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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1

Uplink Achievable Rate and Power Allocation inCooperative LTE-Advanced NetworksXiaoxia Zhang, Student Member, IEEE, Xuemin (Sherman) Shen, Fellow, IEEE,

and Liang-Liang Xie, Senior Member, IEEE

Abstract—This paper studies the achievable rate and powerallocation to improve the uplink spectrum efficiency in an LTE-Advanced cooperative cellular network with the deploymentof Type II in-band decode-and-forward relay stations (RSs).The physical layer uplink transmission technology is based onsingle carrier frequency division multiple access (SC-FDMA)with frequency-domain equalization (FDE). Different from thedownlink orthogonal frequency division multiple access (OFD-MA) system, signals on all subcarriers in the SC-FDMA systemare transmitted sequentially rather than in parallel, thus theuser’s achievable rate is not simply the summation of the rateson all allocated subcarriers. Moreover, each user equipment(UE) has its own transmission power constraint instead of atotal power constraint at the base station in the downlink case.Therefore, the uplink resource allocation problem in the LTE-Advanced system is more challenging. To this end, we firstderive the achievable rates of the SC-FDMA system with twocommonly-used FDE techniques, zero-forcing (ZF) equalizationand minimum mean square error (MMSE) equalization, based onthe joint superposition coding for cooperative relaying. We thenpropose optimal power allocation schemes among subcarriersat both UE and RS to maximize the overall throughput ofthe system. Both theoretical analysis and numerical resultsdemonstrate that our proposed power allocation schemes candrastically improve the system throughput.

Index Terms—Achievable rate, resource allocation, SC-FDMA,decode-and-forward relay, frequency-domain equalization, LTE-Advanced.

I. INTRODUCTION

THE consumer demand for reliable high-speed commu-nications has prompted the rapid evolution of mobile

and cellular technologies over the past decades. Due to theemerging technologies and ever growing user and operatorrequirement, future-generation cellular systems are expectedto further improve service provisioning at substantially re-duced costs. In order to meet or exceed the InternationalMobile Telecommunications-Advanced (IMT-A) requirements,the Third Generation Partnership Project (3GPP) has launchedthe Long-Term Evolution (LTE) and its successor, LTE-Advanced (LTE-A) standard for cellular communications. Thetarget is to support higher peak data rates, higher throughputand coverage, and lower latencies, resulting in a better userexperience [1].

Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Xiaoxia Zhang, Xuemin (Sherman) Shen and Liang-Liang Xie are withthe Department of Electrical and Computer Engineering, University of Wa-terloo, Waterloo, Ontario, Canada, N2L 3G1. E-mail: {x79zhang, sshen,llxie}@uwaterloo.ca.

To improve the spectrum efficiency and transmission rate,the physical layer techniques for LTE and LTE-A includeorthogonal frequency division multiplexing (OFDM) as thedownlink (DL) transmission scheme and SC-FDMA as theuplink (UL) multiple access scheme [2]. OFDM divides thebandwidth into subcarriers and allows flexible spectrum allo-cation to mitigate the time and frequency selective fading ofwireless propagation channels. Although OFDM can substan-tially reduce the intersymbol interference (ISI) and increasethe data rate, a principal weakness is the high peak-to-averagepower ratio (PAPR), which would impose a heavy burdenon the power amplifier of the transmitter, especially for themobile terminals [3]. As a result, SC-FDMA is proposedas the uplink transmission technique to reduce the PAPRand make the mobile terminals more power-efficient. SC-FDMA can be viewed as a discrete Fourier transform (DFT)precoded OFDMA, which is the multi-user version of OFDM.SC-FDMA can achieve similar throughput performance andoverall complexity with OFDMA, yet reduce the PAPR andtransmitter cost due to its inherent single carrier nature. UnlikeOFDMA, both transmission and detection of the SC-FDMAsignals are carried out in the time domain rather than in thefrequency domain.

Besides the advanced physical layer transmission tech-nologies, LTE-Advanced networks further incorporate sever-al enhancements, e.g. carrier aggregation and heterogeneousnetwork topologies to improve the capacity and coverage, andto ensure user fairness [1]. Among these, the introduction ofrelay stations (RSs) is of fundamental significance due to itscapability of utilizing cooperative communications betweenthe base stations/users and the relays [4]. There are mainly twotypes of relays supported by the LTE-Advanced standard. AType I relay is a half-duplex relay deployed near the cell edgeto extend the cellular coverage. It creates its own physical celland appears as an eNodeB (eNB) or base station to all userswithin its transmission range. A Type II relay is a full-duplexrelay which is transparent to all users. This type of relayis capable of cooperative communications and is deployedwithin a cell to increase the capacity of the users. With spatialseparation, filtering, or enhanced interference cancellation, thefull-duplex relays require no specific resource partitioning [5].In terms of cooperation schemes, two most commonly studiedin the literature are amplify-and-forward (AF) and decode-and-forward (DF) [6]. An AF relay simply amplifies the receivedsignals and forwards them to the destination. Besides thedesired signal, it also amplifies and propagates the interferenceand noise from the source-relay link. As the relay does




not decode the message, the transmitted signal would causeinterference to its own receiver as well. Therefore, extraresources such as frequency bands or time slots are needed atthe AF relay for orthogonal transmission. On the other hand,DF relay could completely eliminate the noise since the relaydecodes the received signal before forwarding, so the sourceand the relay are able to transmit on the same frequency band(channel) to improve the spectrum efficiency.

Considering the above physical layer techniques and relay-ing technologies, resource allocation for both downlink anduplink cellular networks has attracted an upsurge of researchinterest to utilize the limited spectral resources and to improvethe network efficiency. Resource allocation in the tradition-al multiuser OFDMA downlink systems has been studiedin numerous works, e.g. [7]–[10]. However, the optimalityconditions and algorithms cannot be directly applied to theuplink case mainly for two reasons. Firstly, the capacity ofthe SC-FDMA system is not simply the summation of thecapacity on each subcarriers as in OFDMA systems. Secondly,each UE has its own transmission power constraint insteadof a total power constraint at the eNB in the downlink case.To this end, [11], [12] derived the single user transmissioncapacity of the SC-FDMA system with both ZF and MMSEequalization. [13] further designed low-complexity subcarrierand power allocation schemes to improve the communica-tion reliability. Considering the unique features of the relaychannels in the LTE-Advanced system, [14] studied the jointsubcarrier, power and relay nodes allocation to maximize thetransmission rate in the OFDMA system with AF relays. [15]–[17] proposed efficient resource allocation schemes for sumrate maximization for OFDMA system with DF relays.

