Nakagami-m fading通道下多用户中继网络的中断概率分析
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收藏 384KB PDF 举报 本文档深入探讨了多用户接力网络（Multiuser Relay Networks, MRNs）在Nakagami-m衰落信道下的性能分析，特别是在单放大转发（Amplify-and-Forward, AF）接力系统中的中断概率。作者Nan Yang、Maged Elkashlan和Jinhong Yuan是IEEE成员，他们对多用户接力网络在不同Nakagami-m分布的衰落条件下的表现进行了详尽且精确的研究。
研究主要关注以下几个关键知识点：
1. **中断概率评估**：作者针对下行链路的MRNs设计了一套全面的分析方法，旨在计算在各种Nakagami-m衰落情况下，网络的中断概率。中断概率是衡量网络可靠性的关键指标，它反映了信号强度不足以支持数据传输时的概率。
2. **闭合形式表达式**：文中提出新的闭合形式公式，用于计算最高端到端信号到噪声比（Signal-to-Noise Ratio, SNR）的分布，特别是当考虑单用户和瑞利衰落作为特殊情况时。这种表达式的简洁性有助于快速估计网络性能，并在实际设计中简化计算。
3. **分组比较**：研究区分了两种不同的增益策略：基于通道状态信息（Channel State Information, CSI）的增益接力和固定的增益接力。通过对比，作者揭示了这两种策略在提高可靠性方面的差异，以及它们如何影响网络的性能。
4. **多样性分析**：文章指出，多用户接力网络能够实现的可达到的多样性等级与第一跳衰落参数、第二跳衰落参数以及目的地数量有关。这意味着通过优化网络配置，可以利用这些参数组合来提升系统的抗干扰能力。
5. **紧凑性与总结**：最后，作者还提供了关于中断概率和最高SNR分布的紧凑近似结果，这不仅方便了理论分析，也简化了实际系统的设计和优化过程。
这篇论文为理解多用户接力网络在Nakagami-m衰落环境下的性能提供了一个坚实的基础，为无线通信网络的设计者和研究人员提供了重要的理论依据。通过掌握这些知识，工程师们可以更好地应对复杂的无线环境挑战，提高网络的可靠性和效率。
2122 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010
first-hop fading parameter or the product of the second-
hop fading parameter and the number of destinations.
5) We derive exact closed-form expressions for the moments
of the highest end-to-end SNR. Based on these new
statistical results, we evaluate other relevant statistics that
characterize the SNR distribution, such as the average
SNR and the amount of fading (AoF).
Our new analytical expressions have the additional merit of
characterizing t he single-user point-to-point dual-hop scenario
as a special case. Moreover, our generalized analysis serves
as a tool to examine the impact of unbalanced hops by tak-
ing into account different per-hop average faded SNRs and/or
different per-hop fading severities on the system performance.
Furthermore, a design criterion is presented to guarantee per-
formance improvements offered by opportunistic scheduling.
Specifically, by varying the per-hop transmission distances, our
results reveal the role of the relay location in determining the
multiuser advantage.
II. S
YSTEM DESCRIPTION
A. Cooperative Transmission and Channel Model
Consider the multiuser wireless relay communication system
depicted in Fig. 1(b). The source communicates with K desti-
nations via the cooperative link with the aid of a single AaF
relay. The direct link between the source and the destinations is
absent. The relay transmission is constrained to a half-duplex
mode, by dividing the transmission period into two consecutive
signaling intervals. In signaling interval 1, the source transmits
the signal to the relay; in signaling interval 2, the relay am-
plifies the received signal with a scaling gain factor and then
forwards the scaled replica toward the destination that has the
most favorable end-to-end channel quality.
We denote the average symbol energies available at the
source and the relay as E
S
and E
R
, respectively. Furthermore,
let the modulated signal transmitted by the source be denoted as
x. In signaling interval 1, the received signal at the relay from
the source can be represented as
y
r
=
E
S
d
−η
SR
αx + n
r
(1)
where α denotes the channel complex fading coefficient be-
tween the source and the relay, and n
r
is the additive white
Gaussian noise (AWGN) component with variance N
0
at the
relay. The path loss is incorporated in the signal propagation,
where d
SR
is the distance between the source and the relay, and
η is the path loss exponent. We define G as the scaling gain
applied at the relay. Hence, in signaling interval 2, the received
signal at the kth destination from the relay is expressed as
y
d
=
E
R
d
−η
RD
β
k
G
E
S
d
−η
SR
αx + n
r
+ n
d
k
(2)
where β
k
denotes the channel complex fading coefficient be-
tween the relay and the kth destination, n
d
k
is the AWGN com-
ponent with variance N
0
at the kth destination, and d
RD
is the
distance between the relay and the destination. Accordingly, the
equivalent instantaneous end-to-end SNR of the kth destination
γ
eq,k
can be obtained from (2) as
γ
eq,k
=
γ
1
γ
2,k
γ
2,k
+
1
G
2
N
0
(3)
where γ
1
= |α|
2
d
−η
SR
E
S
/N
0
, and γ
2,k
= |β
k
|
2
d
−η
RD
E
R
/N
0
are
the instantaneous faded SNRs of the first and second hop,
respectively. From (3), we note that γ
eq,k
is influenced by the
choice of G.
The pdf of the per-hop instantaneous faded SNR Z =
{γ
1
,γ
2,k
} follows a gamma distribution, i.e.,
f
Z
(γ)=
m
m
i
i
γ
m
i
−1
γ
m
i
i
Γ(m
i
)
e
−
m
i
γ
i
γ
(4)
where Γ(·) is the gamma function defined by [17, eq. (8.310.1)]
as Γ(x)=
∞
0
t
x−1
e
−t
dt. The average faded SNR of the first
and second hops is given by
γ
1
= E[γ
1
] and γ
2
= E[γ
2,k
],
respectively, where E[·] is the expectation. The fading param-
eter of the first and second hops is denoted as m
1
and m
2
,
respectively.
It is assumed that the destinations are located within the same
fading environment. In such a homogeneous environment, all
the destinations have the same per-hop fading severity m
2
and
per-hop average faded SNR
γ
2
. On the other hand, the dual-
hop transmission is assumed unbalanced, where the first and
second hops experience different per-hop average faded SNRs
(i.e.,
γ
1
= γ
2
) and/or different per-hop fading severities (i.e.,
m
1
= m
2
). This is typical in most relay applications, where
the relay and the destinations are located in different fading
environments.
The corresponding cdf of Z can be written as
F
Z
(γ)=
γ
m
i
,
m
i
γ
i
γ
Γ(m
i
)
=1−
Γ
m
i
,
m
i
γ
i
γ
Γ(m
i
)
(5)
where γ(·, ·) is the lower incomplete gamma function defined
by [17, eq. (8.350.1)], and Γ(·, ·) is the upper incomplete
gamma function defined by [17, eq. (8.350.2)].
B. Opportunistic Scheduling in Cooperative Transmission
Time-division multiple access (TDMA) is assumed to facil-
itate the sharing of the downlink channel among the multiple
destinations. Specifically, we adopt the opportunistic multiuser
scheduling proposed in [9]. In this policy, only one destination
with the highest instantaneous end-to-end SNR out of K des-
tinations is scheduled for transmission. This policy holds for a
number of time-slotted downlink multiuser systems including
Qualcomm’s HDR [18] and high-speed downlink packet access
[19]. In this case, if γ
s
denotes the highest instantaneous
end-to-end SNR of the scheduled destination (i.e., strongest
destination), then the policy is formulated as
γ
s
= max
1≤k≤K
{γ
eq,k
} (6)
where γ
eq,k
is defined in (3).
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