Communications and Network, 2013, 5, 48-52
http://dx.doi.org/10.4236/cn.2013.53B2010 Published Online September 2013 (http://www.scirp.org/journal/cn)
Power-Minimizing Resource Allocation in Multiuser
Cooperative Relay Communications
Bin Chen, Youming Li, Yaohui Wu, Xiaoqing Liu, Ting Zou
Institute of Communication Technology, Ningbo University, Ningbo 315211, China
Received June, 2013
ABSTRACT
In this paper, we investigate the power-minimizing resource allocation problem in multiuser cooperative relay commu-
nication systems. A joint optimization problem involving subcarrier assignment, relay selection and power allocation is
formulated. Since the problem cannot be solved directly, we decompose it into three subproblems. According to the
equivalent channel gains and the target rates of users, the subcarrier assignment and relay selection are conducted. Mo-
tivated by the water-filling algorithm, we propose a power allocation algorithm with cooperative features. Simulations
results indicate that the proposed algorithm performs better in terms of the total transmit power consumption than the
existing algorithms.
Keywords: Subcarrier Assignment; Relay Selection; Power Allocation; Cooperative Features
1. Introduction
As the demand for high data-rate multi-media wireless
services increases rapidly, the third generation (3G) wireless
communication systems have been unable to meet this
requirement. Therefore, researchers are working on the
future fourth generation (4G) wireless communication
systems.
Orthogonal frequency division multiple access (OF-
DMA) is regarded as a promising technology for the 4G
systems, which can offer high spectral efficiency and
mitigate frequency-selective fading. Besides OFDMA,
the 4G systems adopt many other key technologies. Co-
operative relaying, assisted by additional relay stations,
can increase the coverage and obtain spatial diversity. By
combining these technologies, resource allocation in
OFDMA systems has drawn much attention recently.
According to different optimization objectives and con-
straints, the adaptive resource allocation schemes for
OFDMA systems can be roughly divided into two cate-
gories: Rate adaptive (RA) schemes to maximize the
system throughput [1-3]; and margin adaptive (MA)
schemes to minimize the overall transmit power [4-9].
There are many works that investigate the MA schemes.
Followed with global warming, the growth in energy
consumption provides new topics and issues in commu-
nication systems. Hence, how to reduce energy con-
sumption while meeting throughput requirement in such
communication systems is an urgent task, which is
known as green communication.
In [5], the authors proposed a low-complexity algo-
rithm based on the Lagrange dual decomposition theory
to minimize the downlink transmit power in MIMO-
OFDMA systems. In [6], Lin et al. proposed an algo-
rithm to find suboptimal and optimal solutions to sum
power minimization resource allocation problems in
OFDMA-based networks. In order to minimize the total
transmit power in cooperative uplink systems, the au-
thors in [7] derived two algorithms based on the
flow-optimized cooperative scheme (FCS) and the sin-
gle-relay cooperative scheme (SCS), respectively. Ref-
erence [8] considered the problem of energy-efficient
resource and power allocation in the uplink of multiuser
multichannel OFDM-based systems, and proposed to
maximize the energy efficiency (EE). In [9], the authors
aimed at minimizing the overall transmit power under
total power and target data constraints in cooperative
multiuser OFDMA systems and then proposed a three-
step iterative subopti mal assignment algorithm.
In this paper, we investigate the power-minimizing
resource allocation problem in multiuser cooperative
relay communications. We formulate the problem as a
joint optimization problem involving subcarrier assign-
ment, relay selection and power allocation. Since the
problem cannot be solved directly, we decompose it into
three subproblems. Firstly, according to the average
channel gains and the target rates of users, we d ecide the
number of subcarriers that users will be assigned. Sec-
ondly, we assign users to the subcarriers with the best
equivalent channel gains meanwhile selecting relays to
C
opyright © 2013 SciRes. CN