For the uplink SC-FDMA system with relays, [6] studiedjoint source power allocation and AF relay beamforming inmulti-relay networks to improve the energy efficiency. [18]calculated the signal-to-noise ratio (SNR) and proposed relayselection in an opportunistic AF relay-assisted SC-FDMA sys-tem and [19] studied relay selection and subcarrier allocationfor opportunistic DF relay-aided SC-FDMA systems assumingthat the UE cannot communicate with the eNB directly. How-ever, to the best of our knowledge, there is limited literature onthe capacity analysis and power allocation for the SC-FDMAsystem with cooperative decode-and-forward relays.

In this paper, we study the fundamental achievable rateand power allocation for the uplink communications in anLTE-Advanced network with the deployment of relay stations.We consider the in-band decode-and-forward (DF) Type IIfull-duplex relay since only this type of relay can achievecooperative diversity gain by utilizing the broadcast nature ofwireless channels. The in-band relay allocates the same set offrequency subcarriers for cooperative transmission with eachUE. Upon receiving a signal from UE, the relay first decodesit to eliminate the noise, then retransmits to the eNB in itsown codes. With joint superposition coding at the UE and therelay, higher rate can be achieved by improving the utilizationof existing allocated spectral resources. The loop interferenceassociated with full-duplex relays can be avoided by spatialisolation of the transmitting and receiving transceivers, andutilizing a loop interference suppression technique [20]. The

UE

eNB/BS

RS

Fig. 1. Uplink transmission with the deployment of RSs in an LTE-Advancednetwork.

main contributions of the paper include:• Since SC-FDMA signals are no longer transmitted in

parallel in the time domain, we revisit the joint superposi-tion encoding and decoding processes for DF cooperativerelaying in the frequency domain.

• We design ZF and MMSE equalizers at both RS andeNB taking into account the cooperative relay channels.Based on the proposed equalizers, the expressions ofthe achievable rate in the SC-FDMA relay system arederived.

• We propose optimal power allocation schemes amongsubcarriers at both UE and RS to maximize the overallthroughput of the system.

The remainder of this paper is organized as follows. Sec-tion II introduces the uplink cooperative communicationssystem model in an LTE-Advanced network. The transmittedand received signals at different nodes are shown in Section III.Section IV presents the joint superposition coding processand derives the expressions of the achievable rate of theuplink transmission with both ZF and MMSE equalization.Section V develops the power allocation schemes to maxi-mize the throughput. The numerical results are included inSection VI and Section VII contains concluding remarks andpossible future work.

II. SYSTEM MODEL

The uplink cooperative communications framework in anLTE-Advanced network is shown in Fig. 1. In each cell, aneNB is located in the center where a set of UEs intend toconnect to the eNB simultaneously for uplink transmission.Near the cell edge, several dedicated Type II in-band decode-and-forward relay stations are installed to assist the communi-cations and improve the transmission rate for the users withinthe RS’s communication range. We consider that the inter-ference can be avoided by proper interference coordinationamong neighboring RSs, e.g., through careful carrier selectionenabled by carrier aggregation in LTE-Advanced network. Tosimplify the problem, suppose no cooperation exists amongadjacent RSs, so each user is served by at most one RS.

Each UE within the RS’s coverage area broadcasts itstransmission signals to both its affiliated eNB and the RS. TheRS aids the communication in the sense that it first decodes the




received signals from the UE, then forwards the message to theeNB in its own codes, which forms a three-node cooperativerelay channel. Therefore, the eNB receives the superpositionof the signals from two paths, the direct UE-eNB transmissionlink and the relay transmission link. Our discussion is limitedto two-hop communications due to the drastic increase of thecoding complexity associated with multiple hops [21].

The system model consists of one eNB, one RS and aset of M users, denoted by M = {1, . . . ,M}, transmittingto the eNB with the help of the RS. The total availablebandwidth B is divided into N orthogonal subcarriers indexedby N = {1, . . . , N}, where each subcarrier has a bandwidthof B/N . Ni ⊂ N is the set of subcarriers occupied by useri for the uplink transmission. The number of subcarriers inNi is denoted by Ni. Since LTE systems employ localizedSC-FDMA as the uplink transmission technology, subcarriersassigned to a user need to be adjacent to each other [22].Besides, each subcarrier can only be allocated to at most oneuser, i.e., Ni

∪Nj = ∅, for i, j ∈ M, i = j.

Consider that all wireless channels are independent andsuffer from frequency selective fading and additive whiteGaussian noise (AWGN). As the bandwidth of a single subcar-rier is narrow, signals on each subcarrier experience frequencyflat fading. The channel gain coefficients for user i, i ∈ Mon subcarrier k, k ∈ Ni are denoted by h

(k)sir, h(k)

rd and h(k)sid

representing the channel conditions of the UE-RS, RS-eNBand UE-eNB links, respectively. The corresponding frequencyresponse are denoted by H

(k)sir , H

(k)rd and H

(k)sid

. Based onthe received pilot signals, we assume that RS has perfectknowledge of the channel state information (CSI) of the UE-RS link and eNB has the perfect knowledge of the CSI of alllinks in order to perform equalization and decoding. Based onthe CSI, the resource scheduler located at the eNB allocatessubcarriers and transmission power for both the UE and the RSbefore the uplink transmission. The decision is then fedbackto the SC-FDMA transmitter scheduler at the UE and the RSfor subcarrier mapping and power allocation.

III. SIGNAL REPRESENTATIONS IN THE SC-FDMA RELAYSYSTEM

The block diagram of the SC-FDMA transmitter and re-ceiver structure for transmission of user i’s signals is shownin Fig. 2.

