Improved OFDMA uplink transmission via cooperative relaying in the presence of frequency...

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONSEur. Trans. Telecomms. 2010; 21:224–240Published online 12 October 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/ett.1384

Communication Theory

Improved OFDMA uplink transmission via cooperative relaying in the presenceof frequency offsets—Part I: Ergodic information rate analysis†

Zhongshan Zhang1, Chintha Tellambura2* and Robert Schober3

1Department of Research & Innovation (R&I), Alcatel-Lucent, Shanghai Bell Co., Ltd., No. 388 Ningqiao Road, Pudong, Shanghai, 201206 China2Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada

3Department of Electrical and Computer Engineering, University of British Columbia, Vancouver BC V6T 1Z4, Canada

SUMMARY

In this two-part paper, we evaluate ergodic and outage information rates in an orthogonal frequency-divisionmultiple access (OFDMA) uplink with amplify-and-forward (AF) and decode-and-forward (DF) relays inthe presence of frequency offsets. Each node plays the roles of the source node and the relay, simultaneously,but on different subcarriers. In Part I, the ergodic information rate is derived, and in Part II, the outageinformation rate of the considered scheme is derived. For a given frequency offset, unlike that of the AFmode, the DF ergodic information rate does not monotonically increase with α (the ratio between the powerallocated to the source node and the total transmit power), and 0 < α < 1 can be optimised to maximise theergodic information rate. Numerical results show that AF cooperation does not outperform the conventionaltransmission (without relaying) with regard to ergodic information rate. In contrast, with DF relaying,performance gains are possible. Copyright © 2009 John Wiley & Sons, Ltd.

1. INTRODUCTION

Orthogonal frequency-division multiple access (OFDMA)divides the total signal bandwidth into multiple orthogo-nal subcarrier groups, with each group being allocated toone node [1]. By adaptively allocating and modulating sub-carriers for each node, the frequency diversity gain canbe improved, and, therefore, OFDMA transmission can beoptimised in terms of bit error rate or channel capacity [2, 3].

Besides frequency diversity, spatial diversity can also beexploited to improve the diversity gain. Space–time codesand multiple co-located transmit antennas are typical suchmethods [4, 5]. Alternatively, in cooperative diversity,intermediate nodes assist (relay) source-to-destinationsignal transmission [6–9]. Relays can employ amplify-and-forward (AF) or decode-and-forward (DF) modes. Jointoptimisation of cooperative relay-precoders/decoders isdiscussed in Reference [10], which requires full or partial

* Correspondence to: Chintha Tellambura, Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4, Canada.E-mail: [email protected]†This paper was presented in part at the IEEE Global Telecommunications Conference (GLOBECOM) 2008.

channel state information (CSI). Relay mode selection isdiscussed in Reference [11]. A performance comparisonbetween AF and DF relays is provided in Reference [12],suggesting that geographically close nodes should bechosen as relays to reduce the probability of inter-nodeoutage. Cooperative transmission can also be extended tomulticarrier systems [13, 14].

However, prior works [9–14] do not consider the effect offrequency offset. In multicarrier systems, frequency offsetsare the major cause of interference, resulting in inter-carrier-interference (ICI) and multiple-access-interference (MAI).MAI cancellation in an OFDMA system is discussed inReference [15], which, however, may not be extendable torelay networks. Since such interference degrades the signal-to-interference-plus-noise ratio (SINR) of each subcarrier,per-subcarrier optimisation may be difficult [13]. Both inter-symbol-interference (ISI) and ICI mitigation in a coopera-tive space-frequency block coded (SFBC) OFDM system

Received 18 November 2008Revised 23 May 2009

Copyright © 2009 John Wiley & Sons, Ltd. Accepted 3 August 2009

IMPROVED OFDMA UPLINK TRANSMISSION VIA COOPERATIVE RELAYING 225

is analysed in Reference [16]. A space–time cooperativeOFDM (CO-OFDM) system is proposed in Reference [17].CO-OFDM also achieves diversity gains comparable tothose of conventional space–time coded OFDM. But thosegains can be lost due to the frequency offsets.

In this paper, the OFDMA uplink ergodic and outageinformation rates with cooperative relaying in the pres-ence of frequency offsets are analysed. Following Reference[14], we assume that the mobile nodes can transmit on onesubcarrier and listen on another simultaneously—but notsimultaneously on the same subcarrier, i.e. a half-duplexconstraint is assumed. Furthermore, we assume that thelocal transmitter and receiver of each node are perfectly syn-chronised in both time and frequency. The number of relaysassisting the source node is assumed to be fixed during atransmission period but may change across different trans-mission periods. Furthermore, for ensuring a fair basis forcomparison, the total transmit power per symbol is kept con-stant. As in Reference [9], AF or DF relays are considered.The ergodic information rate of the proposed cooperativeOFDMA uplink transmission is analysed in Part I of thistwo-part paper. In Part II, the outage information rate of theproposed scheme is derived.

The remainder of this paper is organised as follows. Sec-tion 2 introduces the cooperative OFDMA uplink signalmodel. The ergodic information rate of the proposed cooper-ative transmission scheme is analysed in Section 3. Section4 discusses numerical results. Finally, Section 5 concludesthe paper.

Notation: (·)T and (·)H denote the transpose and conju-gate transpose of a matrix, respectively. (·)−1 representsthe inverse of a matrix. The imaginary unit is = √−1.(·)∗ is complex conjugate. A circularly symmetric complexGaussian random variable (RV) with mean a and varianceσ2 is denoted by z ∼ CN(a, σ2). x[i] represents the ith ele-ment of vector x. [A]ij represents the ijth element of matrixA. The N × N identity matrix is IN , and the N × N all-zero matrix is ON . diag{x} represents a diagonal matrixwith the nnth element equal to x[n]. The N × N InverseDiscrete Fourier Transform (IDFT) matrix F is defined by

[F]mn = 1√N

e2πmn

N , 0 � m, n � N − 1. E{x} and Var{x}denote the mean and the variance of x.

2. COOPERATIVE OFDMA UPLINKSIGNAL MODEL

In the OFDMA uplink, the total number of subcarriers isN and M nodes access the base station. Each node is allo-

Figure 1. Cooperative transmission with M relays in OFDMAuplink.

cated Nu unique subcarriers, where MNu � N. Complexsymbols modulating the subcarriers may be taken fromphase-shift keying (PSK) or quadrature amplitude modu-lation (QAM).

