卫星通信中的硬件损伤与干扰影响分析
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"这篇论文研究了在硬件损坏和干扰下，使用双跳解码转发（DF）协议的陆地移动卫星（LMS）通信系统的性能。在Shadowed-Rician（SR）衰落信道环境中，文章建立了一个实用的卫星中继系统模型，考虑了多波束卫星天线、无线电传播损耗以及随机阴影效应。通过假设卫星受到硬件损伤（HIs）和干扰信号的影响，作者推导出了系统的端到端信号与干扰加噪声和失真之比的等效表达式。进一步，他们证明在提出的HIs模型上，源端的最大比率传输和目的端的最大比率组合是最佳的波束成形策略。此外，论文还得到了在独立且均匀分布的平方SR随机变量之和的条件概率密度函数（PDF），并且在有理Nakagami-m衰落参数下，给出了中断电概率（OP）和平均吞吐量的新分析表达式。在高信噪比下，研究了渐近OP和平均吞吐量，以确定系统的分集阶数。最后，通过蒙特卡洛模拟验证了分析结果的准确性。"
本论文探讨的核心知识点包括：
1. **双跳解码转发（DF）协议**：这是一种中继通信策略，其中中继节点首先接收源节点的信号，解码其内容，然后编码并转发到目的地。这种协议在无线通信中用于改善链路质量和可靠性。
2. **陆地移动卫星（LMS）通信**：这是一种通过卫星进行的移动通信方式，适用于地面移动设备，如车载或手持设备，与卫星之间的通信。
3. **Shadowed-Rician（SR）衰落信道**：这是一种更复杂的信道模型，考虑了信号传播中的多径效应、阴影效应以及多普勒频移等因素，更真实地反映了实际通信环境。
4. **硬件损伤（HIs）**：这是指由于硬件组件老化、非理想特性或制造缺陷导致的信号质量下降，如非线性失真、相位噪声等。
5. **干扰信号**：在无线通信中，来自其他信号源的无用信号，可能导致接收端信号质量下降。
6. **最大比率传输/组合**：在多天线通信系统中，通过调整源端和目的端的发射和接收波束成形权重，以最大化信号能量，从而提高通信性能。
7. **中断电概率（OP）**：衡量通信系统在特定信噪比下发生错误的概率，是评估系统可靠性的关键指标。
8. **平均吞吐量**：通信系统在给定时间内能够传输的数据量的平均值，反映系统的数据传输效率。
9. **Nakagami-m衰落**：一种通用的多径衰落模型，可以覆盖Rayleigh、Rician等多种特定衰落情况，m值表示衰落的严重程度。
10. **分集阶数**：在高信噪比下，表示系统能从多径传播中获得的增益，是衡量系统抗衰落能力的指标。
论文通过理论分析和模拟验证，深入研究了在复杂通信环境下LMS系统性能，为设计更加稳健的卫星通信系统提供了理论支持。
GUO et al.: ON THE PERFORMANCE OF LMS COMMUNICATION 1493
where P
s
denotes the transmit power at S, f
u,k
∈ C
N
1
×1
the
uplink channel vector between the multi-antenna source and
the k-th satellite beam; P
j
the transmit power of the j-th inter-
ference; x
j
(t) the j-th interference with unit average power
E
|x
j
(t)|
2
=1, f
j,k
the interference link channel coefficient
from the j-th interferer to the k-th beam; η
1
(t) the distortion
noise term due to the satellite receive HIs, and n
1
(t) ∼
CN
0,δ
2
1
is the additive white Gaussian noise (AWGN)
at R, with variance δ
2
1
given by δ
2
1
= KTB; K, T , B
being the Boltzmann’s constant, receive noise temperature,
and noise bandwidth, respectively. According to [33], η
1
(t)
is often modeled as η
1
(t) ∼CN(0, Υ
1
), with Υ
1
given by
Υ
1
= k
r
P
s
f
H
u,k
w
1
2
+
M
j=1
k
I
P
j
|f
j,k
|
2
, (5)
where the coefficients k
r
and k
I
are introduced to characterize
the aggregate level [51] for the received impairments at R from
the source signal power and interference power, respectively.
2
In the second time slot, the regenerative satellite first
exploits the DF relaying protocol to decode the signal s (t)
from y
r,k
(t) correctly, and then forwards it to the D through
the l-th on-board beam and the corresponding downlink chan-
nel. Similarly, by considering the effect of transmit impair-
ments, the output signal at D can be written as
y
d,l
(t)=
P
r
w
H
2
f
d,l
(s (t)+η
2
(t)) + w
H
2
n
2
(t), (6)
where P
r
is the transmit power of the l-th on-board beam,
w
2
∈ C
N
2
×1
obeying w
2
2
=1is the destination BF
weight vector used to enhance the received signal power,
f
d,l
∈ C
N
2
×1
is the downlink channel vector between the
l-th satellite beam and D, η
2
(t) is the additional distortion
noise term due to satellite transmit HIs which is modeled as
η
2
∼CN(0, Υ
2
) with Υ
2
= k
t
, where the coefficient k
t
characterizes the aggregate level of HIs, and finally n
2
(t) ∼
CN
0,δ
2
2
I
stands for the AWGN vector with δ
2
2
= KTB.
