An Opportunistic Subcarrier Allocation Algorithm

based on Cooperative Coefficient for

OFDM Relaying SystemsHamed Rasouli and Alagan Anpalagan

WINCORE Lab, Ryerson University, Toronto, Canada

Abstract— The downlink subcarrier allocation in a cooperative

multiuser system with an amplify-and-forward relaying is studied

for OFDM systems. We use the cooperation coefficient (Γ) from

the literature as a basis for subcarrier allocation. Mean of the

coefficient is first derived for Rayleigh faded channel. Then, a

well known subcarrier allocation algorithm namely Max-Min is

modified to make use of Γ. In this algorithm, the base station (BS)

allocates the subcarriers to the users based on the combination of

the direct and weighted indirect subcarrier gains. How to weigh

the indirect path depends on the amount of information about Γ

available at BS. Three different scenarios, each with varying level

of implementation complexity, are considered: (a) knowledge of

the instantaneous Γ at BS, (b) knowledge of the mean of Γ at

BS, and (c) an estimate of the mean of Γ at BS. Finally, the

performance of the Γ-modified Max-Min algorithm is evaluated

for the three scenarios using Monte-Carlo simulation. It is shown

that (i) the proposed algorithm outperforms the non-cooperative

counterpart in terms of total throughput, (ii) the throughput gain

moderates with larger group size showing the group diversity

behavior in opportunistic communication and (iii) using the mean

of the coefficient, instead of instantaneous coefficient, in cooperative

subcarrier allocation provides comparable performance in Rayleigh

faded channel environment, giving implementation advantage to the

mean-based implementation of the Γ−modified Max-Min algorithm.

Index Terms— cooperative system, subcarrier allocation, oppor-

tunistic transmission, OFDM, cooperation coefficient, amplify-and-

forward relaying

I. INTRODUCTION

The random fading nature of radio signals has been suc-

cessfully exploited to develop new diversity techniques that

improve the robust performance of wireless systems. Increasing

the diversity order of the system can be achieved by transmitting

the signal over independent fading paths. Cooperative diversity

is a technique [1], [2] that uses other relaying terminals to

achieve diversity gain. Using nearby mobile users for relaying

This work was supported in part by a grant from National Science and

Engineering Research Council (NSERC) of Canada.

was proposed in [3], [4] for total throughput improvement. The

main idea is that, after selecting a partner from the in-cell

mobile users, each user detects a faded and noisy version of

the partner’s transmitted signal and combines this information

with its own data to construct its transmitted signal. Another

diversity technique, known as multiuser diversity, benefits from

the independence of fading processes among multiple users in the

system. In a multicarrier system such as OFDM, total bandwidth

is divided among many subcarriers with each being assigned

dynamically to users. It is unlikely that a subcarrier is in deep

fade for all the users in the system simultaneously and this creates

transmission opportunities. Subcarriers can be assigned dynami-

cally to the users based on their instantaneous channel gains to

benefit from diversity communication and hence to provide robust

performance. Many dynamic resource allocation algorithms and

optimization techniques have been proposed in the literature

for the downlink of non-cooperative and cooperative multiuser

OFDM systems. The ultimate goal of all these algorithms is either

to achieve the highest possible throughput with constraints on

total transmit power [5], [6] or to achieve the minimum total

transmit power with the data rates as constraints [7]. There is

also a third category of rate adaptive dynamic resource allocation

algorithms [8], [9], which are developed to support variable bit

rate services with fairness in the system.

How to opportunistically assign subcarriers to cooperative users

based on a single, derivable and hence practical parameter called

cooperative coefficient, is the focus of this paper. We consider the

subcarrier allocation problem for the downlink of a cooperative

wireless system with users paired to cooperate. One selected user

in a group relays its partner’s signal based on an amplify-and-

forward relaying scheme in different time slots. The idea of the

cooperation coefficient was first introduced in [10]. Cooperation

coefficient quantifies the cooperation level among the users within

a group by using the inter-user channel gains. The objective

parameter in a non-cooperative subcarrier allocation algorithm is

modified by including the cooperation coefficient. In this paper,

978-1-4577-9538-2/11/$26.00 ©2011 IEEE 178

based on the probability distribution function (pdf) of the relaying

channel, mean value of the cooperation coefficient is derived for

Rayleigh faded channels and subsequently applied to subcarrier

allocation. The total throughput of the proposed cooperative

subcarrier allocation algorithm is shown to achieve throughput

improvement over the non-cooperative case [8] even by using

the mean value of cooperation coefficient.

