample, assume the following channel matrix and noise freetransmission:

-0.5377-0.54500.4624 -

0.2854 -

- 0.1229i- 0.0964i-0.2680i-0.1493i

-0.6175 + 0.1516i-0.3271 - 0.0006i0.2058 + 0.3171i-0.5190 + 0.2767i

Then, the received vector at the receiver input equals

y(k) [0.4149 + 0.6606i, 0.4486 + 0.6415i, -0.73040.1944i, 0.4348-O.1361i]'.

The i-MRC detection algorithm is considered in the fol-lowing. The channel is assumed to be known at the receiver.applying the i-MRC detection algorithm to the received vectory(k) results in g = [-1.0000- 1.OOOOi, -0.3271 -0.2978i].Then, the antenna number can be estimated by computingeqn. (6) and results in £ = 1. Similarly, the transmittedsymbol can be estimated by computing eqn. (7) and resultsin xe =-1 -i. Using the respective look-up table in Fig. 2,the transmitted 3-bit sequence can be de-mapped into q(k)[0,1,1], which exactly corresponds to the transmitted bits.The estimation of the transmit antenna number is based

on the cross correlation between different channel paths.Therefore, like in other spatial multiplexing techniques, theperformance of the algorithm is dependent on the channelcorrelation. However, with the proposed new technique, thecorrelation only depends on the characteristics of the channeland not on the spacing between the transmit antennas sinceonly a single antenna transmit at any given time. This is

H(k)=

I

0

0

0

deemed an important feature - especially for uplink transmis-sion.

IV. RESULTS

In the simulation a flat Rayleigh fading channel is assumedwith additive white Gaussian noise (AWGN). The receiver isassumed to have full channel knowledge. The receive antennasare assumed to be separated wide enough to avoid correlation.The total transmit power, P, is the same for all transmissionand the SNR at each receiver input is given by .2, where (2

is the noise power. For V-BLAST transmission, the transmitantennas are assumed to be synchronized and separated wideenough to avoid correlation. Finally, the SNR is assumed tobe known at the receiver when using the MMSE (minimummean square estimation) algorithm for V-BLAST detection.

A. Three bits transmission

The BER (bit-error-ratio) of 4x4 BPSK and 2x4 4QAMspatial modulation is plotted in Fig. 3. The 3x4 BPSK MMSEV-BLAST and lx4 8QAM MRC results are plotted in thesame figure. 4x4 BPSK spatial modulation performs nearlythe same as the lx8 8QAM MRC and 2x4 4QAM spatialmodulation performs almost the same as 3x4 BPSK MMSEV-BLAST. 4x4 BPSK spatial modulation shows a performancedegradation of 2 dB as compared to 2x4 4QAM spatialmodulation and 3x4 BPSK MMSE V-BLAST.

Spatial Modulation, 3 bits transmissionlo'

1o-1

1 o-20

10-3

10

u6-5

io-60 5 10 15 20 25

SNR

Fig. 3. Three bits transmission using spatial modulation, V-BLAST, andMRC

B. Five bits transmission

Five bits transmission BER using 4x4 8QAM and 2x416QAM spatial modulation and lx4 32QAM MRC are plottedin Fig. 4. It is difficult to directly compare this constellation toV-BLAST as 5-bit transmission is not possible. Therefore, theV-BLAST transmission with six bits is chosen, i.e., 2x4 8QAMMMSE. The results are plotted in Fig. 4. Spatial modulationand V-BLAST perform virtually the same. In addition, 2x4

16QAM and the 4x4 8QAM spatial modulation results alsomatch very closely. The spatial modulation technique outper-forms lx4 32QAM MRC by about 4 dB.

Spatial Modulation, 5 bits transmissionF.100

1o-10

0

.75

m

10-2

10-3

10-4

10-5

1o-60 5 10 15 20 25

SNR

Fig. 4. Five bits transmission using spatial modulation and MRC

C. Six bits transmission

Fig. 5 shows the BER performance of spatial modula-tion 4x4 16QAM transmission and 2x4 32QAM transmissioncompared to 2x4 8QAM and 3x4 4QAM MMSE V-BLASTalgorithm and to lx4 64QAM MRC transmission. 4x4 16-QAM transmission and 2x4 8QAM V-BLAST transmissionperform nearly the same. 3x4 4QAM MMSE V-BLAST trans-mission shows a degradation in performance at high SNRdue to the presence of error propagation and the high ICIat the receiver. The new spatial modulation 4x4 16QAMtransmission outperforms lx4 64QAM MRC transmission byapproximately 7 dB.