SC-FDMA is also referred to as DFT-spread OFDMA.The sequence of the time-domain signals for transmission atuser i is firstly transformed into frequency domain by theNi-point DFT, then the sequence goes through the OFDMAprocessing. The decision is carried out in the time domain atthe receiver after the Ni-point IDFT transforms the frequency-domain sequence into time domain.

A. Transmitted Signals at UE

The input to the transmitter at user i is a sequence of Ni

time-domain symbols {xsi(u), u = 1, . . . , Ni}. After the Ni-point DFT, it is transformed into a sequence of frequency-domain symbols {Xsi(v), v = 1, . . . , Ni}.

The frequency-domain scheduler then maps these symbolson a set of Ni active subcarriers selected from a total numberof N subcarriers, and allocates the transmission power on eachsubcarrier. Assume the power allocated to subcarrier k fortransmission at user i is P

(k)si , which needs to satisfy a total

power constraint: ∑k∈Ni

P (k)si ≤ Psi , (1)

where Psi is the total available transmission power at user i.After the subcarrier mapping and power allocation, the

frequency-domain signal on subcarrier k is denoted byX

(k)si , k ∈ Ni. X

(k)si is then transformed back into time do-

main by the N -point inverse DFT (IDFT) before transmittingto the channel.

B. Received and Transmitted Signals at the RSThe sequence of the time-domain signals received at the

RS is firstly transformed into the frequency domain by theN -point DFT. Denote Y

(k)r , k ∈ Ni as the frequency-domain

representation of the received signal on subcarrier k at the RS,which is given by

Y (k)r = H(k)

sirX(k)si +W (k)

r , (2)

where W(k)r with variance σ2

r is the DFT of the additive whiteGaussian noise received at the RS.

The frequency-domain equalization technique is utilized atthe RS in order to mitigate the frequency selective fadingeffect induced by the wireless propagation channel. Then thesequence is transformed back to the time domain, denoted byyr(u), u = 1, . . . , Ni, for decoding, and the decoded messagewill be encoded and transmitted in the subsequent transmissionblock.

Upon receiving the signals from the users, the full-duplexRS transmits a sequence, xr(u), u = 1, . . . , Ni, to the SC-FDMA transmitter for cooperative transmission of user i’smessage. The same set of subcarriers Ni is selected at theRS for the transmission of user i’s message. The frequency-domain representation of the transmitted signal on the kthsubcarrier is X

(k)r , k ∈ Ni, and the power allocated to the

k subcarrier is P(k)r , which satisfies:∑

k∈N

P (k)r ≤ Pr, (3)

where Pr is the total transmission power at the RS.

C. Received Signals at the eNBThe received signal at the eNB on subcarrier k is the

superposition of the signal from the user and the signal fromthe RS, i.e.,

Y(k)d = H

(k)sid

X(k)si +H

(k)rd X(k)

r +W(k)d , (4)

where W(k)d is the additive white Gaussian noise received at

the eNB on subcarrier k, and the variance is given by σ2d.

The corresponding time-domain symbols after the trans-formation for decision is denoted by the vector yd(u), u =1, . . . , Ni.




Ser i al - t o-

par r al l el

Ni - poi nt

DFT

Subcar r i er

Mappi ng/

Power

Al l ocat i on

N - poi nt

I DFT

Par al l el -

t o- ser i al

Add cycl i c

pr ef i x

Equal i zat i on

SC- FDMA Tr ansmi t t er

SC- FDMA Recei ver

Channel

T- domai n F- domai n T- domai n

T- domai n F- domai n T- domai n

Remove cycl i c

pr ef i x

Ser i al - t o-

par r al l el

N - poi nt

DFT

Subcar r i er

De- mappi ng

Ni - poi nt

I DFT

Par al l el -

t o- ser i al

Fig. 2. SC-FDMA transmitter and receiver structure for transmission of user i’s signals.

IV. ACHIEVABLE RATES OF THE SC-FDMA RELAYSYSTEM

To avoid propagating noise and improve the transmissionrate, the decode-and-forward RS cooperates with the UE totransmit the signals to the eNB. The achievable rate in theAWGN channel is attained by joint superposition coding whichcould maximize the cooperation between the source and therelay. The information theoretic achievable rate for the DFrelay channel is given by [23]:

R = maxp(xs,xr)

min{I(Xs;Yr|Xr), I(Xs, Xr;Yd)}. (5)

The first term I(Xs;Yr|Xr) denotes the maximum rate forthe relay to decode (relay decoding rate), and the secondterm I(Xs, Xr;Yd) represents the rate for the destination tosuccessfully decode the message (destination decoding rate).

In this section, we consider the joint superposition codingwith equalization techniques in the SC-FDMA system andderive the expressions of the achievable rate for ZF and MMSEequalization, respectively.

A. Joint Encoding

The joint superposition encoding process of the relay chan-nel consists of a consecutive B blocks of transmission, indexedby b = 1, . . . , B. During block b, a message wb is transmittedover the channel. In each transmission block, two independentcode words, x0 and x1, are employed, both of which containNi i.i.d. random variables generated according to normaldistribution. x0 represents the current transmission block’smessage wb while x1 includes the previous block’s messagewb−1. RS transmits x1 with its full transmission power whileUE transmits a superposition of x0 and x1 to achieve thecooperation, i.e.,

xsi =√βx0 +

√βx1,

xr = x1, (6)

where 0 ≤ β ≤ 1 is the power dividing parameter and β =1− β.

After the transmitter transforms the codes into frequencydomain and performs subcarrier mapping and power alloca-tion, the symbols transmitted on the kth subcarrier at the UEand RS are given by

X(k)si =

√P

(k)si (

√βX

(k)0 +

√βX

(k)1 ),

X(k)r =

√P

(k)r X

(k)1 , (7)

where X(k)0 and X

(k)1 are the frequency-domain representa-

tions of x0 and x1 on the kth subcarrier, respectively.