The rest of the paper is organized as follows: In section II, the

TDMA amplify-and-forward cooperation protocol is overviewed.

Cooperation coefficient is analyzed in section III. Subcarrier

allocation algorithm for the cooperative system is described in

section IV and simulation parameters and results are presented

in section V. The paper is concluded in section VI.

II. COOPERATIVE WIRELESS SYSTEM MODEL AND

ANALYSIS

A cooperative multiuser OFDM system with N subcarriers is

considered. Total bandwidth of the system is B. Therefore, each

subcarrier has bandwidth of BN

. Additive white Gaussian noise

(AWGN) is present with single-sided noise power spectral density

(PSD) of N0 over all subcarriers and for all users. The total

transmit power (Pt) at the base station is equally divided between

active subcarriers. There are G groups of cooperative users in the

cell. In each group1 there are K users cooperating according to

the TDMA cooperation protocol proposed in [11]. We intend to

find the maximum achievable data rate for each user.

A. Relaying System and Signal Model

A single-group consisting of two users (K = 2, G = 1) is

considered for throughput analysis and the simulation results are

given for different number of group size. Multiple users within

a group are assumed to be experiencing similar average SNR

conditions. By forming a group of users with similar average

SNR conditions and not necessarily similar instantaneous SNR

conditions, and picking one of them as relay, group diversity gain

with faster relay selection can be achieved. A single group with

two mobile stations (MSs) is shown in Fig. 1.

Mobile stations MSj,1 and MSj,2 are in the jth group (j =

1, 2, ..., G) and receive their data stream from base station.

Different subcarriers are assigned to MSj,1 and MSj,2; i.e.,

none of the users are sharing subcarriers. Transmission protocol

has two phases: broadcast and cooperation. It is assumed that

the subcarrier gains remain constant during both phases. In the

broadcast phase (the first timeslot), base station broadcasts over

1We assume a proper strategy will select the appropriate relay for each source-

destination combination. Note that multiple relays in a single-hop can possibly

assist the end-to-end communication - these potential relays form a group. Both

relay selection and group forming are out of scope for this paper.

BS

MSj,1

MSj,2

hj,1,m h

j,2,n

hj,1,n

hj,2,m

hr

hr j,2,m

j,1,n

Fig. 1. The relaying system model, K = 2.

all subcarriers with transmit power of Pn on the n’th subcarrier.

In the cooperation phase (second and third timeslot), MSj,1 and

MSj,2 after receiving the other user’s signal in the first timeslot,

amplify and forward it in the second and third timeslot with

transmit power of Pj,1 and Pj,2 respectively. A cooperating user

relays its partner’s signal on the same subcarrier that it has

received its partner’s signal from. The sequence of transmission

is shown in Table I.

TABLE I

TRANSMISSION PROTOCOL FOR A COOPERATIVE GROUP WITH TWO

COOPERATIVE USERS.

BS MSj,1 MSj,2

Timeslot 1 transmits listens listens

Timeslot 2 - transmits listens

Timeslot 3 - listens transmits

Different channel gains between BS and MSj,1, MSj,2 are

shown in Fig. 1. The mth subcarrier is allocated to MSj,1 and

the nth subcarrier to MSj,2. ℎj,k,n is the ntℎ subcarrier gain

between BS and the kth user of jth cooperative group. ℎj,1,m and

ℎj,2,n are BS-MSj,1 and BS-MSj,2 subcarrier gains respectively,

and ℎj,1,n and ℎj,2,m are the channel gains for BS-MSj,1 and

BS-MSj,2 when users are listening to their partner’s subcarriers

respectively. The inter-user channel is denoted as ℎrj,1,n and

ℎrj,2,m , where the former is the subcarrier gain from MSj,1 to

MSj,2 and, the latter is the subcarrier gain from MSj,2 to MSj,1.

