Power Allocation for OFDM-Based Cooperative Relay Systems

JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 10, NO. 2, JUNE2008 1

Power Allocation for OFDM-Based Cooperative RelaySystems

Victor K. Y. Wu, Ye (Geoffrey) Li, Marilynn P. Wylie-Green, Tony Reid, and Peter S. S. Wang

Abstract: Cooperative relays can provide spatial diversity and im-prove performance of wireless communications. In this paper,we study subcarrier power allocation at the relays for orthogonalfrequency division multiplexing (OFDM)-based wireless systems.For cooperative relay withamplify-and-forward (AF) and decode-and-forward (DF) algorithms, we investigate the impact of powerallocation to the mutual information between the source anddes-tination. From our simulation results on word-error-rate (WER)performance, we find that the DF algorithm with power allocationprovides better performance than that of AF algorithm in a singlepath relay network because the former is able to eliminate chan-nel noise at each relay. For the multiple path relay network,how-ever, the network structure is already resistant to noise and channeldistortion, and AF approach is a more attractive choice due to itslower complexity.

Index Terms: Cooperative diversity, cooperative relay, power allo-cation.

I. INTRODUCTION

Recently,relays are being exploited to improve performancein wireless communications systems. The relays are a networkof transceiver nodes between the transmitter and receiver that fa-cilitate the transfer of information. This type of scheme isknownascooperation or cooperative communications in the literaturebecause the relay network is cooperating with the transmitterand receiver to improve performance. One application exampleof such technologies is the MIT-initiated One Laptop per Child(OLPC) project [1], which aims to provide affordable laptopsequipped with meshed networking functionality to childreninthe developing world. Since cellular and Internet connectivityis sparse and sporadic in these regions, such laptops can coop-erate to make the best use of available bandwidth. In this paper,we restrict ourselves to a single path relay network and a mul-tiple path relay network in the context of orthogonal frequencydivision multiplexing (OFDM) systems with power allocation.

The authors in [2]–[4] have provided several physical layerrelay algorithms. These includeamplify-and-forward (AF) anddecode-and-forward (DF). In AF, a node amplifies its receivedsymbols, subject to a power constraint, before forwarding themto the next node. This algorithm is obviously with low com-plexity. In DF, a node fully decodes the received symbols,re-encodes them and then forwards them. In other words, thisscheme attempts to eliminate channel distortion and noise at

Manuscript received November 7, 2007.Wu and Li are with the School of Electrical and Computer Engineering, Geor-

gia Institute of Technology, Atlanta, Georgia, USA, email:[email protected],[email protected].

Green, Reid, and Wang are with the Nokia Siemens Networks, Dallas, Texas,USA, email:{marilynn.green, tony.reid, peter.wang}@nsn.com.

each node by means of the redundancy of error-correct coding.The authors in [5] and [6] have investigated cooperation for

a single path of relays connected in series. The motivation forthis network structure is that broader wireless coverage can beachieved while still maintaining a low power constraint at thetransmitter.Analog relaying anddigital relaying are consideredas two possible relay algorithms. These are equivalent to the AFand DF algorithms, respectively. Each node has a certain trans-mit power limit. The outage probability is then minimized byallocating power among the relay network under these powerconstraints. This power allocation accounts for the channel con-ditions in the network in order to achieve the optimal outageprobability. Simulations indicate that2 dB of total power canbe saved for 5 relays by using optimal power allocation insteadof uniform power allocation. This is for the DF case. However,at high signal-to-noise ratio (SNR) values, the DF and the AFcases are almost the same.

The authors in [7] have investigated cooperation for multi-ple paths of relays connected in parallel. In the conventionalscheme, all relays use AF scheme. This is calledall-participateAF (AP-AF). The authors also consider an algorithm where onlyone relay is selected in the transmission to maximize the mutualinformation. This is calledselection AF (S-AF). S-AF selectsthe relay which results in the maximum mutual information be-tween transmitter and receiver. Simulations of outage probabil-ity indicate that5 dB of SNR can be saved for 3 relays by usingS-AF instead of AP-AF. The authors in [8] derive symbol errorprobabilities for multiple paths of relays.