B. Decoding at the RS

At the end of each transmission block, the relay receives(in the frequency domain):

Y (k)r = H(k)

sirX(k)si +W (k)

r

=

√βP

(k)si H(k)

sirX(k)0 +

√βP

(k)si H(k)

sirX(k)1 +W (k)

r .(8)

To eliminate the intersymbol interference and achieve simi-lar performance of OFDMA with the same overall complexity,frequency-domain equalization is performed before the signalsare transformed and decoded in the time domain. ZF andMMSE are the two commonly used frequency-domain equal-ization techniques in the SC-FDMA system. ZF equalizationcan completely eliminate the ISI with a simple structure.However, it degrades the system performance due to noiseenhancement. Superior performance can be achieved using theMMSE equalization [24], [25]. In the following, the achievablerate of the SC-FDMA relay system is derived for both ZF andMMSE equalization techniques.

1) ZF equalization: If zero-forcing equalization techniqueis employed at the receiver, the output signal of the equalizer




on subcarrier k is given by

Z(k)r =

Y(k)r√

βP(k)si H

(k)sir

=X(k)0 +

√β/βX

(k)1 +

W(k)r√

βP(k)si H

(k)sir

. (9)

The decoding process is carried out in the time domain.After the subcarrier de-mapping and IDFT, the uth element ofthe time-domain sequence zr is given by

zr(u) =1√Ni

Ni∑k=1

Z(k)r ej2πku/Ni = x0(u)+

√β/β · x1(u) +

1√Ni

∑k

W(k)r√

βP(k)si H

(k)sir

ej2πku/Ni . (10)

Since x1 is the RS’s transmitted symbol in the currenttransmission block, at the end of the transmission block b,RS needs to decode x0 and wb, where wb will be re-encodedand transmitted in the subsequent transmission block by theRS. The maximum achievable rate for the RS to decode x0

is given by

RZFr =I(X0;Zr|X1)

=C

(( 1

Ni

∑k

σ2r

βP(k)si |H(k)

sir |2

)−1), (11)

where C(x) = log2(1 + x).

2) MMSE equalization: Unlike ZF equalization, MMSE e-qualization technique also suppresses noise, thus it can achievehigher transmission rate. The output of an MMSE equalizeron the kth subcarrier is given by

Z(k)r =

√βP

(k)si H

(k)∗

sir

βP(k)si |H(k)

sir |2 + σ2r

Y (k)r

=βP

(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

X(k)0 +

√ββP

(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

X(k)1

+

√βP

(k)si H

(k)∗

sir

βP(k)si |H(k)

sir |2 + σ2r

W (k)r . (12)

The uth element of the time-domain sequence zr is givenby

zr(u) =1√Ni

∑k

βP(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

X(k)0 ej2πku/Ni

+1√Ni

∑k

√ββP

(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

X(k)1 ej2πku/Ni

+1√Ni

∑k

√βP

(k)si H

(k)∗

sir

βP(k)si |H(k)

sir |2 + σ2r

W (k)r ej2πku/Ni . (13)

Let

λ =1

Ni

∑k

βP(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

, (14)

N - point

DFT

Equalizer

for X0

Equalizer

for X1

Ni - point

IDFT

N - point

DFT

Equalizer

for X0

Equalizer

for X1

Ni - point

IDFT

Ni - point

IDFT

Ni - point

IDFT

Transmission

block b

Transmission

block b-1

Fig. 3. Equalization and decoding process at the eNB.

the achievable rate to decode x0 with MMSE equalization isthen given by

RMMSEr = C

( λ2

λ− λ2

)

= C

( 1Ni

∑k

βP (k)si

|H(k)sir

|2

βP(k)si

|H(k)sir

|2+σ2r

1− 1Ni

∑k

βP(k)si

|H(k)sir

|2

βP(k)si

|H(k)sir

|2+σ2r

)

= C

([( 1

Ni

∑k

βP(k)si |H(k)

sir |2

βP(k)si |H(k)

sir |2 + σ2r

)−1

− 1

]−1). (15)

C. Decoding at the eNB

On the kth subcarrier, the destination eNB receives thesuperposition of the UE signal and the relay signal, i.e.,

Y(k)d = H

(k)sid

X(k)si +H

(k)rd X(k)

r +W(k)d

=

√βP

(k)si H

(k)sid

X(k)0 +W

(k)d +(√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

)X

(k)1 . (16)

At the end of transmission block b, the eNB decodes the pre-vious block’s message wb−1 in two steps based on the receivedsignals of both block b and b − 1. Denote the time-domainsymbol for decoding as zd. First, x1 from block b is decodedat rate Rd1 = I(X1;Zd) while treating x0 as noise. Thenbased on the decoded x1, x0 from block b− 1 and wb−1 aredecoded at rate Rd = I(X0;Zd|X1) +Rd1 = I(X0, X1;Zd).The structure of the equalization and decoding process at theeNB in the SC-FDMA system is shown in Fig. 3.

At the end of each transmission block, the frequency-domain sequence after the N -point DFT goes into two parallel




equalizers. The first equalizer is designed to equalize X(k)1 and

the second equalizer is for X(k)0 equalization. Combined with

the decoded x1 from block b, the joint decoding process inblock b− 1 is able to decode x0 and wb−1.

1) ZF equalization: The kth element of the output signalof the ZF equalizer for X

(k)1 can be written as the following

frequency-domain representation:

Z(k)d1 =

Y(k)d√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

= X(k)1 +

√βP

(k)si H

(k)sid√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

X(k)0

+1√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

W(k)d . (17)

Then, the frequency-domain signal Z(k)d1 is transformed into

time domain by IDFT. The uth element of the time-domainsignal zd1 is given by

zd1(u) = x1(u)

+ IDFT

( √βP

(k)si H

(k)sid√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

X(k)0

)

+ IDFT

(1√

βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

W(k)d

). (18)

The maximum achievable rate for the eNB to decode x1 isgiven by

RZFd1 = I(X1;Zd1)

= C

((1

Ni

∑k

βP(k)si |H(k)

sid|2 + σ2

d∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2)−1

).