Cooperative transmission with M relays is shown inFigure 1. In each transmission, each node transmits itsown signal on subcarriers assigned to it and simultane-ously transmits signals for the other nodes (its relays) bymodulating the subcarriers allocated to those nodes withtheir signals; i.e. each node plays two roles—the role ofthe source node and the relay—simultaneously. Coopera-tive transmission takes place in two time slots (see Figure 2).An OFDMA symbol is transmitted per time slot. In the firsttime slot, each mobile node transmits on its subcarriers toall its relays and the base station (node D) and simulta-neously receives the transmissions of the other nodes. Inthe second time slot, each node will send on its subcarriersand re-transmit the received transmissions from the othernodes simultaneously. Node S represents the source nodeand Rk, k ∈ {1, . . . , M}, represents the kth relay, where M

is the total number of relays in a transmission period withM � M − 1. Note that in different transmissions, the totalnumber of relays may be different.

2.1. First time slot

In the first time slot, all mobile nodes, including node S

and the relays, transmit their first data. Let us use xS,1 andxRk,1 (1 � k � M) to represent the first transmit vector ofnode S and node Rk, respectively, where both xS,1 andxRk,1 are Nu × 1 vectors, and the elements of these twovectors, i.e. xS,1[i] and xRk,1[i], are independent and iden-tically distributed (i.i.d.) complex Gaussian RVs. We alsouse Gz to represent the set of indices of all the subcarri-ers allocated to the zth node, where Gk

⋂k �=z Gz = ∅, and⋃

z=S,R1,...,RMGz ⊆ {0, 1, . . . , N − 1}.

The received signals at node D, node S and each relaycan be represented as

Copyright © 2009 John Wiley & Sons, Ltd. Eur. Trans. Telecomms. 2010; 21:224–240DOI: 10.1002/ett

226 Z. ZHANG, C. TELLAMBURA AND R. SCHOBER

Figure 2. Cooperative transmission in a two-time-slot period in OFDMA uplink.

yD,1 = ESDFSHSD�S,1︸︷︷︸VSD,1

xS,1

+M∑

k=1

ERkDFRkHRkD�Rk,1︸︷︷︸

VRkD,1

xRk,1 + wD,1 (1)

yS,1 =M∑

k=1

ERkSFRkHRkS�Rk,1︸︷︷︸VRkS

xRk,1 + wS (2)

yRk,1 = ESRkFSHSRk

�S,1︸︷︷︸VSRk

xS,1

+M∑

l=1,l �=k

ERlRkFRl

HRlRk�Rl,1︸︷︷︸

VRlRk

xRl,1 + wRk

(3)

respectively, where yD,1, yS,1 and yRk,1 are N × 1vectors that represent the received time-domain signalsat node D, node S and Rk, respectively. Furthermore, we

also define Ezk = diag{

1, e( 2πεzk

N

), . . . , e

( 2πεzk (N−1)N

)}with εzk representing the normalised carrier frequencyoffset (normalised to one subcarrier bandwidth) betweennodes z and k. In this paper, we assume that eachεzD, z ∈ {S, R1, . . . , RM}, is an i.i.d. RV with zeromean and variance σ2

ε . We also assume that the inte-ger part of the frequency offset has been correctedand only the residual fractional frequency offset existsand, therefore, σ2

ε � 1. Since εzD = εzk + εkD is

satisfied for each z, k ∈ {S, R1, . . . , RM}, we haveVar{εzD} = σ2

ε and Var{εzk} = Var{εzD − εkD} = 2σ2ε ,

z, k ∈ {S, R1, . . . , RM}. Fz is the N × Nu IDFTmatrix for the zth node and can be generated fromthe N × N IDFT matrix F by deleting all thecolumns with the column indices not belonging toGz. �z,1 = diag{√Pz,1,i : i ∈ Gz, z ∈ {S, R1, · · · , RM}}is an Nu × Nu diagonal matrix with each diagonal entryrepresenting the transmit power of one subcarrier allocatedto node z in the first time slot. In this paper, per-subcarrieradaptive power allocation is not performed, and weassume that �z,1 = PINu for each z and i, where P

represents the transmit power of one subcarrier of eachnode in the first time slot.‡ Hzk = diag{H (i)

zk : i ∈ Gz}with H

(i)zk denoting the channel attenuation between

nodes z and k at the ith subcarrier. Both wz and wD,i

are vectors of additive white Gaussian noise (AWGN)with {wz[m],wD,i[m] : z ∈ {S, R1, . . . , RM}, 0 � m �N − 1, i = (1, 2)} ∼ CN(0, σ2

w).Quasi-static wireless channels and the following assump-

tions are made:

1. The fading gain between each pair of mobile nodes is ani.i.d. RV with H

(i)zk ∼ CN(0, 1) for each k �= z, D.

2. The fading gain between each mobile node and D in theith subcarrier is an i.i.d. RV with H

(i)zD ∼ CN(0,Lu) for

‡ Since it requires the knowledge of CSI and related channel estimationtechniques, adaptive power allocation is not performed. Per-subcarrierpower allocation in non-relaying OFDMA transmission is analysed inReference [18], and it is shown that by using a water-filling per-subcarrierpower allocation scheme, the OFDMA uplink channel capacity can beimproved by about 0.88 bit/subcarrier at low SNR for a frequency offsetof 0.1.



each z, where Lu represents the relative pathloss withLu < 1.§

2.2. Second time slot

In the second time slot, as in Reference [9], the relays canoperate in either the AF or DF mode. Since per-subcarrieradaptive power allocation is not considered, the channelgain between S and Rk can be quantified by using �k =trace{HSRk

HHSRk

}. This gain is used to select the relays ofnode S. Consider a channel power threshold ν > 0, andnode k will act as a relay of S if �k � νNu, 1 � k � M − 1.From Reference [19, p. 41] we know that when Nu is largeenough, �k can be approximated as a central χ2 RV with2Nu degrees of freedom with probability density function(PDF) fk(y) = 1

(Nu−1)!yNu−1e−y. The probability of �k �

νNu is Pν = Pr{�k � νNu} = e−Nuν∑Nu−1

m=0νmNm

u

m! , wherePr{Q} denotes the probability of Q. The probability that thesource node has M out of M − 1 nodes as relays is givenby Pν,M = (M−1

M

)PM

ν (1 − Pν)M−M−1.

