Nakagami-m衰落下TDBC协议多用户双向中继系统中断概率分析
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本文探讨了带有Nakagami-m衰落的多用户双向中继系统中的时间分段广播(TDBC)协议的中断概率。在多用户场景下，多个终端节点通过一个半双工放大和转发(AF)中继节点进行信息交换，以实现更高的频谱效率。研究焦点在于利用TDBC协议来优化通信性能，尤其是在Nakagami-m fading（一种广义瑞利衰落模型，其参数m描述了信道的稳定程度）环境中。
论文首先介绍了背景，指出两向中继技术因其在频谱利用率上的优势而受到广泛关注。两种主要的频谱高效协议被提出，其中TDBC协议作为一种关键策略，允许各个终端在特定的时间窗口内轮流发送和接收数据，有效地共享中继节点的带宽资源。
作者Xianfu Lei、Lisheng Fan、Diomidis S. Michalopoulos、Pingzhi Fan和Rose Qingyang Hu针对该系统进行了深入研究。他们主要贡献是推导出了一种紧密的闭合形式下界，用于计算在Nakagami-m衰落信道下的系统中断概率，这种信道模型考虑了整数值的 fading 参数，这在实际无线环境中是非常实用的。
此外，文中还提供了高信号到噪声比(SNR)条件下的 outage probability 的渐近表达式，这有助于分析在理想或接近理想通信条件下的系统性能。这些理论分析得到了数值结果的支持，证实了作者的推导有效。
关键词包括：中断概率、两向中继系统、时间分段广播(TDBC)协议和Nakagami-m fading，这些都反映了论文的核心研究内容和焦点。通过这篇论文，读者可以了解到如何在复杂的无线环境下优化TDBC协议，以减少通信中断并提高多用户双向中继系统的整体性能。
IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 3, MARCH 2013 487
Outage Probability of TDBC Protocol in
Multiuser Two-Way Relay Systems with Nakagami-
m Fading
Xianfu Lei, Lisheng Fan, Diomidis S. Michalopoulos, Pingzhi Fan, and Rose Qingyang Hu
Abstract—This paper considers a multiuser two-way relay sys-
tem with time division broadcast (TDBC) protocol, where multiple
end-sources compete to exchange information with another end-
source through the help of a single half-duplex amplify-and-
forward (AF) relay. We derive a tight closed-form lower bound for
the system outage probability over Nakagami-m fading channels
with integer fading parameters. An asymptotic expression for the
outage probability in high signal-to-noise ratio (SNR) regime is also
obtained. Numerical results corroborate the theoretical analysis.
Index Terms—Outage probability, two-way relay system, time
division broadcast (TDBC), Nakagami-m fading.
I. INTRODUCTION
T
WO-WAY relaying has received many attentions because
of its relatively high spectrum efficiency. There are two
major spectrally efficient protocols proposed for two-way relay
systems, i.e., analogy network coding (ANC) and time division
broadcast (TDBC). The two-way relay systems employing ANC
and TDBC protocols have been studied in the literature [1]–
[7]. Sp ecifically, the outage probability of ANC and TDBC
protocols was studied for a three-node system in [1] and
[2], respectively. The outage probability of ANC and TDBC
protocols with optimal relay selection was investigated in [3] for
multi-relay systems. The outage performance of ANC protocol
over Nakagami-m fading channels has been studied for multi-
relay system in [4]. The authors in [5] analyzed the outage
proba bility of ANC proto col in a multiuser two-way relay
system with optimal source scheduling over mixed Rayleigh
and Rician fading channels. For the same scheme, the average
sum rate was derived in [6], when operating over Rayleigh
fading. The authors in [7] studied the outage probability of
TDBC protocol in a multiuser two-way relay system in Rayleigh
fading, where the source scheduling is only based on the direct
links. However, the performance of TDBC protocol has not been
investigated in multiuser two-way relay systems with optimal
source scheduling, even in a Rayleigh fading environmen t.