(19)

Then, we decode x0 and the message wb−1. The outputsignal of the equalizer for X

(k)0 on the kth subcarrier can be

calculated by

Z(k)d2 =

Y(k)d√

βP(k)si H

(k)sid

= X(k)0 +

1√βP

(k)si H

(k)sid

W(k)d

+

√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd√

βP(k)si H

(k)sid

X(k)1 . (20)

The uth element of the time-domain signal after the IDFTcan be written as

zd2(u) = x0(u) + IDFT

(1√

βP(k)si H

(k)sid

W(k)d

)

+ IDFT

(√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd√

βP(k)si H

(k)sid

X(k)1

). (21)

Then, the total achievable rate for the destination to decodex0 and the previous block’s message wb−1 with ZF equaliza-tion is given by

RZFd = I(X0;Zd2|X1) +RZF

d1

= C

((1

Ni

∑k

σ2d

βP(k)si |H(k)

sid|2

)−1)+

C

((1

Ni

∑k

βP(k)si |H(k)

sid|2 + σ2

d∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2)−1

).

(22)

2) MMSE equalization: If MMSE equalization techniqueis employed at the receiver, the kth element of the outputsignal of the equalizer for X(k)

1 in the frequency domain canbe calculated by

Z(k)d1 =

(√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

)∗∣∣∣√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

Y(k)d

=

∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

X(k)1

+

√βP

(k)si H

(k)sid

(√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

)∗∣∣∣√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

X(k)0

+

(√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

)∗∣∣∣√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

W(k)d . (23)

The signal is then transformed into the time domain by theIDFT and the destination decodes the message based on thetime-domain signal. Let

λ1 =1

Ni

∑k


(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

. (24)

The maximum achievable rate to decode x1 at the eNB isthus given by

RMMSEd1 = C

(λ1

1− λ1

)=

C

([(1

Ni

∑k


(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

)−1

− 1

]−1).

(25)

By the same argument, the kth element of the output signalof the MMSE equalizer for X

(k)0 in the frequency domain is




given by

Z(k)d2 =

√βP

(k)si H

(k)∗

sid

βP(k)si |H(k)

sid|2 + σ2

d

Y(k)d

=βP

(k)si |H(k)

sid|2

βP(k)si |H(k)

sid|2 + σ2

d

X(k)0 +

√βP

(k)si H

(k)∗

sid

βP(k)si |H(k)

sid|2 + σ2

d

W(k)d

+

√βP

(k)si H

(k)∗

sid

(√βP

(k)si H

(k)sid

+

√P

(k)r H

(k)rd

)βP

(k)si |H(k)

sid|2 + σ2

d

X(k)1 .

(26)

Denote λ2 as

λ2 =1

Ni

∑k

βP(k)si |H(k)

sid|2

βP(k)si |H(k)

sid|2 + σ2

d

. (27)

Therefore, the maximum achievable rate for decoding x0

and wb−1 at the eNB with MMSE equalization can be calcu-lated by

RMMSEd = C

(λ2

1− λ2

)+RMMSE

d1

= C

([( 1

Ni

∑k

βP(k)si |H(k)

sid|2

βP(k)si |H(k)

sid|2 + σ2

d

)−1

− 1

]−1)+

C

([(1

Ni

∑k


(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2∣∣∣√βP(k)si H

(k)sid

+

√P

(k)r H

(k)rd

∣∣∣2 + σ2d

)−1

− 1

]−1).

(28)

D. Achievable Rates

The maximum achievable rate for user i to transmit inthe SC-FDMA system with the help of a relay station is theminimum of the RS decoding rate and the eNB decoding rate.If ZF equalization technique is utilized, the achievable rate foruser i’s transmission is given by

RZFi = max

0<β<1min

{RZF

r , RZFd

}, (29)

and the achievable rate with MMSE equalization technique isgiven by

RMMSEi = max

0<β<1min

{RMMSE

r , RMMSEd

}. (30)

V. POWER ALLOCATION FOR THROUGHPUTMAXIMIZATION

Based on the achievable rate of the SC-FDMA relay systemderived in the previous section, we further allocate transmis-sion power among the subcarriers at both UE and RS tomaximize the cooperation gain and the overall throughput ofthe system.

The problem can be modeled mathematically as the follow-

ing optimization problem:

maxP

(k)si

,P(k)r

∑i∈M

Ri

subject to∑k∈Ni

P (k)si ≤ Psi , ∀i ∈ M∑

k∈N

P (k)r ≤ Pr

P (k)si ≥ 0, for all k, i

P (k)r ≥ 0, for all k. (31)

The objective is to maximize the summation of the uplinkachievable rates of all users in the network, where each userhas its individual power constraint and the relay’s transmissionpower on all subcarriers is bounded by a total power constraint.

Since (31) is a max-min problem, generally it is verydifficult to solve. However, as each user occupies an exclusiveset of subcarriers and has individual power constraint, thisproblem can be decomposed into a two-layer power allocationproblem. Specifically, we first maximize the achievable rateof a single user through power allocation among its assignedsubcarriers at both UE and RS assuming a fixed powerconstraint at the RS for the user, i.e.,

maxP

(k)si

,P(k)r

Ri

subject to∑k∈Ni

P (k)si ≤ Psi∑

k∈Ni

P (k)r ≤ Pri

P (k)si ≥ 0, for all k

P (k)r ≥ 0, for all k. (32)

In (32), the total power available for relaying user i’sinformation at the RS is denoted as Pri . In the secondsubproblem, the RS distributes its total available transmissionpower among all users to maximize the overall throughput,i.e.,

maxPri

∑i∈M

Ri

subject to∑i∈M

Pri ≤ Pr

Pri ≥ 0, for all i. (33)

In the following, we consider the uplink SC-FDMA systememploying ZF and MMSE equalization techniques and solvethe two-layer optimization problem separately.

A. Power Allocation with ZF Equalization

The objective is to solve the two-layer optimization problemwhen a ZF equalization is utilized. In the uplink communica-tion system, the transmission power and function at the trans-mitters are normally very limited. To simplify the transmitterdesign, we focus on the asynchronous relaying case with thepower dividing parameter β = 1, i.e., the source and the relayuse independent codes.