B. CHEN ET AL. 49
the users. Finally, combined with cooperative features,
we propose a power allocation algorithm based on the
water-filling algorithm. Simulations results indicate that
the proposed algorithm performs better in terms of the
total transmit power consumption than the existing algo-
rithms, while meeting the target rates of users.
The remainder of this paper is organized as follows.
Section 2 provides the system model and formulates the
resource allocation problem. Section 3 analyzes the op-
timization problem and proposes the algorithm. Simula-
tion results are given and discussed in Section 4. Finally,
Section 5 draws the conclusio ns.
2. System Model and Problem Formulation
In this section, we first describe the model for multiuser
cooperative relay communication systems, and then for-
mulate the resource allocatio n problem.
2.1. System Model
We consider an OFDMA-based uplink cooperative relay
communication system as shown in Figure 1. There are
K mobile stations (MS) and M relay stations (RS) trans-
mitting on N subcarriers to one base station (BS), where
all stations are equipped with only one antenna. Due to
long distance and heavy blockage, it is assumed that
there is no direct transmission between the BS and the
MSs. We consider two phases in uplink relay transmis-
sion. During the first phase, each MS k broadcasts its
data to available RSs. In the second phase, the RSs for-
ward the data to the BS, where we only consider de-
code-and-forward (DF) mode. For simplicity, we assume
that the RSs forward the received data to the BS on the
same subcarrier. It is further assumed that the channels
are slow fading, thus the channel state information (CSI)
of all links can be estimated and fed back to the BS.
Figure 1. The system model of uplink cooperative relay
communication.
Let ,,krn and ,,rBn represent respectively the
channel gains between kth MS and rth RS, rth RS and
BS on subcarrier n. The transmit powers of kth MS to rth
RS, and rth RS to BS spent on subcarrier n are ,,krn
and ,,rBn, respectively. According to Shannon formula,
the achievable rate of kth MS on subcarrier n forwarded
by rth RS is given by
H H
p
p


,2,,,,
2,,,,
1min{log 1,
2
log1}
knkrn krn
rBn rBn
rpH
pH


(1)
2.2. Problem Formulation
We define ,, {0,1}
krn


as the subcarrier assignment
variable, where ,, 1
krn


indicates the assignment of
subcarrier n to kth MS and rth RS pair, and ,, 0
krn


,
otherwise. Our goal is to minimize the total transmit
power while meeting the target rates of users, so that the
optimization problem can be formulated as
,,,,, ,
11 1
,,
,,
11
,,, ,
,
1
min
.. 1. {0,1},,,;
2. 1,;
3. 0,0,,,;
4. ,,
NMK
krnkrn rBn
nr k
krn
NM
krn
nr
krn kBn
N
kn k
n
pp
stCk r n
Cn
Cp pkrn
CrRkn



 










 


(2)
Here, constraint C2 guarantees that every subcarrier is
allocated to at most one RS-MS pair. C3 indicates the
powers of MSs and RSs are non-negative. In C4, is
the target rate of kth MS. k
R
3. Resource Allocation Algorithm
The optimization in (2) is a joint optimization problem.
Since it cannot be solved directly, we decompose it into
three subproblems: the number of subcarrier assignment,
subcarrier assignment and relay selection, and power
allocation.
3.1. The Number of Subcarrier Assignment
In order to maximize (1), we can obtain that
,,,,,,,,krnkrnrBnrBn
pH pH (3)
Thus the sum power consumed in the link of kth MS
on subcarrier n forwarded by rth RS is
,,,, ,,kBnkrn rBn
ppp

 (4)
According to [3], the equivalent channel gain in the
link of kth MS on subcarrier n forwarded by rth RS is

B. CHEN ET AL.
50
,,,,krn rBn
equ HH
H
,, ,,, , krn krn rBn
HH(5)
Consequently, Equation (1) can be rewritten as

,2,,,
1log 1
2
equ
knkBnkrn
rp
,
H (6)
Based on [4], we assume that each MS k experiences
an average channel gain on every subcarrier with
,,
11
NMequ
krn
nr
k
H
HMN


 (7)
Let MS k be allocated subcarriers. When the gain
on k
m
sa each subcarrier is theme, the optimal rate-power
allocation is to transmit kk Rm bits on each subcarrier,
resulting in total transmi as t power

21
kk
Rm
kk
mH.
Thus in order to determine the nums
assigned to each MS {,1,2,..., }
k
mk K
ber of subcarrier

, the objective
function can be expressed as
1
1
max
min(2 1)
.. 1. ,
C2. ,...,,
k
k
R
Kmkm
kk
K
k
k
k
k
H
st CmN k
R
mNk
B














 (8)
where is the number of maximum modulation bit.
3.2. Subcarrier Assignment and Relay Selection
e maximum equivalent channel gain for each
M
,
(9)
b) According to the average channel gain of each sub-
ca
max
B
According to equivalent channel gain, we should assign
the better subcarriers to each MS. Becaus e every subcarr ier
is allocated to at most one RS-MS pair, we propose an
algorithm of subcarriers selecting users. The algorithm is
as follows.
a) Find th
S on each subcarrier.
H
,,
1
max equ
kn krn
rM
H


rrier ,
1
K
nkn
k
H
HK, arrange the channel gain ma-

trix (,)
K
N in increasing order.
12
(,),(... )
N
KN HHH (10)
c) For each subcarrier, find the MS whos
ga
(11)
where indicates the set of subcarriers
is the number
of elem
ing lgorithm, we propose a power
h also has cooperative features.
s.
e channel
in is the largest on the subcarrier, then assign the sub-
carrier to the MS. Detailed process is as follows.
1,2,...,for nNdo
,
1
arg max kn
kK
kH