2.2.1. AF mode. Relay k is chosen as an active relay if�k � νNu. We assume that M out of M − 1 relays satisfythis requirement, and the received vector at node D is

yAFD,2 = ESDFSHSD�t

S,2︸︷︷︸VSD,2

xS,2

+M∑

k=1

ERkDFRkHRkD�t

Rk,2︸︷︷︸VRkD,2

xRk,2

+M∑

k=1

RkSESDFRkHSD�r

S,2FHRk

yS,1

+M∑

k=1

SRkERkDFSHRkD�r

Rk,2FHS yRk,1

§ When modelling the wireless channel, path loss is usually modelled asLu = dα

zD, where dzD represents the distance between nodes z and D, and2 � α � 6. dzD is some relative distance. Lu accounts for the fact thatthe distance between the relays themselves is smaller than the distancebetween the relays and the destination.

+M∑

k=1

M∑l=1,l �=k

RlRkERkDFRl

HRkD�rRk,2F

HRl

yRk,1

+wD,2 (4)

where xS,2 and xRk,2 represent the second transmitvector of node S and node Rk (1 � k � M), respec-

tively. zk = (θνP + σ2w)−

12 , z ∈ {S, R1, . . . , RM} and k ∈

{R1, . . . , RM} represent the amplification coefficients atnode k when it re-transmits the signal for node z,‖ where

θν = 1 + (Nu!∑Nu−1

m=0νm−NuN

m−Nuu

m! )−1, as derived in Equa-

tion (40) in Appendix II. �tz,2 = diag{(Pt

z,2,i)12 : i ∈ Gz}

and �rz,2 = diag{(Pr

z,2,i)12 : i ∈ Gz} (z ∈ {S, R1, · · · , RM})

represent the power allocation to node z used to transmit itsown signal and to re-transmit signals for the other nodes inthe second time slot, respectively.

We can represent Equation (4) into a more compact for-mat as

yAFD,2 = VSD,2xS,2 +

M∑k=1

VRkD,2xRk,2

+M∑

k=1

RkSESDFRkHSD�r

S,2FHRk

VRkS︸︷︷︸VAF

RkSD,2

xRk,1

+M∑

k=1

RkSESDFRkHSD�r

S,2FHRk

wS︸︷︷︸wSD

+M∑

k=1

SRkERkDFSHRkD�r

Rk,2FHS VSRk︸︷︷︸

VAFSRD,2

xS,1

+M∑

k=1

M∑l=1,l �=k

RlRkERkDFRl

HRkD�rRk,2F

HRlVRlRk︸︷︷︸

VAFRlRkD,2

xRl,1

‖ Since identical powers are allocated to all relays, and per-subcarrier powerallocation is not performed, the amplification coefficients for differentrelays are identical.



+M∑

k=1

SRk

ERkDFSHRkD�rRk,2F

HS +

M∑l=1,l �=k

RlRkERkDFRl

HRkD�rRk,2F

HRl

wRk

︸︷︷︸wRD

+wD,2

= VAFSRD,2xS,1 + VSD,2xS,2︸︷︷︸

Useful signal

+M∑

k=1

VAFRkSD,2xRk,1 +

M∑k=1

M∑l=1,l �=k

VAFRlRkD,2xRl,1 +

M∑k=1

VRkD,2xRk,2︸︷︷︸ηS=Interference to S

+ wSD + wRD + wD,2︸︷︷︸wD,2=Additive noise

(5)

In the second time slot, the total transmit power NuP isshared by the source node and its M relays. By allocatingpower αNuP to transmit its second symbol, the source nodewill use the remaining power (1 − α)NuP to forward signalsfor the other nodes, where 0 < α � 1. Therefore, Pt

z,2,i =αP and Pr

z,2,i = (1−α)PM

, and we have �z,1�Hz,1 = PINu ,

�tz,2�

tHz,2 = αPINu and �r

z,2�rHz,2 = (1−α)P

MINu for each z.

The demodulated source signals at node D are

rAFS,1 = FH

S yD,1 = FHS VSD,1xS,1

+

ξAFS,1︷︸︸︷

FHS

M∑k=1

VRkD,1xRk,1︸︷︷︸µS,1

+FHS wD,1 (6)

and

rAFS,2 = FH

S yAFD,2 = FH

S VAFSRD,2xS,1 + FH

S VSD,2xS,2

+ξAFS,2︷︸︸︷

FHS ηS︸︷︷︸µS,2

+FHS wD,2 (7)

We can combine Equations (6) and (7) into a compact equa-tion as

rAFS =

[rAFS,1

rAFS,2

]=[

FHS VSD,1 ONu

FHS VAF

SRD,2 FHS VSD,2

]︸︷︷︸

AAFS

[xS,1

xS,2

]︸︷︷︸xS

+[

ξAFS,1

ξAFS,2

]︸︷︷︸

ξAFS

(8)

2.2.2. DF mode. In the first time slot, the transmit–receiverelationship of the DF mode is identical to that of the AFmode, as given by Equations (1)–(3). However, in the sec-ond time slot, each DF relay demodulates and decodesbefore retransmission, which we assume to be an error-freeprocess¶. The received vector at node D is

yDFD,2 = ESDFSHSD�t

S,2︸︷︷︸VSD,2

xS,2

+M∑

k=1

ERkDFRkHRkD�t

Rk,2︸︷︷︸VRkD,2

xRk,2

+M∑

k=1

ESDFRkHSD�r

S,2︸︷︷︸VDF

RkSD,2

xRk,1

+M∑

k=1

ERkDFSHRkD�rRk,2︸︷︷︸

VDFSRD,2

xS,1

+M∑

k=1

M∑l=1,l �=k

ERkDFRlHRkD�r

Rk,2︸︷︷︸VDF

RlRkD,2

xRl,1 + wD,2

¶ This condition holds if the transmit rate of S does not exceed the capacityof the S → Rk channels, k = 1, . . . , M. In the transmission of S, we canchoose the rate low enough so that this condition is satisfied. Here, weassume that the relay k with �k � νNu is chosen as an active relay. IfS transmits at a low enough rate, we can always guarantee the correctdecoding in relay k.



= VDFSRD,2xS,1 + VSD,2xS,2︸︷︷︸

Useful signal

+M∑

k=1

VDFRkSD,2xRk,1 +

M∑k=1

M∑l=1,l �=k

VDFRlRkD,2xRl,1 +

M∑k=1

VRkD,2xRk,2︸︷︷︸ηDFS

=Interference to S

+wD,2 (9)

Note that in Equation (9), M out ofM − 1 correct-decodingnodes are chosen as relays of node S in the current trans-mission, and both M and the Rk may change for differenttransmissions.

