638 IEEE COMMUNICATIONS LETTERS, VOL. 16, NO. 5, MAY 2012
Outage Probability Analysis and Power Allocation for Two-Way Relay
Networks with User Selection and Outdated Channel State Information
Lisheng Fan, Xianfu Lei, Pingzhi Fan, and Rose Qingyang Hu
Abstract—This paper considers a multiuser two-way relay net-
work (TWRN) consisting of one base station (BS), one amplify-
and-forward (AF) relay and K mobile stations (MSs) among
which the Nth-best MS is selected to exchange information
with the BS. Specifically, we study the impact of outdated
channel state information (CSI) on the system over time-varying
Rayleigh block-fading channels by deriving a tight closed-form
lower bound for the outage probability. We also obtain an
asymptotic outage probability expression for high signal-to-noise
ratio (SNR). Moreover, by minimizing the asymptotic outage
probability, we optimize the power allocation (PA) among the
network nodes. Numerical and simulation results collaborate the
proposed studies.
Index Terms—Two-way relay networks (TWRN), user selec-
tion, outdated channel state information (CSI), outage probabil-
ity, power allocation (PA).
I. INTRODUCTION
D
UE to its capability of providing high spectral efficiency,
there has been a growing interest in investigating two-
way relay network (TWRN), in which the source nodes
exchange their information with the help of relays [1]–[4].
Specifically, sym bol error probability and outage probability of
TWRN were analyzed in [1], [2] for one or more relays. When
there are multiple u sers in TWRN, user selection technique
can be used to effectively exploit the channel fading [3], [4].
In [3], average sum rate was studied for user selection in mul-
tiuser TWRN with Rayleigh fading. In [4], the authors derived
the outage probability of the same system in mixed Rayleigh-
Rician fading channels. However, when user selection is im-
plemented in time-varying chan nels, there is a possibility that
user selection is performed based on outdated channel state
information (CSI) due to the schedu ling delay, and thus the
Manuscript received December 2, 2011. The associate editor coordinating
the review of this letter and approving it for publication was H. Suraweera.
L. Fan is with the Department of Electronic Engineering, Shantou Univer-
sity, and also with the Key Laboratory of Cognitive Radio and Information
Processing (Guilin University of Electronic Technology), Ministry of Educa-
tion) (e-mail: lsfan@stu.edu.cn).
X. Lei and P. Fan are with the Provincial Key Lab of Information Coding
and Transmission, Southwest Jiaotong University, Chengdu, China (e-mail:
xflei81@yahoo.com.cn, p.fan@ieee.org).
Rose Q. Hu is with the Department of Electrical & Computer Engineering,
Utah State University, USA (e-mail: rosehu@ieee.org).
L. Fan and X. Lei are also with the State Key Laboratory of Integrated
Services Networks, Xidian University, Xi’an, China.
This work wa s supported by the National Natural Science Foundation of
China (No. 61002015/60902023/61171096), 111 project (No. 111-2-14), Na-
tional Basic Research Program of China (973 Program No. 2012CB316100),
the Opening Project of Key Laboratory of Cognitive Radio and Information
Processing (Guilin University of Electronic Technology), Ministry of Edu-
cation (No. 2011KF04), the Open Research Fund of State Key Laboratory
of Integrated Services Networks (No. ISN11-04), and the Foundation for
Distinguished Young T alents in Higher Education of Guangdong, China (No.
LYM09077).
Digital Object Identifier 10.1109/LCOMM.2012.031212.112448
selected user may not be the desired one when the transmission
actually starts [5]– [13]. Therefore, we study in this paper
how the outdated CSI impacts the multiuser TWRN with user
selection. Moreover, we con sid er the N th-best user selection
[5], [14], which includes the scheme in [3], [4] as a special
case. Specifically, we derive a tight closed-form lower bound
for the outage probability of multiuser TWRN with outdated
CSI over time-varying Rayleigh block-fading channels. We
also get an analytical expression for the asymptotic outage
probability at large signal-to-noise ratio (SNR). Further, we
devise an optimal power allocation (PA) strategy, which can
enhance the system performance significantly.
The rest o f this paper is organized as follows. Section II
introduces the system model of multiuser TWRN in outdated
CSI environments. Section III derives the closed-form lower
bound for the outage probability as well as an asymptotic
expression. In Section IV, we present the method to optimally
allocates the transmit power among network nodes in the
system. Numerical and simulation results are provid ed in
Section V and conc lusions are d rawn in Section VI.
II. S
YSTEM MODEL
We consider a two-phase multiuser TWRN consisting of
one base station (BS), one AF relay R and K mobile stations
(MSs) [3], [4]. There is no direct link between the MS and
BS due to severe shadowing. The channels in the system
are assumed to remain constant over a block while correlate
across blocks [15], where the block duration T
b
depends
on the channel coherence time. Let g(m) ∼CN(0,α) and
h
k
(m) ∼CN(0,β) denote the channels of R-BS and MS
k
-R
(k =0, 1,...,K−1) links, r espectively, where m is the block
index.
To select the N-th best user among K ones, a distributed
selection strategy is adopted [10]–[13], which can minimize
the overhead involved in the selection and hence is easy
to be implemented in practice [16]. Specifically, each user
firstly estimates the channel of the connectivity with R at the
beginning of block, assisted by one pilot broadcast by R. Then
each user starts a timer, which is a function of its estimated
channel quality. When the timer expires, the associated user
notifies the other users via a flag packet through a dedicated
link. Once N flag p ackets are sent, the last user who has sent
the flag packet is the N-th best user MS
k
∗
and other users
will keep silent
1
. When user selection is performed slower
than the channel coherence time, the selection will be based
1
The strategies to avoid collision can be found in [16], and the associated
discussion is beyond the scope of the current work.
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2012 IEEE