In the asynchronous case, the single user’s uplink achievablerate can be written as:

RZFi = min

C

(( 1

Ni

∑k

σ2r

P(k)si |H(k)

sir |2

)−1),

C

(( 1

Ni

∑k

P(k)si |H(k)

sid|2 + σ2

d

P(k)r |H(k)

rd |2

)−1)+

C

(( 1

Ni

∑k

σ2d

P(k)si |H(k)

sid|2

)−1) , (34)

where the first term denotes the relay decoding rate and thesecond term represents the eNB decoding rate.

Consider that in the uplink communications, the transmis-sion power at the relay station is generally much greater thanthe available power at the mobile terminal, i.e., P (k)

r >> P(k)si ,

which means that the relay decoding rate is the bottleneckof the achievable rate for user i. Since the relay decodingrate only depends on the allocated transmission power at theUE, (32) can be solved in two steps. First, we try to findthe optimal power allocation among the assigned subcarriersat the UE to maximize the relay decoding rate, which is theupper bound of user i’s achievable rate. Then, the optimalallocation of RS transmission power on each subcarrier canbe determined to ensure that this upper bound is achievable.

Finding the optimal power allocation at the UE is equivalentto solving the following optimization problem:

minP

(k)si

∑k∈Ni

σ2r

P(k)si |H(k)

sir |2

subject to∑k∈Ni

P (k)si ≤ Psi

P (k)si ≥ 0. (35)

Since (35) is a convex optimization problem, the Kuhn-Tucker condition (KKT condition) characterizes the necessaryand sufficient condition that the optimal solution needs tosatisfy. The Lagrangian can be written as

L =∑k∈Ni

σ2r

P(k)si |H(k)

sir |2+ λ

( ∑k∈Ni

P (k)si − Psi

), (36)

and the KKT condition is given by

∂L∂P

(k)si

= λ− σ2r

|H(k)sir |2

1

P(k)si

2 = 0, (37)

where λ is chosen to satisfy the UE’s transmission powerconstraint

∑k∈Ni

P(k)si ≤ Psi .

Solving (37), the optimal P (k)∗si is given by

P (k)∗si =

Psi

|H(k)sir | ·

∑k∈Ni

|H(k)sir |

−1 . (38)

Then, the optimal P (k)∗r should maximize the eNB decoding

rate with P(k)∗si given in (38). Specifically, P

(k)∗r can be

obtained by the KKT condition with the following Lagrangian:

L =∑k∈Ni

P(k)si |H(k)

sid|2 + σ2

d

P(k)r |H(k)

rd |2+ µ

( ∑k∈Ni

P (k)r − Pri

). (39)

The KKT condition is given by

∂L∂P

(k)r

= µ−P

(k)si |H(k)

sid|2 + σ2

d

P(k)r |H(k)

rd |2· 1

P(k)r

2 = 0, (40)

where µ is chosen to satisfy the RS power constraint∑k∈Ni

P(k)r ≤ Pri .

Solving (40), the optimal P (k)∗r is given by

P (k)∗r =

Pri∑k∈Ni

√P

(k)∗si

|H(k)sid

|2+σ2d

|H(k)rd |

·

√P

(k)∗si |H(k)

sid|2 + σ2

d

|H(k)rd |

.

(41)To solve subproblem (33), we need to allocate the RS trans-

mission power among users to maximize the overall through-put of the system. Consider that the available transmissionpower at the RS is sufficient enough compared with the totalpower at the UE, and the eNB decoding rate increases with Pri

while the RS decoding rate remains unchanged. The optimalP ∗ri is the smallest value that can make the eNB decoding

rate equal the RS decoding rate, thus the upper bound of eachuser’s achievable rate can be achieved. Therefore, the optimalRS transmission power for relaying user i’s information P ∗

rican be attained by solving the following equation:

C

(( 1

Ni

∑k

P(k)∗si |H(k)

sid|2 + σ2

d

P(k)∗r |H(k)

rd |2

)−1)

= C

(( 1

Ni

∑k

σ2r

P(k)∗si |H(k)

sir |2

)−1)−

C

(( 1

Ni

∑k

σ2d

P(k)∗si |H(k)

sid|2

)−1). (42)

B. Power Allocation with MMSE Equalization

The single user’s achievable rate in the asynchronous relay-ing case when MMSE equalization technique is employed isgiven by

RMMSEi =

min

C

([( 1

Ni

∑k

P(k)si |H(k)

sir |2

P(k)si |H(k)

sir |2 + σ2r

)−1

− 1

]−1),

C

([( 1

Ni

∑k

P(k)r |H(k)

rd |2

P(k)r |H(k)

rd |2 + σ2d

)−1

− 1

]−1)+

C

([( 1

Ni

∑k

P(k)si |H(k)

sid|2

P(k)si |H(k)

sid|2 + σ2

d

)−1

− 1

]−1) . (43)

When P(k)r >> P

(k)si , the relay decoding rate is the

bottleneck of (43). To find the optimal user transmission powerallocation to maximize the relay decoding rate, we first solve




the following optimization problem:

maxP

(k)si

∑k∈Ni

P(k)si |H(k)

sir |2

P(k)si |H(k)

sir |2 + σ2r

subject to∑k∈Ni

P (k)si ≤ Psi

P (k)si ≥ 0. (44)

(44) is also a convex optimization problem where theLagrangian is given by

L =∑k∈Ni

P(k)si |H(k)

sir |2

P(k)si |H(k)

sir |2 + σ2r

− λ( ∑

k∈Ni

P (k)si − Psi

), (45)

and the KKT condition is given by

∂L∂P

(k)si

=|H(k)

sir |2σ2r(

P(k)si |H(k)

sir |2 + σ2r

)2 − λ = 0, (46)

where λ is determined by the transmission power constraintat user i, i.e.,

∑k∈Ni

P(k)si ≤ Psi .