The demodulated vectors of node S at node D are

rDFS,1 = FH

S yD,1 = FHS VSD,1xS,1

+

ξDFS,1︷︸︸︷

FHS

M∑k=1

VRkD,1xRk,1︸︷︷︸µS,1

+FHS wD,1 (10)

and

rDFS,2 = FH

S yDFD,2 = FH

S VDFSRD,2xS,1 + FH

S VSD,2xS,2

+ξDFS,2︷︸︸︷

FHS ηDF

S︸︷︷︸µS,2

+FHS wD,2 (11)

respectively. We can represent Equations (10) and (11) in acompact equation as

rDFS =

[rDFS,1

rDFS,2

]=[

FHS VSD,1 ONu

FHS VDF

SRD,2 FHS VSD,2

]︸︷︷︸

ADFS

[xS,1

xS,2

]︸︷︷︸xS

+[

ξDFS,1

ξDFS,2

]︸︷︷︸

ξDFS

(12)

3. ERGODIC CHANNEL INFORMATION RATEANALYSIS

This section analyses the ergodic channel information rateof the cooperative relaying schemes.

3.1. AF ergodic information rate

As in Equation [9], for a given M and each given εzk, themutual information of the AF mode is

IAFM

(xS ; rAF

S

∣∣∣εzk,Hzk

)= 1

2log2 det

(I2Nu +

(GAF

S

)− 12 AAF

S

(AAF

S

)H

×(GAF

S

)− H2)

bps/Hz (13)

where

GAFS =

µS,1 + σ2

wINu

µS,2 +[Lu(M+1)(1−α)P

θνP+σ2w

+ 1]σ2

wINu

µS,1 + σ2

wINu

µS,2 +[Lu(M+1)(1−α)P

θνP+σ2w

+ 1]σ2

wINu

H

(14)

µS,1 = FHS

M∑k=1

VRkD,1xRk,1 (15)

and

µS,2 = FHS

M∑k=1

(VAF

RkSD,2 + VRkD,2

)xRk,1

+M∑

l=1,l �=k

VAFRlRkD,2xRl,1

(16)

Since the frequency offset between each pair of nodes is ani.i.d. RV, this offset should be averaged out when derivingthe expectation of IAF

M (xS ; rAFS |εzk,Hzk), so that

IAFM

(xS ; rAF

S

)= 1

2EH,ε

{log2 det

(I2Nu +

(GAF

S

)− 12

× AAFS

(AAF

S

)H (GAF

S

)− H2)}

(17)



where EH,ε is the expectation over the channel attenu-ations and frequency offsets. Since both GAF

S and AAFS

are functions of the frequency offsets, analytical averagingthe frequency offsets in Equation (17) appears intractable.Appendices I and II show that, for i.i.d. frequency offsetswith variance σ2

ε being small enough, the interference canbe approximated as a Gaussian RV, and as N increases,its power depends more on frequency offset variance σ2

ε

rather than on the exact PDF of the frequency offset. WhenN is large enough (e.g. N = 1024), the interference powerbecomes a function of frequency offset variance σ2

ε . If theinterference is approximated as a function of frequency off-set variance σ2

ε and Equation (17) is obtained by averagingthe frequency offsets for the signal part only, the expec-

tation can be simplified considerably. The validity of thisassumption is confirmed by simulation in Section 4.

Define the correlation matrix of ξAFS as

CξAFS

= E{

ξAFS

(ξAFS

)H}

=

E

{ξAFS,1

(ξAFS,1

)H}E

{ξAFS,1

(ξAFS,2

)H}

E

{ξAFS,2

(ξAFS,1

)H}E

{ξAFS,2

(ξAFS,2

)H} (18)

where E{ξAFS,1(ξAF

S,2)H} = FHS

∑Mk=1 E{VRkD,1xRk,1x

HRk,1

VHRkSD,2}FS . Since E{HRkDHH

RkS} = ONu for each k,

we have E{ξAFS,1(ξAF

S,2)H} = ONu , and Equation (18) can be

simplified as CξAFS

= diag{E{ξAFS,1(ξAF

S,1)H},E{ξS,2(ξAFS,2)H}}.

From Appendices I and II, E{ξAFS,1(ξAF

S,1)H} = σ2ξAFS,1

· INu and

E{ξAFS,2(ξAF

S,2)H} = σ2ξAFS,2

· INu , where σ2ξAFS,1

= LuMπ2σ2ε P

3M +σ2

w, σ2ξAFS,2

= 2Luθν(M2−M+1)(1−α)π2σ2ε P2

3M(θνP+σ2w)

+ LuαMπ2σ2ε P

3M +Lu(M+1)(1−α)Pσ2

w

θνP+σ2w

+ σ2w, and then

rAFS = C

− 12

ξAFS

rAFS = C

− 12

ξAFS

AAFS︸︷︷︸

AAFS

xS + C− 1

2

ξAFS

ξAFS︸︷︷︸

ξAFS

(19)

so that Equation (13) can be rewritten as

IAFM

(xS ; rAF

S

) = IAFM

(xS ; rAF

S

)= 1

2log2 det

(I2Nu

+ AAFS

(AAF

S

)H)

bps/Hz

(20)

where

AAFS

(AAF

S

)H =

ZAF11︷︸︸︷

σ−2ξAFS,1

FHS VSD,1VH

SD,1FS

ZAF12︷︸︸︷

σ−1ξAFS,1

σ−1ξAFS,2

FHS VSD,1

(VAF

SRD,2

)HFS

σ−1ξAFS,1

σ−1ξAFS,2

FHS VAF

SRD,2VHSD,1FS︸︷︷︸

ZAF21

σ−2ξS,2

FHS

(VAF

SRD,2

(VAF

SRD,2

)H + VSD,2VHSD,2

)FS︸︷︷︸

ZAF22

(21)

Let λAF(i)11 , λ

AF(i)22,r and λ

AF(i)22,t be the ith eigen-

value of ZAF11 , σ−2

ξAFS,2

FHS VAF

SRD,2

(VAF

SRD,2

)H FS , and

σ−2ξAFS,2

FHS VSD,2VH

SD,2FS , respectively. We can rewrite

det(I2Nu + AAFS (AAF

S )H) as

det

(I2Nu + AAF

S

(AAF

S

)H)