In this paper, we continue to investigate the series and parallelcooperative relay networks using OFDM signals. We considerasingle path relay network and a multiple path relay network.Us-ing the AF relay algorithm, we derive the input-output relationsand the mutual informations for both networks. Using a powerconstraint at each relay, we consider two relay power allocationschemes: Constant gain allocation and equal power allocation.Using the DF relay algorithm, we derive input-output relationsfor both networks. We also compareword-error-rates (WERs)for the two networks using the AF and DF relay algorithms. Therest of this paper is organized as follows. We study power allo-cation for the single path relay network in [5], [6] and the multi-ple path relay network in [7] in Sections II and III, respectively.Finally, Section IV concludes the paper and provides futurere-search directions.

II. SINGLE PATH RELAY NETWORK

In this section, we consider the single path relay network. Wefirst study the impact of power allocation to the mutual infor-mation for the AF and the DF relay networks, respectively, andthen present their WER performance from computer simulation.

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2 JOURNAL OF COMMUNICATIONS AND NETWORKS, VOL. 10, NO. 2, JUNE2008

r0

r1

rm

rm+1n

(0)k

n(m−1)k

n(m)k

h(0)k

h(1)k

h(m−1)k

h(m)k

Transmitter

Receiver

Fig. 1. Single path relay network.

A. Amplify-and-Forward

Fig. 1 shows the single path relay network. In the figure,r0

is the transmitter,rm+1 is the receiver, andr1, · · ·, rm aremrelay nodes connected in series forming a single path link be-tween the transmitter and receiver. The relays perform AF re-laying. We assume that OFDM withN subcarriers is used in thesystem.h(0)

k , · · ·, h(m)k are the complex subchannel gains at the

kth subcarrier in the link, fork = 1, · · ·, N . n(0)k , · · ·, n

(m)k are

the corresponding noises, which are assumed to be mutually in-dependent and circular symmetric complex Gaussians all withzero mean and varianceN0B/N , whereN0 is the power spec-tral density of the underlying continuous time noise process andB is the OFDM bandwidth of the system. Letp

(0)k = Ptot/N be

the transmit power on thekth subcarrier, wherePtot is the net

transmitter power and√

p(l)k be the amplifying gain used in the

AF algorithm at thelth relay, forl = 1, · · ·, m. Thekth receive

symbol atrl is amplified by√

p(l)k before it is forwarded to the

next node. Letx(0)k be thekth transmit symbol with zero mean

and unit variance,yk be thekth receive symbol at the receiver,andx

(l)k be thekth receive symbol at thelth relay. Note thatx(l)

k

is also thekth transmit symbol at thelth relay.Using Fig. 1, the input-output relation at thelth relay is

x(l)k =

(

l−1∏

i=0

h(i)k

√

p(i)k

)

x(0)k +

l−1∑

j=0

l−1∏

i=j+1

h(i)k

√

p(i)k

n(j)k .

(1)

The input-output relation at the receiver is

yk =

(

m∏

i=0

h(i)k

√

p(i)k

)

x(0)k +

m∑

j=0

m∏

i=j+1

h(i)k

√

p(i)k

n(j)k .

(2)

Denote

hk =

m∏

i=0

h(i)k

√

p(i)k , γ

(j)k =

m∏

i=j+1

h(i)k

√

p(i)k , (3)

and

wk =

m∑

l=0

γ(l)k n

(l)k . (4)

Then, (2) can be written as

yk = hkxk + wk. (5)

Now, consider the variance ofwk. Using (3) and (4), we have

Rwkwk= E [wkw∗

k]

=N0B

N

m∑

j=0

m∏

i=j+1

b(i)k p

(i)k

(6)

whereE [·] is the expectation operator,(·)∗ is the complex con-

jugate operator for a scalar, andb(i)k =

∣

∣

∣h(i)k

∣

∣

∣

2

, for i = 0, · · ·, m.

Rwkwkis positive for a nonzeroN0. We define a normalized

version of the system in (5)

yk = hkxk + wk (7)

where yk = yk/√

Rwkwk, hk = hk/

√

Rwkwk, and wk =

wk/√

Rwkwk. The variances ofwk andyk are

E [wkw∗k] = 1 (8)

and

E [yky∗k] =

1

Rwkwk

(

m∏

i=0

b(i)k p

(i)k

)

+ 1, (9)

respectively. The cross terms do not appear in (9) becausehk,wk, andxk are mutually independent. Note that the normalizedsystem has unit variance noise.