100

10 1

10o2

0

*t -3

10

10-5

10-6

10

Spatial Modulation, 6 bits transmission and V-BLAST Comparison

MRRC 64QAM 1x4spatial modulation 16QAM 6bits 4x4 I.X X

spatial modulation 32QAM 6bits 2x4

V-BLAST MMSE 8QAM 2x4 ..

V-BLAST MMSE 4QAM 3x4 :::::

0 5 10 15SNR

20 25 30

Fig. 5. Six bits transmission using spatial modulation, V-BLAST, and MRC

MRRC 32QAM 1x4spatial modulation 8QAM 5bits 4x4

. spatial modulation 16QAM 5bits 2x4V-BLAST MMSE 8QAM 2x4

MRRC 8QAM 1x4spatial modulation 3bits 4-QAM 2x4

. = spatial modulation 3bits BPSK 4x4V-BLAST MMSE BPSK 3x4

t::::::::::::: .............:: i: : : :: :: ....:

;...........

D. System Complexity Estimation

The system complexity of the discussed transmission tech-niques in this paper is considered in the following.

Consider only multiplication and addition of a complexnumbers as an operation.

The MMSE criterion requires two matrix multiplications,one inversion and one addition. It is assumed that the matrixtransposes are not computed explicitly. The first matrix multi-plication requires Nt2Nr, the matrix addition requires Nt2 andthe matrix inverse needs 4Nt3 (using Gaussian Elimination)operations [11], [12]. The second matrix multiplication takesNt3 operations. Therefore, a total of (5Nt3 + NrNt2 + Nt2)complex operations are needed. For V-BLAST these steps arerepeated for i = 1 ... Nt [13]. This means that the MMSEis computed for deflated H but with decreasing dimensionsof (Nr x (Nt- L)), L = 0 ... .Nt- 1. As a result, the totalnumber of complex operations is given by:

Nt

( + Nri2 + i2). (8)i=l

i-MRC requires NtNr complex multiplications andNt(Nr -1) complex additions. So, a total of:

[2NtNr -Nt] (9)complex operations are required.

In the following, let ( be the number of complex operations.The receiver complexity comparisons between the spatialmodulation and V-BLAST are shown in Table I for three bitstransmission and in Table II for six bits transmission.

TABLE I

THREE BITS TRANSMISSION REVIVER COMPLEXITY COMPARISON

V-BLAST Spatial ModulationMMSE BPSK 4QAM

( ll 560 28 14

TABLE II

SIX BITS TRANSMISSION REVIVER COMPLEXITY COMPARISON

8QAM V-BLAST 4QAM V-BLAST Spatial ModulationMMSE MMSE 16QAM 32QAM110 560 28 14

V. CONCLUSION

A novel spectral efficient multiple antenna transmissionscheme that utilizes the spatial information in an innovativefashion has been presented. A new modulation scheme, calledspatial modulation, maps multiple information bits into a

single information symbol and into the physical location ofthe single transmitting antenna. Spatial modulation avoids ICIat the receiver input, produces no correlation between thetransmit antennas and requires no synchronization betweenthem. Moreover, spatial modulation does not suffer from theerror propagation problem that exists in V-BLAST. In addition,

a special transmit antenna number detection algorithm tailoredfor the new spatial modulation technique has been proposed.While the new spatial modulation technique shows almost thesame BER performance for the same spectral efficiency asideal V-BLAST, it results in a significant reduction in receivercomplexity. In addition, only one RF (radio frequency) chain isrequired at the transmitter because at any given time only oneantenna transmits. This means that the cost of the transmittercan be significantly reduced. Spatial modulation is expectedto outperform V-BLAST under more realistic assumptions,i.e. taking into consideration transmit antenna correlation andfrequency and antenna synchronization issues. This is subjectto future research.

ACKNOWLEDGEMENT

The authors would like to thank Samsung, and in particularthe Samsung Advanced Institute of Technology (SAIT) inKorea for supporting this work.

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