Hence the optimal P (k)∗si is a water-filling solution given by

P (k)∗si =

(σr

|H(k)sir |

√λ− σ2

r

|H(k)sir |2

)+

, (47)

where function (·)+ is defined as

(x)+ =

{x, if x ≥ 0;0, if x < 0. (48)

The optimal power allocated to subcarrier k at the RS,P

(k)∗r , needs to maximize the eNB decoding rate with P

(k)∗si

given in (47). The Lagrangian is given by

L =∑k∈Ni

P(k)r |H(k)

rd |2

P(k)r |H(k)

rd |2 + σ2d

− µ( ∑

k∈Ni

P (k)r − Pri

), (49)

and the KKT condition can be written as

∂L∂P

(k)r

=|H(k)

rd |2σ2d(

P(k)r |H(k)

rd |2 + σ2d

)2 − µ = 0, (50)

where µ is chosen to satisfy the transmission power constraintat the RS, i.e.,

∑k∈Ni

P(k)r ≤ Pri .

The optimal P (k)∗r is also a water-filling solution given by

P (k)∗r =

(σd

|H(k)rd |√µ

− σ2d

|H(k)rd |2

)+

. (51)

To maximize the overall throughput of the system, theoptimal RS transmission power allocated for relaying user i’smessage, P ∗

ri , is the smallest value that can achieve the upperbound of user i’s achievable rate. Specifically, P ∗

ri makes theuser i’s RS decoding rate equal the eNB decoding rate and

thus can be obtained by solving the following equation:

C

([( 1

Ni

∑k

P(k)∗r |H(k)

rd |2

P(k)∗r |H(k)

rd |2 + σ2d

)−1

− 1

]−1)

=C

([( 1

Ni

∑k

P(k)∗si |H(k)

sir |2

P(k)∗si |H(k)

sir |2 + σ2r

)−1

− 1

]−1)−

C

([( 1

Ni

∑k

P(k)∗si |H(k)

sid|2

P(k)∗si |H(k)

sid|2 + σ2

d

)−1

− 1

]−1). (52)

VI. NUMERICAL RESULTS

To verify the derived uplink achievable rates and evaluatethe performance of the proposed power allocation schemesin SC-FDMA relay systems, in this section, we present ournumerical results considering practical network scenarios.

We consider that all wireless channels suffer from indepen-dent frequency selective fading and each subcarrier is subjectto frequency flat Rayleigh fading. In our simulation, a typicalurban area propagation model with 9 paths is employed [26],and the parameters are listed in Table I.

TABLE IRELATIVE POWERS OF THE DELAY PROFILE.

Delay (µs) 0.0 0.05 0.12 0.2 0.23 0.5 1.6 2.3 5.0Power (dB) -1.0 -1.0 -1.0 0.0 0.0 0.0 -3.0 -5.0 -7.0

Fig. 4 shows the RS decoding rate and the eNB decodingrate with different power dividing parameter β for both ZFequalization and MMSE equalization in a single user SC-FDMA system. The uplink user equipment is allocated withone resource block, i.e., 12 consecutive subcarriers for trans-mission. The transmission power is 15dBm at both UE and RS,and is equally assigned to all allocated subcarriers. The noisevariance received at the RS on each subcarrier is normalized to1, and the noise variance at the eNB is 2. It can be seen that

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

β

Ach

ieva

ble

rate

(bp

s/H

z)

ZF, RS decoding rateZF, eNB decoding rateMMSE, RS decoding rateMMSE, eNB decoding rate

Maximum achievable rate

Fig. 4. RS decoding rate and eNB decoding rate with ZF and MMSEequalization.

MMSE equalization generally achieves higher rate than ZFequalization due to noise suppression. The user’s achievablerate is the minimum of its RS decoding rate and eNB decodingrate. The maximum user’s achievable rate is achieved with the




optimal power dividing parameter which ensures that the user’sRS decoding rate equals its eNB decoding rate.

Fig. 5 shows the maximum achievable rate of a single userin both OFDMA and SC-FDMA systems with MMSE and ZFequalization techniques. We compare the derived achievablerate of the decode-and-forward relay channel with the singleuser’s capacity of the direct transmission without the help ofRSs. The user’s achievable rate of the relay channel in theOFDMA network is calculated based on equation (4) in [16].The capacity of the SC-FDMA system is determined accordingto equation (9) and (12) for ZF equalization and MMSEequalization, respectively. The total transmission power at theUE and RS ranges from 20dBm to 30dBm for the relayingcase while the UE power matches the total transmission powerfor the direct transmission case in order to conduct a faircomparison. The transmission power is equally distributedon all subcarriers in both cases. The rest of the simulationparameters remain unchanged.

20 22 24 26 28 300

0.2

0.4

0.6

0.8

1

Total transmission power at the UE and RS (dBm)

Ach

ieva

ble

rate

(bp

s/H

z)

RS, OFDMARS, SC−FDMA (MMSE)RS, SC−FDMA (ZF)No RS, OFDMANo RS, SC−FDMA (MMSE)No RS, SC−FDMA (ZF)

Fig. 5. Rate comparison of SC-FDMA and OFDMA relay systems.

In Fig. 5, it can be seen that the spectrum efficiency ofboth SC-FDMA and OFDMA systems with and without relaystations increases with the total transmission power. In wirelessenvironment, OFDMA achieves higher rate than SC-FDMAdue to the parallel transmission structure of OFDMA signals.Fig. 5 also shows that the cooperative transmission with thehelp of a decode-and-forward relay can significantly improvethe user rate compared with non-cooperative transmission,which demonstrates the benefits of deploying relay stationsin the cellular network.

To evaluate the performance of our proposed power al-location schemes for both ZF and MMSE equalization, wefirst compare the single user’s achievable rate achieved byour proposed power allocation schemes with an equal powerallocation scheme, which is most commonly employed forderiving capacity and resource allocation schemes [11], [12]as shown in Fig. 6. The equal power allocation scheme assignsthe transmission power at both UE and RS equally to allsubcarriers. Consider that the transmission power at the UEis 25dBm and the transmission power at the RS for each useris fixed and ranges from 30dBm to 45dBm.

It can be seen that our proposed power allocation schemes

30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4

Transmission power at the RS (dBm)

Ach

ieva

ble

rate

(bp

s/H

z)

Proposed power allocation, ZFProposed power allocation, MMSEEqual power allocation, ZFEqual power allocation, MMSE

Fig. 6. Comparison of single-user uplink achievable rates.

can improve the single user’s achievable rate for both ZF andMMSE equalization compared with the equal power allocationscheme. As the RS’s transmission power increases, the eNBdecoding rate rises accordingly while the RS decoding rateremains unchanged. Thus, the single user’s achievable ratereaches an upper bound, which is determined by the RSdecoding rate.