C. Problem Formulation
Here we employ the above described system and signal
models to derive the optimal transmit and receive BF
such that the output signal-to-interference-plus-noise-and-
distortion-ratio (SINDR) is maximized. By using (1) and (4),
the SINDR at the k-th satellite beam can be expressed as
γ
1,k
=
P
s
f
H
u.k
w
1
2
k
r
P
s
f
H
u,k
w
1
2
+(1+k
I
)
M
j=1
P
j
|f
j,k
|
2
+ δ
2
1
=
P
s
C
k
h
H
u,k
w
1
2
k
r
P
s
C
k
h
H
u,k
w
1
2
+(1+k
I
)
M
j=1
P
j
|f
j,k
|
2
+ δ
2
1
. (7)
Since γ
1,k
is monotonously increased with C
k
h
H
1
w
1
2
,
the max output SINDR in (7) is obtained when both
2
In this paper, we assume that each interference ES is equipped with a
parabolic antenna. However, our analysis can be directly extended to the case
of multi-antenna ES.
C
k
and
h
H
u,k
w
1
2
are max. According to (3), it can be
found that the satellite beam gain is determined by the source
position. By considering that the locations of all earth stations
are available at the gateway [49], the on-board beam with
θ
k
→ 0 is selected to receive the signal from the source
during the first time slot, resulting in G
k
≈ G
max
. Meanwhile,
in order to obtain the optimal transmit BF weight vector w
1
,
we formulate a constrained optimization problem as
arg max
w
1
h
H
u,k
w
1
2
, (8a)
s.t. w
1
2
=1. (8b)
From [52], we know that when w
1
=
h
u,k
h
u,k
,
h
H
u,k
w
1
2
gets the largest value. By substituting w
1
=
h
u,k
h
u,k
into (7)
and after some necessary computations, the max outage
SINDR at R can be expressed as
γ
max
1,k
=
γ
s
γ
s
k
r
+ γ
I
(1 + k
I
)+1
, (9)
where γ
s
= P
s
C
max
h
u,k
2
/δ
2
1
Δ
=
γ
s
h
1
2
and γ
I
=
M
j=1
P
j
|f
j.k
|
2
/δ
2
1
Δ
=
γ
I
M
j=1
|f
j,k
|
2
.
In a similar manner, when the l-th beam with θ
l
→ 0 is used
to transmit the signal to D, and when w
2
= h
d.l
/h
d.l
2
is
chosen as the receive BF weight vector at the D, the max
output signal-to-noise-and-distortion-rate (SNDR) at D can be
written as
γ
max
2,l
=
γ
r
γ
r
k
t
+1
, (10)
where γ
r
= P
r
C
max
h
d,l
2
/δ
2
2
Δ
=
γ
r
h
2
2
. In the sequel,
we will use γ
1
to replace γ
max
1,k
and γ
2
to replace γ
max
2,l
for brevity. Thus, the equivalent end-to-end SINDR of the
regenerative satellite-based relay system with DF protocol is
given by
γ
e
=min
γ
max
1,k
,γ
max
2,l
Δ
=
min (γ
1
,γ
2
). (11)
III. S
TATISTICAL PROPERTIES OF SATELLITE CHANNELS
According to [3], the probability density function (PDF) of
γ
i
= γ
i
|h
i
|
2
with |h
i
|
2
Δ
=
[h
k
]
i
being the i-th element of SR
channel vector h
k
is given by
f
γ
i
(x)=
α
i
γ
i
e
−
β
i
γ
i
x
1
F
1
m
i
;1;
δ
i
γ
i
x
,x>0, (12)
where
1
F
1
(a
1
; b
1
; z) denotes the confluent hyper-
geometric function defined in [53, eq. (9.210)].
α
i
=
2b
i
m
i
2b
i
m
i
+Ω
i
m
i
/2b
i
, β
i
=
1
2b
i
, δ
i
=
Ω
i
2b
i
(2b
i
m
i
+Ω
i
)
with Ω
i
, 2b
i
and m
i
≥ 0 being the average power of the LOS
component, the average power of the multi-path component,
and the fading severity parameter ranging from 0 to ∞,
respectively [54]. In what follows, by considering two cases
of m
i
, namely, integer and rational, we will discuss the PDF
expressions of γ =
N
i=1
γ
i
in detail.
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