Each user, after receiving the signal from both direct and relaying

paths, uses a maximal ratio combining (MRC) to combine the two

signals. Throughout this paper, we refer to ℎj,1,m and ℎj,2,n as

direct subcarriers. ℎj,1,n and ℎj,2,m are considered as indirect

subcarriers and ℎrj,1,n and ℎrj,2,m are known as the relaying

subcarriers.

179

B. Throughput Analysis and Cooperation Coefficient

The received signal at MSj,1 and MSj,2 in the first timeslot

can be written as:

yj,1,m =√

PmTℎj,1,mxj,1 + vj,1,m (1)

yj,1,n =√

PnTℎj,1,nxj,2 + vj,1,n (2)

yj,2,n =√

PnTℎj,2,nxj,2 + vj,2,n (3)

yj,2,m =√

PmTℎmxj,1 + vj,2,m (4)

where yj,k,m is the received signal at MSj,k (k = 1, 2) on the

mth subcarrier. vj,k,m is AWGN added to the received signal

at MSj,k on the mth subcarrier. Pn × T is the average received

energy of MSj,k over one symbol period T on the nth subcarrier,

and xj,k is the data stream of MSj,k. Note that Pn + Pm = Pt.

Each user MSj,k normalizes the received signal of the other

user by the factor of√

E{∣yj,k,n∣2} and retransmits it in the

second or third timeslots with the energy of Pj,kT to its partner.

The received signal, yrj,k,m, in the second and third timeslots at

MSj,k is then:

yrj,1,m =√

Pj,2Tℎrj,2,m

yj,2,m√

E{∣yj,2,m∣2}+ vrj,1,m (5)

yrj,2,n =√

Pj,1Tℎrj,1,n

yj,1,n√

E{∣yj,1,n∣2}+ vrj,2,n (6)

where vrj,k,mis the additive noise at MSj,k on the mth subcarrier,

E{∣yj,k,m∣2} is the average energy of the received signal at MSj,k

in the first timeslot. The noise power is assumed to be the same

for all mobile stations; therefore, we can assume �2v = BN0

N

to be AWGN noise at all mobile stations over all subcarriers.

Knowing that the expectations E{∣yj,2,m∣2} = (Pm + �2v) T and

E{∣yj,1,n∣2} = (Pn + �2v) T , we can rewrite (5) and (6) as:

yrj,1,m =

√

Pj,2Pm

Pm + �2v

T ℎrj,2,mℎj,2,mxj,1 + vrj,1,m , (7)

yrj,2,n =

√

Pj,1Pn

Pn + �2v

T ℎrj,1,nℎj,1,nxj,2 + vrj,2,n , (8)

where the effective noise term, vrj,k,m, is also Gaussian and its

variance is:

�2vj,1,m

= �2v

(

1 +

(

Pj,2∣ℎrj,2,m ∣2

Pm + �2v

))

(9)

�2vj,2,n

= �2v

(

1 +

(

(Pj,1∣ℎrj,1,n ∣

2

Pn + �2v

))

. (10)

The receiver combines both signals from the direct and indirect

paths using MRC, where the total output SNR is the sum of the

SNR’s of all the diversity paths [12].

The instantaneous SNR of the direct paths can be calculated

as:

SNRj,1,m =Pm∣ℎj,1,m∣2

�2v

(11)

SNRj,2,n =Pn∣ℎj,2,n∣2

�2v

. (12)

The instantaneous SNR of the relaying paths are:

SNRrj,1,n =PnPj,1∣ℎrj,1,n ∣

2∣ℎj,1,n∣2

�2v(Pn + �2

v + Pj,1∣ℎrj,1,n ∣2)

(13)

SNRrj,2,m =PmPj,2∣ℎrj,2,m ∣2∣ℎj,2,m∣2

�2v(Pm + �2

v + Pj,2∣ℎrj,2,m ∣2). (14)

Therefore, the maximum error-free data rate of MSj,1 and MSj,2,

rj,1,m and rj,2,n, can be written as [12]:

rj,1,m =B

3Nlog2

(

1 + SNRj,1,m + SNRrj,2,m

)

(15)

=B

3Nlog2

(

1+Pm∣ℎj,1,m∣2

�2v

+PmPj,2∣ℎrj,2,m ∣2∣ℎj,2,m∣2

�2v(Pm + �2

v + Pj,2∣ℎrj,2,m ∣2)