= det(INu + ZAF

22

)× det

(INu + ZAF

11 − ZAF12

(INu + ZAF

22

)−1ZAF

21

)

=∏i∈GS

(1 + λ

AF(i)22,r + λ

AF(i)22,t

)

×∏i∈GS

(1 + λ

AF(i)11 − λ

AF(i)11 λ

AF(i)22,r

1 + λAF(i)22,r + λ

AF(i)22,t

)

=∏i∈GS

(1 + λ

AF(i)11 + λ

AF(i)22,r + λ

AF(i)22,t

(1 + λ

AF(i)11

))(22)



where

λAF(i)11 = P · |H (i)

SD|2 · β(εSD)

σ2ξAFS,1

λAF(i)22,t = αP · |H (i)

SD|2 · β(εSD)

σ2ξAFS,2

β(x) =∣∣∣∣ sin(πx)

N sin(πxN

)

∣∣∣∣2

and

λAF(i)22,r = θν(1 − α)P2∑M

k=1 |H (i)RkD

|2 · β(εSRk+ εRkD)

Mσ2ξAFS,2

(θνP + σ2w)

= θν(1 − α)P2∑Mk=1 |H (i)

RkD|2 · β(εSD)

Mσ2ξAFS,2

(θνP + σ2w)

The ergodic information rate of the proposed cooperativetransmission can be obtained by taking the expectation ofIAF

M (xS ; rAFS |εzk,Hzk) with respect to the channel attenua-

tion as

IAFM = 1

2EH,ε

{log2 det

(I2Nu + AAF

S

(AAF

S

)H)}

= 1

2EH,ε

log2

∏i∈GS

(1 + λ

AF(i)11 + λ

AF(i)22,r

+ λAF(i)22,t

(1 + λ

AF(i)11

))

= 1

2

∑i∈GS

EH,ε

{log2

(1 + λ

AF(i)11 + λ

AF(i)22,r

+ λAF(i)22,t

(1 + λ

AF(i)11

))}bps/Hz (23)

When Nu is large, all subcarrier statistics are identical, andwe can approximate IAF

M as

IAFM

∼= Nu

2EH,ε

{log2

(1 + λ

AF(i)11 + λ

AF(i)22,r

+ λAF(i)22,t

(1 + λ

AF(i)11

))}bps/Hz (24)

In an OFDMA uplink transmission with a total of M nodesaccessing a base station, for a given channel power thresholdν, the expectation of the ergodic information rate is givenby IAF

erg = ∑M−1M=1 Pν,MIAF

M . From Appendix III, we havethe following inequality:

IAFerg

∣∣∣α=1

− IAFerg

∣∣∣0�α<1

> 0 (25)

which means that the maximum IAFerg is obtained at α = 1;

i.e. the conventional transmission (without using a coopera-tive relay) outperforms cooperative transmission in terms ofthe ergodic information rate. This finding can be explainedas follows: in a fast-fading channel (implicitly assumedfor the ergodic information rate analysis), the full chan-nel diversity gain is achieved in the conventional OFDMAuplink transmission, provided that the codes transmittedare long enough. However, in the cooperative transmission,the transmit power of each node should be shared with theM cooperative relays and, therefore, the effective SINR ofeach subcarrier is reduced. In addition, the accumulation ofthe interference and noise in AF relaying also degrades theSINR.

3.2. DF ergodic information rate

The DF channel information rate is different from that ofthe AF mode. Let the transmission rate of node S in the firsttime slot be ρ1. For a given M and assuming that the relaysare able to decode xS,1 correctly, ρ1 should satisfy

ρ1 � ρ∗1 = min

{ρ1,1, . . . , ρ1,M

}(26)

where ρ1,k = log2 det(INu + FHS VSRk

VHSRk

FS) representsthe mutual information between S and Rk. The maximuminformation rate in the first time slot, i.e. ρ1, should notexceed the minimum of {ρ1,1, . . . , ρ1,M} to guarantee suc-cessful decoding in each chosen relay. If Equation (26) issatisfied, we assume that the relays can always decode xS,1correctly.

In the second time slot, the uplink is a typical multiple-access channel (MAC). From References [9, 20], we candefine the transmission rate constraint as

ρ1 � min{

log2 det(INu + FH

S

(VDF

SRD,2

(VDF

SRD,2

)H

+ VSD,1VHSD,1

)FS

), ρ∗

1

}(27a)

ρ2 � log2 det(INu + FH

S VSD,2VHSD,2FS

)(27b)



ρ1 + ρ2 � log2 det

(I2Nu + (GDF

S

)− 12 ADF

S

(ADF

S

)H

× (GDFS

)− H2

)(27c)

where

GDFS =

[µS,1 + σ2

wINu

µS,2 + σ2wINu

][µS,1 + σ2

wINu

µS,2 + σ2wINu

]H

As in the AF mode, here we also approximate the interfer-ence as a Gaussian RV and average out the frequency offsetsin the interference first (the interference is approximated asa function of frequency offset variance σ2

ε only), so that themutual information of the DF mode is given by

IDFM

(xS ; rDF

S

) = 1

2min

{ρ1 + ρ2, log2 det

(I2Nu

+ ADFS

(ADF

S

)H)}

bps/Hz (28)

where

rDFS = C

− 12

ξDFS

rDFS = C

− 12

ξDFS

ADFS︸︷︷︸

ADFS

xS + C− 1

2

ξDFS

ξDFS︸︷︷︸

ξDFS

(29)

with CξDFS

= E{ξDFS (ξDF

S )H} = (LuMπ2σ2ε P

3M + σ2w

)︸︷︷︸

σ2ξDFS

·I2Nu .

Therefore, ADFS (ADF

S )H is

ADFS

(ADF

S

)H =

σ−2ξDFS

FHS VSD,1VH

SD,1FS︸︷︷︸ZDF

11

σ−2ξDFS

FHS VSD,1

(VDF

SRD,2

)HFS︸︷︷︸

ZDF12

σ−2ξDFS

FHS VDF

SRD,2VHSD,1FS︸︷︷︸

ZDF21

σ−2ξDFS

FHS

(VDF

SRD,2

(VDF

SRD,2

)H + VSD,2VHSD,2

)FS︸︷︷︸

ZDF22

(30)

Using λDF(i)11 , λ

DF(i)22,r and λ

DF(i)22,t to represent the ith

eigenvalue of ZDF11 , σ−2

ξDFS

FHS VDF

SRD,2

(VDF

SRD,2

)H FS and

σ−2ξDFS

FHS VSD,2VH

SD,2FS , respectively, we can derive λDF(i)11 ,

λDF(i)22,r and λ

DF(i)22,t as λ

DF(i)11 = P ·|H (i)

SD|2·β(εSD)

σ2ξDFS

, λDF(i)22,t =

αP ·|H (i)SD

|2·β(εSD)

σ2ξDFS

and λDF(i)22,r = (1−α)P

∑M

k=1|H (i)

RkD|2·β(εRkD)

Mσ2ξDFS

.