A.1 Mutual Information

To derive the mutual information, note that the differential en-tropy of a circular symmetric complex Gaussian vector,v, withcovariance matrix,K, is h (v) = log2 det (πeK) [9]. When thecircular symmetric complex Gaussian is a scalar,v, the differ-ential entropy ish (v) = log2

(

πeσ2v

)

, whereσ2v is the variance

of v. Let Ik be the mutual information between the transmitterand receiver on thekth subcarrier

Ik = h (yk) − h (wk)

= log2

[

1

Rwkwk

(

m∏

i=0

b(i)k p

(i)k

)

+ 1

]

. (10)

The total mutual information between the transmitter and re-ceiver,I, is the sum of allIk divided byN . That is, after sub-stituting (6) into (10), we have

I =1

N

N∑

k=1

log2

1 + SNR

b(0)k

(

∏m

i=1 b(i)k p

(i)k

)

∑m

j=0

(

∏m

i=j+1 b(i)k p

(i)k

)

(11)

where SNR= Ptot/N0B.

A.2 Relay Power Allocation

We assume that the net transmit power at the transmitter andat each each relay isPtot, that is,

N∑

k=1

E

{

∣

∣

∣

∣

√

p(l)k x

(l)k

∣

∣

∣

∣

2}

= Ptot. (12)

WU et al.: POWER ALLOCATION FOR ODFM-BASED COOPERATIVE DIVERSITY RELAY SYSTEMS 3

At the transmitter, we assume a uniform power distribution,thatis, p(0)

k = Ptot/N . To derive the power constraint at each relay,substitute (1) into (12) to arrive at

N∑

k=1

p(l)k

N

b(0)k

(

l−1∏

i=1

b(i)k p

(i)k

)

+1

SNR

l−1∑

j=0

l−1∏

i=j+1

b(i)k p

(i)k

= 1.

(13)

Note that (13) is defined recursively. The power constraint forp(l)k depends onp(1)

k , · · ·, p(l−1)k . p

(1)k is the base case in the re-

cursion, which follows from (13), whenl = 1.One power allocation at thelth relay is to setp(l)

k constant

for all subcarriers. This results in movingp(l)k in (13) out of the

summation because it is no longer a function ofk

p(l)k,ct = p

(l)ct =

NSNRN∑

k=1

SNRb(0)k

(

l−1∏

i=1

b(i)k p

(i)ct

)

+

l−1∑

j=0

l−1∏

i=j+1

b(i)k p

(i)ct

. (14)

We call thisconstant gain allocation (CT). This is in fact the AFscheme as defined in [2], where a receive symbol is multipliedby a constant gain to satisfy a power constraint. In our context,this means that every subcarrier is multiplied by the same gain,p(l)ct . Note that this power allocation does not require each relay

to have any channel state information (CSI). That is, we do notactually need to use (14). We can use (12) directly to solve forp(l)ct .

A second power allocation is to choosep(l)k such that every

subcarrier transmits the same power at thelth relay. That is,

(12) becomesE{∣

∣

√

p(l)k,eqx

(l)k

∣

∣

2}= Ptot/N , for k = 1, · · ·, N .

This is equivalent to setting every summand on the left hand sideof (13) to1/N . We then have

p(l)k,eq =

SNR

SNRb(0)k

(

l−1∏

i=1

b(i)k p

(i)k,eq

)

+

l−1∑

j=0

l−1∏

i=j+1

b(i)k p

(i)k,eq

. (15)

We call thisequal power allocation (EQ). Note that this powerallocation does require each relay to have the CSI of its upstreamchannels.

B. Decode-and-Forward

In DF, each relay fully recovers the information bits (withpossible errors) after receiving an OFDM symbol. It then con-verts the information bits back into an OFDM symbol and thentransmits it. The transmitter and all the relays transmit with thesame uniform power distribution. That is,

p(0)k = p

(l)k =

Ptot

N(16)

for k = 1, · · ·, N and forl = 1, · · ·, m.Let x

(0)k be thekth transmit symbol from the transmitter and

x(l)k be thekth transmit symbol from thelth relay, all with with

0 3 6 9 12 15 18 21 2410

−2

10−1

100

WE

R

SNR (dB)

Hard, AF, CT

Hard, AF, EQ

Hard, DF

Soft, AF, CT

Soft, AF, EQ

Soft, DF

(a)

0 3 6 9 12 15 18 21 2410

−2

10−1

100

WE

R

SNR (dB)

Hard, AF, CT

Hard, AF, EQ

Hard, DF

Soft, AF, CT

Soft, AF, EQ

Soft, DF

(b)