)

(16)

rj,2,n =B

3Nlog2

(

1 + SNRj,2,n + SNRrj,1,n

)

(17)

=B

3Nlog2

(

1 +Pn∣ℎj,2,n∣2

�2v

+PnPj,1∣ℎrj,1,n ∣

2∣ℎj,1,n∣2

�2v(Pn + �2

v + Pj,1∣ℎrj,1,n ∣2)

)

(18)

Applying the definition of cooperation coefficient as in [10] we

have:

rj,1,m =B

3Nlog2

(

1 +Pm

�2v

(

∣ℎj,1,m∣2 + Γj,2,m∣ℎj,2,m∣2))

(19)

rj,2,n =B

3Nlog2

(

1 +Pn

�2v

(

∣ℎj,2,n∣2 + Γj,1,n∣ℎj,1,n∣

2

))

(20)

where Γj, 1, n and Γj, 2,m are:

Γj, 1, n =

Pj,1

�2v∣ℎrj,1,n ∣

2

1 + Pn

�2v+

Pj,1

�2v∣ℎrj,1,n ∣

2(21)

Γj, 2,m =

Pj,2

�2v∣ℎrj,2,m ∣2

1 + Pm

�2v+

Pj,2

�2v∣ℎrj,2,m ∣2

(22)

III. DERIVATION OF COOPERATION COEFFICIENT STATISTICS

Mean of the cooperation coefficient is used in the proposed

cooperative subcarrier allocation algorithm in section IV. It is

possible to find a closed-form expression for mean of cooperation

coefficient. We intend to find mean of Γj, 1, n which would be

similar to mean of Γj, 2, n. To do this, we first need to find

the probability density function (pdf) of cooperation coefficient.

Equation (21) can be rewritten as:

Γj, 1, n = 1∣ℎrj,1,n ∣

2

1 + + 1∣ℎrj,1,n ∣2, (23)

180

where = P�2 and 1 = P1

�2 where we have dropped the

indices corresponding to direct and inter-user links. Assuming

� = ∣ℎrj,1,n ∣2 and defining � = +1

1

, Eq. (23) can be written as:

Γ =�

� + �. (24)

The parameter � describes the ratio of direct link average transmit

SNR to the relaying link average transmit SNR. As seen in

(24), cooperation coefficient is a function of � (or cooperative

user subcarrier gain in general) and �. Therefore, following the

procedure shown in [13] for finding pdf of a function of random

variable, we can show that the pdf of cooperation coefficient, Γ,

is:

fΓ(Γ) =�

(1− Γ)2f�

(

� Γ

1− Γ

)

, 0 < Γ < 1 (25)

where f�(�) is the pdf function of �. Cooperation coefficient is

distributed in the interval(

0, 1)

. We can assume any distribution

for pdf of the relaying channel. Assuming commonly used

Rayleigh distribution for ∣ℎrj,1,n ∣, � would have an exponential

distribution with � = 1 (mean value of one) as follows:

f�(�) = exp(−�), � > 0 (26)

Using (25) and (26), the closed-form expression for mean of

cooperation coefficient can be calculated by integrating over pdf

of cooperation coefficient as follows:

Γ = E[Γ] =

∫ 1

0

Γ fΓ(Γ) dΓ

Γ =

∫ 1

0

Γ�

(1− Γ)2exp

(

−� Γ

1− Γ

)

dΓ = 1 + �e� E1(−�), (27)

where E1(x) is the exponential integral function and is defined

as:

E1[x] =

∫

∞

x

e−t dt

t. (28)

IV. Γ−MODIFIED MAX-MIN COOPERATIVE SUBCARRIER

ALLOCATION ALGORITHM

The problem of resource allocation in a cooperative multiuser

OFDM system is to determine the elements of subcarrier allo-

cation matrix: C = [cj,k,n]G×K×N specifying which subcarrier

should be assigned to which user of which group. cj,k,n = 1,

if and only if subcarrier n is allocated to user k in group j;

otherwise it is zero. None of the users shares subcarrier, so in

case that cj,k,n = 1 then ci,l,n = 0 for all i ∕= j and l ∕= k. The

total throughput of the k’th users in the j’th group, Rj,k, after

subcarrier allocation can be written as:

Rj,k =

N∑

n=1

cj,k,nrj,k,n, (29)

where rj,k,n is as given in (15) and (17) for k = 1, 2 using

subcarrier m and n respectively.