The ergodic information rate in the DF mode can be repre-sented as

IDFM = 1

2EH,ε

{min

{ρ1 + ρ2,

log2 det(I2Nu + ADF

S

(ADF

S

)H)}}

∼= 1

2EH,ε min

{ρ1 + ρ2, Nu · log2

(1 + λ

DF(i)11

+ λDF(i)22,r + λ

DF(i)22,t

(1 + λ

DF(i)11

))}bps/Hz.

(31)

In an OFDMA uplink transmission with a total of Mnodes accessing a base station, for a given channel powerthreshold ν, the expectation of the ergodic information rateis represented as IDF

erg = ∑M−1M=1 Pν,MIDF

M .

4. NUMERICAL RESULTS

We consider an OFDMA uplink system with a bandwidthof 10 MHz and N = 128/256/1024. A total of 16/64 nodesare assumed to access the base station.

For a given power allocation ratio α, the average ergodicinformation rates for the AF and DF modes, i.e. IAF

erg and

IDFerg, are functions of channel power threshold ν. This power

threshold offers a basic tradeoff when choosing the relays.For large ν, fewer relays are selected, but the averagechannel gain between node S and each chosen relay is

higher. For each (SNR, α, σ2ε ),** there are threshold values

that maximise IAFerg and IDF

erg. Since the maximum ergodicinformation rate achieved by using the optimum ν is thepotential transmission capability of the proposed cooper-ative scheme, the ergodic information rates with respect

** SNR stands for signal-to-noise ratio.



Figure 3. Ergodic information rate as a function of channel power threshold ν.

to the optimum ν should be defined as IAFerg = maxν IAF

erg

and IDFerg = maxν IDF

erg, for the AF and DF modes, respec-

tively. By taking the partial derivative of IAFerg and IDF

erg withrespect to ν and setting the result to zero, the optimum ν

can be found. A closed-form solution of optimum ν appearsintractable, and we use a numerical search.

Figure 3 shows the AF and DF ergodic information ratesas functions of channel power threshold ν for SNR = 20 dBand σ2

ε = 10−3. This figure shows the maximum ergodicinformation rates. For example, with α = 0, a maximumAF ergodic information rate of 31.3 bps/Hz can be achievedfor ν = 1.37. Similarly, the optimum ν that maximises theDF ergodic information rate can also be found. For given(α, σ2

ε , SNR), the optimum ν for the AF and DF modes maybe different. For each α, the power threshold ν is criticalfor the ergodic information rate optimisation. For a small ν,more relays are involved. In this case, although the potentialspatial diversity gain increases, the relays introduce moreinterference and noise, which negates the diversity bene-fits. As ν increases, SINR improves, which concomitantlyincreases the ergodic information rate. However, further

increase of ν may in fact degrade the ergodic informa-tion rate, because fewer relays are chosen. The diminishedspatial diversity gain reduces the ergodic information rate.

The ergodic information rate in each relaying mode ishighly dependent on the channel power threshold ν

(Figure 3). Thus, in the remaining four figures(Figures 4–7), the maximum AF and DF informationrates are compared. The ergodic information rate of theproposed cooperative transmission as a function of powerallocation ratio α is evaluated in Figure 4. As mentionedbefore, we derived the AF and DF ergodic information ratevia the Gaussian approximation of the interference. MonteCarlo simulation of i.i.d. frequency offsets Figure 4 isused to validate this approximation. In our simulation, theergodic AF and DF information rates are calculated basedon Equations (17) and (27), respectively. The numericalresults in Figure 4 show that the Gaussian approximationis sufficiently accurate in both the AF and the DF modes.In real systems, error variances as small as 10−3 can beachieved in each relay after frequency offset correction,although the frequency offsets of different relays are differ-ent and it is impossible to totally compensate for them. In



Figure 4. Ergodic information rate as a function of power allocation ratio α with N = 1024.

Figure 5. Ergodic information rate as a function of power allocation ratio α with N = 128/256.



Figure 6. Ergodic information rate as a function of frequency offset variance σ2ε with α = 0.5/0.9/1.

Figure 7. Ergodic information rate for jointly optimised (ν, α) as a function of frequency offset variance σ2ε .



this case, the deviation between the theoretical analysis andthe simulation result is negligible. Figure 4 also shows thatthe AF mode’s ergodic information rate is a monotonicallyincreasing function of α, but this is not true for the DF mode.The case α = 1 denotes conventional transmission withoutrelaying. The maximum IDF

out is achieved at α = 0.9. Fora given SNR and α < 1, the DF ergodic information rateis always higher than that of the AF mode because of thenoise and interference accumulation in the latter.

We also evaluate the ergodic information rate of the sys-tem as a function of α with N = 128/256 (Figure 5). Thissimulation uses 16 nodes and the other parameters are thesame as in Figure 4. The AF ergodic information rates withN = 128/256 are still monotonically increasing functionsofα, and the DF mode always outperforms the AF mode. Fora given α, a larger N implies a higher ergodic informationrate in each relaying mode.

The ergodic information rate as a function of frequencyoffset variance σ2

ε is illustrated in Figure 6. For each powerallocation ratio α, the AF and DF ergodic information ratesare monotonically decreasing functions of frequency offsetvariance σ2

ε , and the DF mode always outperforms the AFmode. The AF relaying mode does not outperform the con-ventional transmission (without relaying; i.e. α = 1), butthe DF mode can achieve some performance advantage interms of the ergodic information rate when α = 0.9.

By considering the joint optimisation of the ergodic infor-mation rates with respect to the optimum channel powerthreshold ν and power allocation ratio α, the ergodic infor-

mation rates should be defined as IAFerg = maxν,α IAF

erg and

IDFerg = maxν,α IDF

erg, for the AF and DF modes, respectively.Simulation results are shown in Figure 7 for N = 128and 16 users. As in Figure 6, the ergodic informationrate of each mode is always a monotonically decreasingfunction of σ2

ε , and the DF mode always outperforms theAF mode.