Fig. 7 compares the overall throughput of our proposedpower allocation schemes and the equal power allocationscheme in the uplink transmission of a cellular network. TheRS’s total available transmission power is 50dBm, which isallocated among all users according to (42) and (52). Somesimulation parameters are summarized in Table II:

TABLE IISIMULATION PARAMETERS.

Parameter ValueCellular layout Hexagonal grid, 6 sectors per cell

Relay station layout 1 relay station per sectorRelay protocol Decode-and-Forward

Transmission bandwidth 20MHzSubcarrier separation 15kHz

♯ of subcarriers in a resource block 12Carrier frequency 2GHz for uplinkChannel model Frequency selective Rayleigh fadingUE distribution Uniformly random

UE transmission power 25dBmRS transmission power 50dBm

Since each user occupies only one resource block, the uplinktransmission bandwidth is sufficient. Therefore, it can be seenthat both throughput achieved by our proposed power alloca-tion schemes and the throughput achieved by equal power allo-cation scheme increase with the number of users. Furthermore,our proposed power allocation schemes outperform the equalpower allocation scheme drastically, especially in the MMSEequalization scenario. The ZF equalization shows a poor noiseperformance and the improvement is relatively limited as thenoise contributions of highly attenuated subchannels are ratherlarge, which limit the overall system performance.

VII. CONCLUSION

In this paper, we have studied the cooperative transmissionand power allocation to improve the transmission efficiency in




5 10 150

5

10

15

20

25

30

Number of UEs

Tho

ughp

ut (

bps/

Hz)

Proposed power allocation, ZFProposed power allocation, MMSEEqual power allocation, ZFEqual power allocation, MMSE

Fig. 7. Comparison of the overall throughput in an uplink cellular network.

an uplink LTE-Advanced cellular system with Type II in-banddecode-and-forward relays. As SC-FDMA is the physical layertechnique for the LTE-Advanced system, the capacity andresource allocation schemes for the downlink OFDMA systemcannot be applied directly to the SC-FDMA system. Therefore,we have first studied the joint superposition coding and derivedthe expressions of the achievable rate of an uplink SC-FDMArelay system with both ZF and MMSE equalization. Then wehave proposed optimal power allocation schemes to maximizethe overall throughput of the system.

For the future work, we will jointly consider subcarrierand power allocation, and propose efficient resource allocationalgorithms for practical uplink communication scenarios tofurther improve the spectrum efficiency.

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Xiaoxia Zhang received the B.E. de-gree from Beijing University of Postsand Telecommunications, Beijing, Chinain 2008 and M.A.Sc. degree in Elec-trical and Computer Engineering fromthe University of Waterloo, Waterloo,ON, Canada in 2010. She is currentlyworking towards the Ph.D. degree at theDepartment of Electrical and Computer

Engineering, University of Waterloo, Waterloo, ON, Canada.Her research interests include resource management for broad-band communication networks, cooperative communication,wireless sensor networks and network information theory.




Xuemin (Sherman) Shen (IEEEM’97-SM’02-F’09) received the B.Sc.(1982) degree from Dalian Maritime U-niversity (China) and the M.Sc. (1987)and Ph.D. degrees (1990) from Rutger-s University, New Jersey (USA), all inelectrical engineering. He is a Professorand University Research Chair, Depart-ment of Electrical and Computer Engi-

neering, University of Waterloo, Canada. He was the AssociateChair for Graduate Studies from 2004 to 2008. Dr. Shen’sresearch focuses on resource management in interconnectedwireless/wired networks, wireless network security, socialnetworks, smart grid, and vehicular ad hoc and sensor net-works. Dr. Shen served as the Technical Program CommitteeChair/Co-Chair for IEEE Infocom’04, IEEE VTC’10 Fall, theSymposia Chair for IEEE ICC’10, the Tutorial Chair for IEEEVTC’11 Spring and IEEE ICC’08, the Technical ProgramCommittee Chair for IEEE Globecom’07, the General Co-Chair for Chinacom’07 and QShine’06, the Chair for IEEECommunications Society Technical Committee on WirelessCommunications, and P2P Communications and Network-ing. He also serves/served as the Editor-in-Chief for IEEENetwork, Peer-to-Peer Networking and Application, and IETCommunications; a Founding Area Editor for IEEE Trans-actions on Wireless Communications; an Associate Editorfor IEEE Transactions on Vehicular Technology, ComputerNetworks, and ACM/Wireless Networks, etc.; and the GuestEditor for IEEE JSAC, IEEE Wireless Communications, IEEECommunications Magazine, and ACM Mobile Networks andApplications, etc. Dr. Shen received the Excellent GraduateSupervision Award in 2006, and the Outstanding PerformanceAward in 2004, 2007 and 2010 from the University of Water-loo, the Premier’s Research Excellence Award (PREA) in 2003from the Province of Ontario, Canada, and the DistinguishedPerformance Award in 2002 and 2007 from the Faculty ofEngineering, University of Waterloo. Dr. Shen is a registeredProfessional Engineer of Ontario, Canada, an IEEE Fellow, anEngineering Institute of Canada Fellow, a Canadian Academyof Engineering Fellow, and a Distinguished Lecturer of IEEEVehicular Technology Society and Communications Society.

Liang-Liang Xie (IEEE M’03-SM’09)received the B.S. degree in mathematicsfrom Shandong University, Jinan, China,in 1995 and the Ph.D. degree in controltheory from the Chinese Academy ofSciences, Beijing, China, in 1999.

He did postdoctoral research withthe Automatic Control Group, LinkopingUniversity, Linkoping, Sweden, during

1999-2000 and with the Coordinated Science Laboratory, U-niversity of Illinois at Urbana-Champaign, during 2000-2002.He is currently a Professor at the Department of Electricaland Computer Engineering, University of Waterloo, Waterloo,ON, Canada. His research interests include wireless networks,information theory, adaptive control, and system identification.

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