,
,
1
,0
argmax
{}
1
kk
kn
kn
kK
kk
kk
while cmdo
Hn
kH
end while
CCn
cc
end for






{1,2,...,}
k
CN
assigned to the kth MS, ,
ents in the set k C{1,2,...,N}
k
c
.
3.3. Power Allocation
Based on the water-fill a
allocation algorithm, whic
The algorithm is as follow
a) Extract the channel gain of the subcarriers assigned
to the MS from the channel gain matrix (,)
K
N, and
store them into a row vector {(,),hkmk. 1,2,..., }K
k
b) Arrange (, )
k
hkm in decrease order.
,1
( ,)[,,...,]
kk
hkmh hh
,2,
,1
(
k
k km
k
h,2, ... )
k
kkm
hh

 2)
c) Compute the water-filling constant.
(1
1
,
1,
k
MA km
nkn
Kh





2k
km
R 
(13)
d) Test subcarrier energy.
,,
10
kk
mMAkkm
Kh


 
(14)
If yes, then 1
kk
mm

, go to step c), otherwise
continue.
f) Compute subcarrier energy and rate
,,,
1, 1,2,...,
knkn kMAk
K
hn m

 (15)

,2,,
log (k
knMAkkm
bKh)

 (16)
4. Simulation Results and Analysis
In this section, simulation results are provided to evaluate
ency-selec-
. The max-
the system performance. Here, six-path frequ
tive Rayleigh fading channels are considered
imum Doppler shift is 30Hz. The total bandwidth is set to
be 1MHz and the number of subcarriers is 256. Assume
that the Gaussian white noise power spectral density is
-36 dB/Hz and the number of maximum modulation bit is
4. The total power consumption of each power allocation
scheme is averaged over 1,000 independent Monte-Carlo
simulations. The performance comparison is conducted
among the algorithm in [9], static resource allocation

B. CHEN ET AL. 51
algorithms based on Greedy and Water-Filling algorithm,
respectively, and the pro- posed algorithm.
Figure 2 indicates the total transmit power consump-
tion in uplink versus the total number of MSs. In order to
reflect different wireless services, the target rates of MSs
ar
dition of a fixed total target rate, we conduct
eq
e 1 ~ 10 b/s/Hz. It is seen that for a fixed total number
of MSs, the total transmit power consumption under the
proposed algorithm is always the smallest among the
four algorithms. Meanwhile, with the increase of the total
number of MSs, the total transmits power consumption
under the proposed algorithm increases at the slowest
speed.
Figure 3 illustrates the total transmit power consump-
tion in uplink versus the total target rate of 10 MSs. In
the con
ual rate allocation for 10 MSs. It is observed that the
total transmit power of the proposed algorithm is the
lowest among the four algorithms.
510 15 20 25
0
5
10
15
20
25
30
Total Number of MS s
Total Transmi t Power (dB)
Algorithm in [9]
P roposed Al go rithm
S t atic Greedy
Static W ater-Filling
Figure 2. Total transmit power in different number of MSs.
20 30 40 50 60 708
0
14
16
18
20
22
24
26
Total Target Rate of 10 MSs (b/s/Hz)
Total Transmit P ower (dB)
Algorithm in [9]
P roposed Al gori thm
S tatic G reedy
Static Water-Filling
Figure 3. Total transmit power in different total target rate
of 10 MSs.
In this paper, we propose a power-minimizing algorithm
rative relay communication, which
This work was supported in part by the National Science
1119), the Ningbo Natural
[1] W. Shim, Y. Han and S. Kim, “Fairness-Aware Resource
Allocation in Uplink System,”
IEEE Transacology, Vol. 59, No.
5. Conclusions
in multiuser coope
fully embodies the concept of green communication and
makes a contribution to sustainable development. Simu-
lation results show that compared with other algorithms,
the proposed algorithm performs better in terms of the
total transmit power consumption while meeting the tar-
get rates of users.
6. Acknowledgements
Foundation of China (6107
Science Foundation (2012A610017), the Innovation
Team of Ningbo (2011B81002), the Ningbo Natural
Science Foundation (2012A610061).
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