5. CONCLUSIONS

The AF and DF ergodic information rate of OFDMA uplinkcooperative transmission were derived. With frequencyoffsets, the AF mode does not outperform conventionaltransmission (i.e. without relaying) in terms of ergodicinformation rate, but the DF mode does. The accumulationof interference and noise in the AF relays, which degradesthe effective SINR, explains the superior performance of theDF mode. However, DF relays require additional process-ing complexity. Part II of this paper shows that significant

gains in terms of outage information rate can be obtainedfor both relay modes.

APPENDIX I: INTERFERENCE-ξAFS,1 ANALYSIS

Define

CξAFS,1

= E{

ξAFS,1

(ξAFS,1

)H}

= FHS

M∑k=1

E{VRkD,1xRk,1x

HRk,1V

HRkD,1

}FS

+FHSE{wD,1wH

D,1

}FS

= FHS

M∑k=1

ERkDFRkE{HRkD�Rk,1xRk,1x

HRk,1�

HRk,1

×HHRkD

}FH

RkEH

RkDFS + σ2

w · INu (32)

Also, define µS,1 = FHS

∑Mk=1 VRkD,1xRk,1; we can repre-

sent the nth entry of µS,1 as

µS,1[n] =M∑

k=1

∑i∈GRk

√PxRk,1[i]H (i)

RkD

sin[π(i − n + εRkD)]

N sin[

π(i−n+εRkD)N

](33)

and then we have[CξAF

S,1

]mn

= E{µ∗S,1 [m] µS,1 [n]

}

= E

M∑k=1

∑i∈GRk

Px∗Rk,1[i]H (i)∗

RkDxRk,1

× [i + m − n]H (i+m−n)RkD

sin2[π(i − n + εRkD)]

N2 sin2[

π(i−n+εRkD)N

]

(34)

where n �= m and [CξAFS,1

]nn = E{|µS,1[n]|2} + σ2w.

By exploiting that E{x∗Rk,1

[p]xRk,1} = 0 for eachp, q �= p and k, we can easily prove that [CξAF

S,1]mn = 0

for each m, n �= m. When εRkD � 1, we havesin[π(i − n + εRkD)] = (−1)i−n sin(πεRkD) ∼= (−1)i−nπ

εRkD and sin[π(i−n+εRkD)

N] ∼= sin[π(i−n)

N], so that



µS,1[n] ∼=M∑

k=1

∑i∈GRk

(−1)i−n√

PxRk,1[i]H (i)RkD

π

N sin[

π(i−n)N

] · εRkD

(35)

By assuming that each εzk is an i.i.d. RV with zero meanand variance σ2

ε , we have

E{|µS,1[n]|2} = π2σ2ε P

M∑k=1

∑i∈GRk

Lu

N2 sin2[

π(i−n)N

] (36)

Note that in OFDMA, the interference of the nth sub-carrier mainly comes from the subcarriers near to n

(i.e. |i − n| � N in Equation (36)), as proved in Ref-erences [21, 22]. When N is large enough, we havesin[π(i−n)

N] = π(i−n)

Nfor each 0 � i � N − 1, and, there-

fore,∑N−1

i=0,i�=n1

N2 sin2[ π(i−n)N

]= ∑N−1

i=0,i �=n1

π2(i−n)2∼= 1

3 .

Note that the subcarriers of each node are allocatedarbitrarily (and are not necessarily contiguous) in thefrequency-domain, and that µS,1[n] is a random functionof M and the subcarrier allocation of each relay. Sinceeach node is allocated Nu subcarriers, from the statisticalperspective, µS,1[n] is proportional to M, and the statisticalcharacter of µS,1[n] for each n is identical. Based on theabove analysis, Equation (36) can be further simplified as

E{|µS,1[n]|2} ∼= LuMπ2σ2ε P

3M (37)

APPENDIX II: INTERFERENCE-ξAFS,2 ANALYSIS

Define

CξAFS,2

= E{

ξAFS,2

(ξAFS,2

)H}

= FHS

M∑k=1

E

{VAF

RkSD,2xRk,1xHRk,1

(VAF

RkSD,2

)H}

FS

+FHS

M∑k=1

M∑l=1,l �=k

E

{VAF

RlRkD,2xRl,1xHRl,1

×(VAF

RlRkD,2

)H}

FS

+FHS

M∑k=1

E{VRkD,2xRk,1x

HRk,1V

HRkD,2

}FS

+ FHSE{wD,2wH

D,2

}FS︸︷︷︸

=[Lu(M+1)(1−α)Pσ2

w

θνP+σ2w

+σ2w

]·INu

(38)

From Appendix I, we know that [CξAFS,2

]mn = 0 for n �= m,

and

[FH

S

M∑k=1

E

{VAF

RkSD,2xRk,1xHRk,1

(VAF

RkSD,2

)H}

FS

]nn

= 2Luθν(1 − α)π2σ2ε P2

3M(θνP + σ2w)

(39a)

FH

S

M∑k=1

M∑l=1,l �=k

E

{VAF

RlRkD,2xRl,1xHRl,1

(VAF

RlRkD,2

)H}

FS

nn

= 2LuθνM(M − 1)(1 − α)π2σ2ε

3M(θνP + σ2w)P−2 (39b)

[FH

S

M∑k=1

E{VRkD,2xRk,1x

HRk,1V

HRkD,2

}FS

]nn

= LuαMπ2σ2ε P

3M (39c)

where

θν = 1

Nu

E {�k|�k � νNu} = 1

Nu

∫ ∞

νNu

y · fk(y)

Pν

dy

= 1 + 1

Nu!∑Nu−1

m=0νm−NuN

m−Nuu

m!

