872 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 5, MAY 2013
Joint Power Allocation and Subcarrier Pairing for
Cooperative OFDM AF Multi-Relay Networks
Xueyi Li, Qi Zhang, Guangchi Zhang, and Jiayin Qin
Abstract—For conventional subcarrier pairing scheme in co-
operative orthogonal frequency division multiplexing amplify-
and-forward multi-relay networks, to avoid interference, each
subcarrier pair (SP) is assigned to only one relay, over a specific
subcarrier, the destination receives signals transmitted from only
one relay. In this letter, we propose to assign each SP to all the
relays. Thus, over a specific subcarrier, the destination receives
signals transmitted from all the relays. We propose a joint power
allocation and subcarrier pairing scheme which maximizes the
transmission rate subject to total network power constraint. The
problem is simplified and solved by using dual method.
Index Terms—Orthogonal frequency division multiplexing
(OFDM), multi-relay, subcarrier pairing, power allocation.
I. INT RODUCTION
C
OOPERATIVE communications can improve the relia-
bility of wireless transmission and extend its coverage
[1]. For cooperative amplify-and-forward (AF) orthogonal
frequency division multiplexing (OFDM) single relay net-
works, optimal power allocation and subcarrier pairing were
studied to maximize the transmission rate in [2] and [3].
For cooperative AF multi-relay OFDM networks, some power
allocation schemes have been proposed in [4]-[6]. In [6],
joint optimization o f subcarrier pairing, subcarrier-pair-to-
relay assignment, and power allocation was proposed under
the individual power constraint on each node or the total
network power constraint. For multi-relay networks, if mul-
tiple relays participate relaying simultaneously an d different
relays have different subcarrier pairs (SPs), interference may
be introduced. The proposed scheme in [6] assigns each SP to
only one relay to avoid interference. Over a specific subcarrier,
the destination receives signals transmitted from only one
relay. In this letter, we propose to assign each SP to all
the relays. Thus, over a specific subcarrier, the destination
receives signals transmitted from all the relays. We propose
a joint power allocation and subcarrier pairing scheme which
maximizes the transmission rate subject to total network power
constraint.
Manuscript received December 3, 2012. The associate editor coordinating
the review of this letter and approving it for publication was D. Popescu.
This work was supported by the National Natural Science Foundation
of China (61173148, 61102070, and 61202498), the Industry-University-
Research Project of Guangdong Province, and the Ministry of Education
(2011B090400581), the Scientific and Technological Project of Guangzhou
City (12C42051578 and 11A11060133).
The authors are with the Department of Electronics and Communi-
cations Engineering, Sun Yat-Sen Univ ersity, Guangzhou 510006, China.
X. Li and G. Zhang are also with the School of Information Engineer-
ing, Guangdong University of Technology, Guangzhou 510006, China (e-
mail: leexue yi@163.com, zhqi26@mail.sysu.edu.cn, guangchi@gmail.com,
issqjy@m ail.sysu.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2013.031913.122714
II. SYSTEM MODEL
We consider a two-hop cooperative OFDM AF multi-relay
network, which consists of one source, one destination and
K relays. In the relay network, the transmission bandwidth is
uniformly divided into N subcarriers. The half duplex relaying
scheme is employed. Thus, in the first time slot, the source
transmits signals to all relays and the destination over all
subcarrier s. In the second time slot, all th e re lays amplify and
forward the signals simultaneously to the destination, while the
source keeps silent. The destination combines signals received
in the two time slots and performs the optimal signal detection.
The wireless channel between any two nodes on any subcarrier
is assumed to be frequency-flat. Furthermore, we assume that
the channel state information (CSI) of the whole network is
perfectly known at every node. The joint power allocation
and subcarrier pairing optimization is performed by a central
processor which is located at the destination or the source.
Since the subcarrier pairing is adopted, after receiving the
signal from source on the i
th
, i ∈{1, 2, ··· ,N}, subcarrier in
first time slot, the k
th
relay amplifies it and forwards it on the
j
th
, j ∈{1, 2, ··· ,N}, subcarrier in second time slot. The
subcarriers i and j form a SP (i, j). If different relays have
different SPs, interference may be introduced. For example,
if one relay has SP (i
1
,j) and the other relay has SP (i
2
,j),
i
1
= i
2
, the received signal on the j
th
subcarrier at destination
in the second time slot is the mixture of signals on subcarriers
i
1
and i
2
in the first time slot. To avoid interference, we
propose that all relays have same SPs in this letter.
The wireless channel coefficient between the source and
destination on the i
th
subcarrier is denoted as h
i,0
.The
channel coefficients between the source and k
th
relay and
between the k
th
relay and destination on the i
th
subcarrier
are denoted as h
i,k,1
and h
i,k,2
, respectively, i =1, 2, ··· ,N,
k =1, 2, ··· ,K.Atthek
th
relay and destination on the
i
th
subcarrier, the received additive white Gaussian noises
(AWGNs) are with zero mean and variances of σ
2
i,k
and σ
2
i,d
,
respectively. In the first time slot, the received signal at the
destination on the i
th
subcarrier, denoted as y
i,1
,is
y
i,1
= h
i,0
x
i
+ n
i,d,1
(1)
where x
i
and n
i,d,1
denote the signal transmitted from the
source and the AWGN at the destination on the i
th
subcarrier,
respectively. In the second time slot, for the SP (i, j),the
received signal at the destination from all the relays on the
j
th
subcarrier, denoted as y
i,j,2
,is
y
i,j,2
=
K
k=1
h
j,k,2
f
k
(i,j)
e
jφ
k
(i,j)
(h
i,k,1
x
i
+ n
i,k,1
)+n
j,d,2
(2)
1089-7798/13$31.00
c
2013 IEEE