The subcarrier allocation algorithms originally proposed in [8]

(referred to as Max-Min algorithm) is used as the benchmark

for cooperative subcarrier allocation with K = 2 and G =

{1...9}. The objective parameter in assigning the subcarriers

should include the partner’s channel gain. If all the direct

and relaying channels are known at BS, we can choose the

objective parameter as ∣ℎj,1,n∣2 + Γj, 2, n∣ℎj,2,n∣2 for user 1,

and ∣ℎj,2,n∣2 + Γj, 1, n∣ℎj,1,n∣2 for user 2, of the jth group

respectively. This will require feedback of the relaying channels

to BS. We propose to use the mean of cooperation coefficient

instead of its instantaneous value in subcarrier allocation in all

the algorithm as discussed in the following.

A. Cooperative Max-Min Algorithm based on Γ

After modifying the objective parameter of the Γ-modified

Max-Min subcarrier allocation algorithm, the cooperative Max-

Min subcarrier allocation algorithm is proposed as follows:

————————————————————————

∙ Initializationcj,k,n = 0, ∀j, k, n

Rj,k = 0, ∀j, k

A = {1, 2, ..., N}

objj,1,n = ∣ℎj,1,n∣2 + E[Γj, 2, n]∣ℎj,2,n∣2

objj,2,n = ∣ℎj,2,n∣2 + E[Γj, 1, n]∣ℎj,1,n∣2

∙ Subcarrier Allocation

– for k = 1 to 2 and j = 1 to G

(a) find n satisfying

objj,k,n ≥ objj,k,m ∀m ∈ A

⇒ cj,k,n = 1

(b) update Rj,kwith Rj,k =∑N

n=1cj,k,nrj,k,n

A = A− {n}– while A ∕= ∅

(a) find j and k satisfying Rj,k ≤ Ri,l;

∀i = 1, 2, ..., G and l = 1, 2

(b) for the found j and k, find n satisfying

objj,k,n ≥ objj,k,m ∀m ∈ A

⇒ cj,k,n = 1

(c) update Rj,k and A with j, k, n

Rj,k =∑N

n=1cj,k,nrj,k,n

A = A− {n}

∙ End

————————————————————————

In the first step, the objective parameter is calculated for all

the subcarriers of all the users. In the second step, one subcarrier

is assigned to each user based on the objective parameter. All

the groups are checked to select the satisfying subcarrier. After

all the users have been assigned one subcarrier each, in the third

step, the user with the lowest throughput is given the priority to

181

choose its next subcarrier. This procedure continues until all the

subcarriers are allocated.

V. PERFORMANCE EVALUATION

Performance of the proposed cooperative subcarrier allocation

algorithms is compared with non-cooperative Max-Min coun-

terpart in terms of total throughput. As stated earlier. It is

assumed that the relaying channel has a Rayleigh distribution.

The simulations are run for four different cases:

1) Case 1: Perfect knowledge of instantaneous cooperation

coefficient at the base station is assumed (cooperative Max-

Min, instantaneous Γ).

2) Case 2: Mean value of the cooperation coefficient is

computed at the base station by using (27). (cooperative

Max-Min, mean of Γ)

3) Case 3: No knowledge about the statistics and instanta-

neous value of cooperation coefficient is assumed at the

base station. A constant Γ is assumed randomly for all the

cases (cooperative Max-Min, Γ = 0.5).

4) Case 4: Cooperation coefficient is not used at all in

subcarrier allocation process(non-cooperative Max-Min).

In the simulation results for Case 1, we have assumed that

base station has perfect knowledge of the cooperation coefficient.

This will provide an upper-bound on the total throughput of the

algorithm and help us to analyze the performance degradation

due to the use of the mean of cooperation coefficient instead of

its instantaneous value.

A. Simulation Parameters

The channel is modeled as frequency selective with six in-

dependent multipaths and exponential delay profile as in [14].