Fig. 2. WERs in a single path relay network with TU channels using AFand DF for N = 128: (a) m = 2 and (b) m = 4.

zero mean and unit variance. Lety(m+1)k be thekth receive

symbol at the receiver andy(l)k be thekth receive symbol at the

lth relay. Using Fig. 1, the input-ouput relation at thelth relay is

y(l)k = h

(l−1)k

√

Ptot

Nx

(l−1)k + n

(l−1)k . (17)


y(m+1)k = h

(m)k

√

Ptot

Nx

(m)k + n

(m)k . (18)

C. Simulations

We simulate WERs versus SNR for both the AF and DF cases.At the transmitter (and at the transmitter structure of a relayusing DF), each information word contains 83 bits. We use arate1/3 convolutional encoder with generator sequences[111],[111], and[110] to encode the information word into a 255-bitcodeword. A zero bit is padded at the end to make 256 bits. Thebits are then interleaved and modulated ontoN = 128 QPSK


subcarriers to form one OFDM symbol. At the receiver (and atthe receiver structure of a relay using DF), the codeword is re-covered (with possible errors) using a matched filter and dein-terleaving. A Viterbi decoder is used to decode the codeword.Both hard decisions and soft decisions are used.

We consider them = 2 and4 relays cases. We assume thatall distances between any two adjacent transceiver nodes are thesame. Therefore, all path loss effects are normalized to 0 dB.Shadowing is assumed to be log-normally distributed. That is,the received power gain due to shadowing in dB is a zero-meanGaussian with variance of 8 dB, which is typical for cellularlandmobile applications [10]. We model frequency selective fadingas Typical Urban (TU) channels [10]. We use an OFDM band-width of 800 kHz divided intoN = 128 equal blocks. Maintain-ing OFDM orthogonality, this translates into an OFDM sym-bol period ofTs = 160 µs. The simulation results are shownin Fig. 2.

As shown in the plots, there are significant error rate perfor-mance gains when using DF instead of AF. The gains are evenlarger when we increase the distance between the transmitterand receiver (and thus, add more relays). The AF error ratessuffer because more channel distortion and noise enter the sys-tem. The DF error rates suffer only slightly because noise andchannel distortion are eliminated at each relay. This results inthe large performance gains form = 4. In terms of power al-location when using AF, CT is the preferable choice since EQrequires CSI and only results in small performance gains overCT. As expected, soft decisions give better performance thanhard decisions in Viterbi decoding.

III. MULTIPLE PATH RELAY NETWORK

In this section, we consider a multiple path relay network,following the same structure as Section II.

A. Amplify-and-Forward

Fig. 3 shows the multiple path relay network. In the figure,r0 is the transmitter,rm+1 is the receiver, andr1, · · ·, rm aremrelay nodes connected in parallel forming a multiple path linkbetween the transmitter and receiver. The relays perform AFre-laying. We assume that OFDM withN subcarriers is used inthe system.h(0|1)

k , · · ·, h(0|m)k , h

(1|m+1)k , · · ·, h

(m|m+1)k are the

complex subchannel gains at thekth subcarrier in the link, fork = 1, · · ·, N . n

(0|1)k , · · ·, n

(0|m)k , n

(1|m+1)k , · · ·, n

(m|m+1)k are

the corresponding noises, which are assumed to be mutually in-dependent, zero-mean, circular symmetric complex Gaussiansall with varianceN0B/N , whereN0 is the power spectral den-sity of the underlying continuous time noise process andB isthe OFDM bandwidth of the system. Letp

(0)k = Ptot/N be the

transmitter power on thekth subcarrier, wherePtot is the net

transmitter power and√

p(l)k be the amplifying gain used in the

AF algorithm at thelth relay, forl = 1, · · ·, m. Thekth receive

symbol atrl is amplified by√

p(l)k before it is forwarded to the

next node. Letxk be thekth transmit symbol with zero meanand unit variance andy(l)

k be thekth receive symbol from thelthpath at the receiver.

r0

r1

rm

rm+1

n(0 1)k

n(0 m)k

n(1 m+1)k

n(m m+1)k

h(0 1)k

h(0 m)k

h(1 m+1)k

h(m m+1)k

Transmitter Receiver

|

|

|

|

|

| |

|

Fig. 3. Multiple path relay network.