(40)

Therefore,

[CξAF

S,2

]nn

= 2Luθν(M2 − M + 1)(1 − α)π2σ2ε P2

3M(θνP + σ2w)

+ LuαMπ2σ2ε P

3M + Lu(M + 1)(1 − α)Pσ2w

θνP + σ2w

+ σ2w (41)



APPENDIX III: ERGODIC INFORMATIONRATE ANALYSIS

When σ2ε � 1, we can easily prove that σ2

ξAFS,1

< σ2ξAFS,2

. Also,

define λAF(i)11 = P ·β(εSD)

σ2ξAFS,1

, we have λAF(i)11 = |H (i)

SD|2 · λAF(i)11 ,

λAF(i)22,t <

αP ·|H (i)SD

|2·β(εSD)

σ2ξAFS,1

= α|H (i)SD|2 · λ

AF(i)11 = αλ

AF(i)11 and

λAF(i)22,r <

(1−α)∑M

k=1|H (i)

RkD|2

M· λ

AF(i)11 , and, therefore, for each

(M, M, σ2ε , SNR(P/σ2

w)),

IAFerg

∣∣∣α=1

− IAFerg

∣∣∣0�α<1

= Nu

2

M−1∑M=1

Pν,MEH,ε

{log2

(1 + λ

AF(i)11

)2}

− Nu

2

M−1∑M=1

Pν,MEH,ε

{log2

(1 + λ

AF(i)11 + λ

AF(i)22,r

+ λAF(i)22,t

(1 + λ

AF(i)11

)) ∣∣∣0�α<1

}

>Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln(

1 + λAF(i)11

)2}

− Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln((

1 + λAF(i)11

)

×(

1 + αλAF(i)11

)+ (1 − α)λAF(i)

11 + ρλ

)}

= Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln(

1 + λAF(i)11

)2}

−Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ ∞∑n=0

a2n+1λ

2n + 1

}

− Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln((

1 + λAF(i)11

)

×(

1 + αλAF(i)11

)+ (1 − α)λAF(i)

11

)}(42)

where aλ = ρλ

2((1+λAF(i)11 )(1+αλ

AF(i)11 )+(1−α)λAF(i)

11 )+ρλ

with ρλ being defined as ρλ = (1 −α)

(∑M

k=1|H (i)

RkD|2

M· λ

AF(i)11 − λ

AF(i)11

). Evidently, ρλ is

a RV of zero mean, and its PDF, i.e. fρ(x), is an evenfunction of x. For each n � 0, the expectation of a2n+1

λ canbe derived as

EH,ε

{a2n+1λ

}=

+∞∫0

ρ2n+1λ fρ(ρλ)[

2((

1 + λAF(i)11

)(1 + αλ

AF(i)11

)+ (1 − α)λAF(i)

11

)+ ρλ

]2n+1 dρλ

−−∞∫0

|ρλ|2n+1 fρ(ρλ)[2((

1 + λAF(i)11

)(1 + αλ

AF(i)11

)+ (1 − α)λAF(i)

11

)− |ρλ|

]2n+1 dρλ

< 0 (43)

Therefore, Equation (42) can be simplified as

IAFerg

∣∣∣α=1

− IAFerg

∣∣∣0�α<1

>Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln(

1 + λAF(i)11

)2}

− Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln((

1 + λAF(i)11

)

×(

1 + αλAF(i)11

)+ (1 − α)λAF(i)

11

)}

= Nu log2 e

2

M−1∑M=1

Pν,MEH,ε

{ln(

1 + 2λAF(i)11

+(λ

AF(i)11

)2)

− ln

(1 + 2λ

AF(i)11 + α

(λ

AF(i)11

)2)}(44)

For each α < 1, since λAF(i)11 > 0, we always have

α(λAF(i)11 )2 � (λAF(i)

11 )2, and, therefore, ln(1 + 2λAF(i)11 +

(λAF(i)11 )2) − ln(1 + 2λ

AF(i)11 + α(λAF(i)

11 )2) > 0 is satisfiedfor each (εzk,Hzk).



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AUTHORS’ BIOGRAPHIES

Zhongshan Zhang (M’04) received the M.S. degree in computer science and the Ph.D. degree in electrical engineering from theBeijing University of Posts and Telecommunications, Beijing, China, in 2001 and 2004, respectively.

In August 2004, he was an Associate Researcher with DoCoMo Beijing Laboratories, where he was promoted to Researcher inDecember 2005. In February 2006, he joined the University of Alberta, Edmonton, AB, Canada, as a Postdoctoral Fellow. From April2009, he has been a Research Engineer in Alcatel-Lucent Shanghai Bell Co., Ltd., Shanghai, China. His main research interests includestatistical signal processing, synchronization and channel estimation in multiple-input-multiple-output orthogonal frequency-divisionmultiplexing systems, and cooperative communications.

Chintha Tellambura (SM’02) received the B.Sc. degree (with first-class honors) from the University of Moratuwa, Moratuwa, SriLanka, in 1986, the M.Sc. degree in electronics from the University of London, London, U.K., in 1988, and the Ph.D. degree in electricalengineering from the University of Victoria, Victoria, BC, Canada, in 1993.

He was a Postdoctoral Research Fellow with the University of Victoria, from 1993 to 1994 and with the University of Bradford,West Yorkshire, U.K., from 1995 to 1996. From 1997 to 2002, he was with Monash University, Melbourne, Australia. He is currentlya Professor with the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada. His researchinterests include diversity and fading countermeasures, multiple-input-multiple-output systems and space-time coding, and orthogonalfrequency-division multiplexing.

Prof. Tellambura is an Associate Editor for the IEEE Transactions on Communications and an Area Editor for Wireless Commu-nications Systems and Theory of the IEEE Transactions on Wireless Communications. He was the Chair of the CommunicationTheory Symposium at Globecom’05 held in St. Louis, MO.



Robert Schober (M01, SM07) was born in Neuendettelsau, Germany, in 1971. He received the Diplom (Univ.) and the Ph.D. degreesin electrical engineering from the University of Erlangen-Nuermberg in 1997 and 2000, respectively. From May 2001 to April 2002 hewas a Postdoctoral Fellow at the University of Toronto, Canada, sponsored by the German Academic Exchange Service (DAAD). SinceMay 2002 he has been with the University of British Columbia (UBC), Vancouver, Canada, where he is currently an Associate Professorand Canada Research Chair (Tier II) in Wireless Communications. His research interests fall into the broad areas of CommunicationTheory,Wireless Communications, and Statistical Signal Processing.

Dr. Schober received the 2002 Heinz MaierLeibnitz Award of the German Science Foundation (DFG), the 2004 Innovations Awardof the Vodafone Foundation for Research in Mobile Communications, the 2006 UBC Killam Research Prize, and the 2007 WilhelmFriedrich Bessel Research Award of the Alexander von Humboldt Foundation. In addition, he received best paper awards from theGerman Information Technology Society (ITG), the European Association for Signal, Speech and Image Processing (EURASIP), IEEEICUWB 2006, the International Zurich Seminar on Broadband Communications, and European Wireless 2000. Dr. Schober is also theArea Editor for Modulation and Signal Design for the IEEE Transactions on Communications.


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