The total bandwidth of the system is B = 1MHz and the total

transmit power is Pt = 1W in downlink. It is assumed that there

are N = 128 subcarriers to be allocated to the cooperating users

and the average required received SNR at mobile station is equal

for all subcarriers. Random cooperation coefficients are assumed

among the users of different groups. Cooperation coefficient mean

is computed using (27) for Case 2. Total number of 10000 channel

gain realizations were used and the results were averaged. We

have run the Monte-Carlo simulation for the above mentioned

with K = 2, G = {1...9}.

B. Simulation Results

The total throughput of the system versus different number

of groups is shown in Figs. 2-4 for different values of SNR

ratios between direct and relay links, � (= 1, 0.33, 0.1). It is

observed that cooperative subcarrier allocation algorithm provides

better performance compared to non-cooperative algorithm. For

a certain value of (= 20dB), smaller values of � lead to a

better performance improvement compared to the non-cooperative

case as evident from the figures. It means the inter-user (or

relay) channels are stronger relatively and cooperation is more

effective. Cooperation coefficient distribution shifts closer to one

for smaller values of � which translates into better cooperation

throughput.

2 3 4 5 6 7 8 9 10 11 122.38

2.4

2.42

2.44

2.46

2.48

2.5

Tota

l C

apac

ity (

bit

s/s/

Hz)

Number of Groups (G)

Cooperative Max−Min, instantaneous Γ

Cooperative Max−Min, Mean of Γ

Cooperative Max−Min, Γ = 0.5

Non−cooperative Max−Min

Fig. 2. Total throughput for Max-Min subcarrier allocation algorithms, � = 1

( = 20dB, 1 = 20dB).

2 3 4 5 6 7 8 9 10 11 122.44

2.46

2.48

2.5

2.52

2.54

2.56

Tota

l C

apac

ity (

bit

s/s/

Hz)

Number of Groups (G)

Cooperative Max−Min, Instantaneous Γ

Cooperative Max−Min, Mean of Γ

Cooperative Max−Min, Γ = 0.5

Non−cooperative Max−Min

Fig. 3. Total throughput and Max-Min subcarrier allocation algorithms, � = 0.33

( = 20dB, 1 = 25dB).

Using the mean of cooperation coefficient in subcarrier al-

location results in better performance compared to the case

that cooperation coefficient is not used. It is observed that the

performance of the subcarrier allocation algorithm is degraded

182

2 3 4 5 6 7 8 9 10 11 12

2.5

2.52

2.54

2.56

2.58

2.6

2.62

Tota

l C

apac

ity (

bit

s/s/

Hz)

Number of Groups (G)

Cooperative Max−Min, Instantaneous Γ

Cooperative Max−Min, Mean of Γ

Cooperative Max−Min, Γ = 0.5

Non−cooperative Max−Min

Fig. 4. Total throughput and Max-Min subcarrier allocation algorithms, � = 0.1

( = 20dB, 1 = 30dB).

by using an arbitrary (inaccurate) estimate of the cooperation

coefficient mean as in Case 3. In all the cases, performance

improves with the group size and moderates with larger group

size showing the group diversity behavior. As � decreases, that

is inter-user (or relay) link becomes stronger compared to the

direct link, the performance difference between cooperative and

non-cooperative becomes more evident as seen in Figs. 2-4.

VI. CONCLUSIONS

In this paper, the problem of subcarrier allocation in the

downlink of an amplify-and-forward OFDM cooperative system

was studied. Cooperation coefficient was defined as a function

of the relaying channel between cooperating users, and BS-MS

and RS-MS average SNR’s. Assuming Rayleigh distribution for

the relaying channel, pdf and mean of the cooperation coefficient

was derived. Cooperative Max-Min algorithm was simulated and

shown to have a higher total throughput compared to the non-

cooperative one. It was shown that by using the mean of coopera-

tion coefficient instead of its instantaneous value, the performance

of the cooperative algorithm degrades negligibly for small values

of �. This work can be extended to other cooperation protocols.

Proportional data rates can be considered and their performance

of the algorithm can be evaluated. Other algorithms proposed for

non-cooperative system can also be modified and applied using

the mean cooperation coefficient and their performance can be

investigated for future work.

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