Using Fig. 3, the input-output relation for thelth path is

y(l)k =

(

h(0|l)k h

(l|m+1)k

√

p(0)k

√

p(l)k

)

xk +

h(l|m+1)k

√

p(l)k n

(0|l)k + n

(l|m+1)k . (19)

Denote

yk =[

y(1)k · · · y

(m)k

]T

, (20)

hk =

h(0|1)k h

(1|m+1)k

√

p(0)k

√

p(1)k

...

h(0|m)k h

(m|m+1)k

√

p(0)k

√

p(m)k

, (21)

Γk =

h(1|m+1)k

√

p(1)k 0

. . . Im×m

0 h(m|m+1)k

√

p(m)k

,

(22)

nk =

n(0|1)k...

n(0|m)k

n(1|m+1)k

...

n(m|m+1)k

, (23)

and

wk = Γknk. (24)

Then, (19), for alll = 1, · · ·, m, can be written as

yk = hkxk + wk. (25)

The large boldface zeros in (22) represent zero values in theoffdiagonal entries in the leftm × m submatrix ofΓk.

Now, consider the covariance ofwk. Using (21) to (24), wehave

Rwkwk=

N0B

N

b(1|m+1)k p

(1)k + 1 0

. . .

0 b(m|m+1)k p

(m)k + 1

(26)


whereb(i|j)k =

∣

∣h(i|j)k

∣

∣

2, for i = 0, · · ·, m, for j = 1, · · ·, m + 1,

andi 6= j. Since the diagonal entries ofRwkwkare never zero,

R−1wkwk

andR− 1

2

wkwkare well defined, whereR

− 1

2

wkwkR

− 1

2

wkwk=

R−1wkwk

. Also, if we defineRwkwkasR

1

2

wkwkR

1

2

wkwk= Rwkwk

,

thenR− 1

2

wkwkR

1

2

wkwk= R

1

2

wkwkR

− 1

2

wkwk= I. We define a normal-

ized version of the system in (25)

yk = hkxk + wk (27)

where yk = R− 1

2

wkwkyk, hk = R

− 1

2

wkwkhk, and wk =

R− 1

2

wkwkwk. The covariance matrices ofwk andyk are

E[

wkwHk

]

= I (28)

and

E[

ykyHk

]

= hkhHk + I, (29)

respectively. The cross terms do not appear in (29) becausehk,wk andxk are mutually independent. Note that the normalizedsystem has identity covariance noise.

A.1 Mutual Information

Let Ik be the mutual information between the transmitter andreceiver on thekth subcarrier

Ik = h (yk) − h (wk)

= log2

(

1 + hHk R−1

wkwkhk

)

. (30)

The total mutual information between the transmitter and re-ceiver,I, is the sum of allIk divided byN . That is, after sub-stituting (21) and (26) into (30), we have

I =1

N

N∑

k=1

log2

[

1 + SNRm∑

i=1

(

b(0|i)k b

(i|m+1)k p

(i)k

b(i|m+1)k p

(i)k + 1

)]

. (31)

A.2 Relay Power Allocation

We assume that the net transmit power at the transmitter andat each each relay isPtot, as in (12). At the transmitter, weassume a uniform power distribution, that is,p

(0)k = Ptot/N .

To derive the power constraint at each relay and thus, possiblepower allocations, we use a derivation similar to the one in Sec-tion II-A to arrive at

N∑

k=1

p(l)k

N

(

b(0|l)k +

1

SNR

)

= 1. (32)

CT in this case is

p(l)k,ct = p

(l)ct =

NSNRN∑

k=1

(

SNRb(0)k + 1

)

. (33)

Again, this power allocation does not require each relay to haveany channel state information (CSI). Thelth relay only has to

multiply its entire OFDM receive symbol by a constant,√

p(l)ct ,

such that the total transmit power isPtot, similar to constantgain allocation in Section II-A.

Equal power allocation (EQ) in this case is

p(l)k,eq =

SNR

SNRb(0|l)k + 1

. (34)

Note that this power allocation does require each relay to havethe CSI of its upstream channel.