Manuscript received October 20, 2012. The associate editor coordinating the
review of this letter and approving it for publication was M. Xiao.
This work was supported by the National Basic Research
Program of China (973 Program No. 2012CB316100), NSFC
(No. 60971116/61032002/61002015), the Open Research Fund of State
Key Laboratory of ISN (No. ISN13-04), the NSF of Guangdong Province (No.
S2012010010062), and the 111 project (No. 111-2-14).
X. Lei is with Utah State Uni versity, Logan, Utah, USA. He was with South-
west Jiaotong Uni versity, Chengdu, China (e-mail: xflei81@yahoo.com.cn).
P. Fan is with Southwest Jiaotong University , China (e-mail: p.fan@ieee.org).
L. Fan is with Shantou University, Shantou, China (e-mail: lsfan@stu.edu.cn).
X. Lei and L. Fan are also with the State Key Laboratory of Integrated
Services Networks, Xidian University, Xi’an, China.
D. S. Michalopoulos is with the Unive rsity of British Columbia, Vancouver,
Canada (e-mail: dio@ece.ubc.ca).
R. Q. Hu is with Utah State University, Logan, Utah, USA (e-mail:
rosehu@ieee.org).
Digital Object Identifier 10.1109/LCOMM.2013.020413.122338
A
B
1
B
k
B
K
R
3rd phase
2nd phase
1st phase
Fig. 1. System model.
In this paper, we study the outage probability of the TDBC
protocol in a multiuser two-way relay system with optimal
source scheduling, operating over Nakagami-m fading channels
with integer fading parameters. A tight closed-form lower bound
for the outage probability of the scheme under consideration is
derived. The asy mptotic outage behavior is then investigated
in high signal-to-noise ratio (SNR) regime, providing useful
insights into the system’s diversity order.
Notation: We use CN(0,σ
2
) to denote a circularly symmetric
complex-valued Gaussian random variable with mean 0 and
variance σ
2
. The notation X ∼ Naka(m, α) denotes that the
random variable X follows the Nakagami-m distribution so
that the probability density function (PDF) of Y = |X|
2
is
f
Y
(y)=
m
m
y
m−1
α
m
Γ(m)
e
−
my
α
. Pr[·] denotes p robability. Moreover,
Γ(x) and Γ(α, x) are the Gamma function [8, eq. (6.1.1)] and
incomplete Gamma function [8, eq. (6.5.3)], respectively.
II. S
YSTEM MODEL
The scheme under investigation is depicted in Fig. 1. We
consider a m ultiuser two-way relay system with on e amplify-
and-forward (AF) relay R, in which end-source A intends to
exchange information with one out of other K end-sources B
k
(k =1, 2, ···,K). We use h
B
k
,R
∼ Naka(m
1
,α), h
A,B
k
∼
Naka(m
2
,β) and h
A,R
∼ Nak a(m
3
,ε) to denote the channels
of B
k
-R, A-B
k
and A-R, respectively. All the channels are
reciprocal. Moreover, all terminals have a single antenna and
operate in the half-duplex mode. For each transmission, one
out of K end-sources B
k
is selected to exchange information
with end-source A. Before presenting the selection criteria in
(9), we first give the details on how the TDBC protocol works,
as follows. Assuming B
k
is selected, terminal A will exchange
information with B
k
during three phases. Specifically, in the first
phase, A sends signal s
A
with unit energy, hence the signals
received at R and B
k
can be expressed as
y
(1)
R
= h
A,R
√
Ps
A
+ n
(1)
R
, (1)
y
(1)
B
k
= h
A,B
k
√
Ps
A
+ n
(1)
B
k
, (2)
where P is the transmit power, n
(1)
R
∼CN(0, 1) and n
(1)
B
k
∼
CN(0, 1) are the additive white gaussian noise (AWGN) at the
relay and B
k
, respectively, in the first phase. In the second
1089-7798/13$31.00
c
2013 IEEE
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