B. Decode-and-Forward

In DF, each relay fully recovers the information bits (withpossible errors) after receiving an OFDM symbol. It then con-verts the information bits back into an OFDM symbol and thentransmits it. The transmitter and all the relays transmit with thesame uniform power distribution. That is,

p(0)k = p

(l)k =

Ptot

N(35)

for k = 1, · · ·, N and forl = 1, · · ·, m.Let x

(0)k be thekth transmit symbol from the transmitter and

x(l)k be thekth transmit symbol from thelth relay, all with with

zero mean and unit variance. Lety(m+1)k be thekth receive sym-

bol at the receiver andy(l)k be thekth receive symbol at thelth

relay. Using Fig. 3, the input-ouput relation at thelth relay is

y(l)k = h

(0|l)k

√

Ptot

Nx

(0)k + n

(0|l)k . (36)


y(m+1)k =

m∑

i=1

(

h(i|m+1)k

√

Ptot

Nx

(i)k + n

(i|m+1)k

)

. (37)

Note that in this situation, there arem (modified in gen-eral) copies of the originalkth transmit symbolx(0)

k , namely,

x(1)k , · · ·, x

(m)k . Therefore, the receiver has to assume (incor-

rectly in general) that allm relays perform perfect recovery ofthe information bits so thatx(l)

k = x(0)k . That is, the receiver as-

sumes thekth receive symbol is

y(m+1)k =

(

m∑

i=1

h(i|m+1)k

√

Ptot

N

)

x(0)k +

m∑

i=1

n(i|m+1)k . (38)

This allows the receiver to use a filter that is matched tom∑

i=1

h(i|m+1)k .

C. Simulations

We simulate WERs versus SNR for both the AF and DF cases.We use exactly the same configuration in Section II-C. The sim-ulation results are shown in Fig. 4.

The performance gains resulting from using DF instead ofAF diminish as we add more paths between the transmitter andreceiver (and thus, add more relays). This is because form = 4


0 3 6 9 12 15 18 21 2410

−2

10−1

100

WE

R

SNR (dB)

Hard, AF, CT

Hard, AF, EQ

Hard, DF

Soft, AF, CT

Soft, AF, EQ

Soft, DF

(a)

0 3 6 9 12 15 18 21 2410

−2

10−1

100

WE

R

SNR (dB)

hard, AF, CT

hard, AF, EQ

hard, DF

soft, AF, CT

soft, AF, EQ

soft, DF

0 3 6 9 12 15 18 21 2410

−2

10−1

100

WE

R

SNR (dB)

Hard, AF, CT

Hard, AF, EQ

Hard, DF

Soft, AF, CT

Soft, AF, EQ

Soft, DF

(b)

Fig. 4. WERs in a multiple path relay network with TU channels usingAF and DF for N = 128: (a) m = 2 and (b) m = 4.

relays and thus, for 4 paths, the system is already resistanttonoise and channel distortion. Therefore, DF cannot provideanymore significant improvement over AF. In such a situation, AFmight be a more attractive choice due to its lower complexity. Interms of power allocation when using AF, CT is the preferablechoice because it gives better performance than EQ and does notrequire CSI. As expected, soft decisions give better performancethan hard decisions in Viterbi decoding.

IV. CONLCUSIONS

In this paper, we exploit cooperative relays by studying twosubcarrier power allocation schemes as well as the system mu-tual information in OFDM-based wireless networks. WER sim-ulations indicate that the DF relay algorithm provides better per-formance than that of AF in a single path relay network becausethe former is able to eliminate channel noise at each relay. Forthe multiple path relay network, however, the network structureis already resistant to noise and channel distortion, and AFismore attractive due to its lower complexity.

Future research includes investigating additional relay algo-

rithms, such as hybrid schemes. For example, depending on thechannel conditions, a relay can AF, DF, or even just discard sub-carrier symbols. This in turn leads to more possibilities for relaypower allocation. In this paper, we only investigate the singlepath relay network and the multiple path relay network. Othergeneral relay networks need to be considered in the context ofOFDM as well. This will lend more insight into developing ageneral theoretical framework for OFDM in cooperative relaynetworks.

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Victor K. Y. Wu received his B.A.Sc. in 2005, fromthe Division of Engineering Science at the Universityof Toronto, Toronto and his M.S. in 2006, from theSchool of Electrical and Computer Engineering at theGeorgia Institute of Technology, Atlanta. He is cur-rently pursuing a Ph.D. from the Department of Elec-trical and Computer Engineering at the University ofIllinois at Urbana-Champaign. His research interestsare wireless networks and RFID systems.

Ye (Geoffrey) Li received his B.S.E. and M.S.E. de-grees in 1983 and 1986, respectively, from the De-partment of Wireless Engineering, Nanjing Instituteof Technology, Nanjing, China, and his Ph.D. degreein 1994 from the Department of Electrical Engineer-ing, Auburn University, Alabama. He was a teachingassistant and then a lecturer with Southeast Univer-sity, Nanjing, China from 1986 to 1991, a research andteaching assistant with Auburn University, Alabamafrom 1991 to 1994, and a post-doctoral research asso-ciate with the University of Maryland at College Park,

Maryland from 1994 to 1996. He was with AT&T Labs—Research atRed Bank,New Jersey as a senior and then a principal technical staff member from 1996to 2000. Since 2000, he has been with the School of Electricaland ComputerEngineering at Georgia Institute of Technology as an associate and then a fullprofessor. He is also holding a visiting chair professor position at the Universityof Electronic Science and Technology of China since March 2006. His generalresearch interests include statistical signal processingand telecommunications,with emphasis on OFDM and MIMO techniques, cross-layer optimization, andsignal processing issues in cognitive radios. In these areas, he has published over


100 papers in refereed journals or conferences and filed about 20 patents. Healso has two books, entitled, Blind Equalization and Identification (co-authoredwith Z. Ding, published by Mercel Dekker, Inc. in 2000) and OFDM for Wire-less Communications (co-authored with G. Stüber, published by Springer in2006). He is active in professional societies. He once served or is currentlyserving as an editor, a member of editorial board, and a guesteditor for 6 techni-cal journals. He organized and chaired many international conferences, includ-ing technical program vice-chair of the IEEE 2003 International Conference onCommunications. He has been awarded an IEEE fellow for his contributions tosignal processing for wireless communications in 2005.

Marilynn P. Wylie-Green received the B.S. andM.S.E. degrees in electrical engineering from Tem-ple University in 1989 and 1991, respectively and theM.S.E.E. and Ph.D. degrees in electrical engineeringfrom the University of Pennsylvania in 1993 and 1995,respectively. In 1995, she worked at the Wireless In-formation Laboratory (WINLAB) of Rutgers Univer-sity on the research topic of mobile location estima-tion. In 1997, she joined the Nokia Research Centerwhere she became involved with various aspects of ad-vanced physical layer design for several wireless sys-

tems, including GSM, W-CDMA, UWB, and WiMAX. In 2007, she transitionedinto the Research and Technology arm of Nokia Siemens Networks. She is theauthor of approximately 45 international publications and26 granted/pendingpatents. She is a senior member of the IEEE.

She is a member of several national honor societies including Eta KappaNu National Engineering Honor Society, Golden Key NationalHonor Society,Alpha Lambda Delta National Honor Society, and she is a former recipient ofthe National Science Foundation Fellowship for graduate study. Her current re-search interests include statistical signal processing, optimized transceiver de-sign and cross-layer optimization.

Anthony Reid received his B.S.E.E. (Cum Laude)from Rensselaer Polytechnic Institute, M.S.E.E. fromStanford University and Ph.D. from Southern MethodistUniversity (SMU). He has over 3 decades of indus-try experience in the telecommunications and militarydefense arenas. He has worked in the telecomm indus-try at Bell Labs, Nortel Networks and Nokia ResearchCenter (NRC) and in the defense industry at SandiaLaboratories, TI, and Raytheon Company. Most re-cently he is an Engineering Fellow at Raytheon work-ing in the areas of algorithms and systems for Space

and Airborne Systems. As a Principal Scientist at NRC his work covered design,research and standardization of physical layer for wireless mobile systems (e.g.,WiMAX, WLAN, 4G, and GSM/EDGE). He is senior member of IEEE. He hasover 20 publications and 25 granted/pending patents. His research interests arein mobile wireless communications and also applied optimalestimation theoryand statistical signal processing.

Peter S. S. Wangreceived his M.S.E. and Ph.D. de-grees in 1986 and 1991, respectively, from the Depart-ment of Electrical Engineering Department at the Uni-versity of Texas at Arlington, Texas. He was a visitingassistant professor with University of Texas at Arling-ton from 1991 to 1994. He was a staff engineer withMotorola Research Lab. in Texas from 1994 to 1998.He was a senior research scientist at Nokia ResearchCenter in Texas from 1998 to 2006. Since 2006, he hasbeen work with Nokia Siemens Networks in Texas.His work covers wireless mobile location services, RF

channel modeling, and wireless communication systems. Hisresearch interestsare mobile wireless communications and diffractive optics.

Power Allocation for OFDM-Based Cooperative Relay Systems

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