全双工大规模MIMO中继系统：功率缩放与性能分析
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更新于2024-07-15
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本文主要探讨了全双工（FD）两路大规模多输入多输出（MIMO）中继系统在具有相关天线和最大比率组合/最大比率传输（MRC/MRT）处理的情况下的性能分析。该研究突破了以往的分析框架，特别关注了多对MIMO用户和中继用户之间的天线相关性对系统性能的影响。
首先，作者针对一个流行的线性中继策略——最大比率组合/最大比率传输（MRC/MRT）进行深入研究。通过分析，他们推导出了一般情况下系统的渐近求和率，这有助于理解系统在不同条件下的行为。研究着重于四种特殊的功率缩放情况，通过简化的形式展示了这些情况下的渐近求和速率，揭示了自环干扰、组内干扰以及天线相关性对系统性能的具体影响。
值得注意的是，他们的研究发现了一个重要的功率缩放定律：在中继器处的天线数量增加的同时，如果适当调整MIMO用户和中继器的发射功率，可以维持合理的总速率。这种灵活性对于优化网络资源分配具有实际意义。
进一步的对比分析显示，当处于特定的功率缩放条件下，全双工（FD）系统相较于半双工（HD）系统能够实现两倍的总和速率，体现出FD技术在容量提升方面的优势。然而，在其他两种功率缩放情况下，由于自环干扰和组内干扰的存在，FD系统的性能可能劣于HD系统。作者明确了允许的最大自环干扰水平，这对于设计和实施FD系统时避免性能下降至关重要。
此外，文中还深入探讨了天线相关性对用户和中继器性能的影响。在某些功率缩放情况下，用户处的天线相关性对求和率的影响变得复杂，这为优化天线配置和设计提供了新的视角。这项研究为理解并优化FD两路大规模MIMO中继系统的性能，尤其是在考虑天线相关性和干扰管理方面，提供了详尽的理论支持。
FENG et al.: POWER SCALING OF FD TWO-WAY MASSIVE MIMO RELAY SYSTEMS WITH CORRELATED ANTENNAS AND MRC/MRT PROCESSING 4741
y
S
i
(n) =
√
P
S
√
M
u
H
RS
i
FH
S
¯
i
R
s
¯
i
(n − δ)
1
+
√
P
S
√
M
u
H
RS
i
F
2K
j=i,
¯
i
H
S
j
R
s
j
(n − δ)
2
+
j∈
i
/i
√
P
S
√
M
u
H
S
j
S
i
s
j
(n)
3
+ H
RS
i
FH
RR
x(n − δ)
4
+
√
P
S
√
M
u
H
S
i
S
i
s
i
(n)
5
+H
RS
i
Fn
R
(n − δ)
6
+n
S
i
(n)
7
. (5)
length of the training sequences scales linearly with the
number of antennas at the users, but not with the number
of massive antennas at the relay. When the training sequences
are sufficient long, the accuracy of channel estimation is very
high and channel estimation errors can be ignored. Thus here
we assume both the users and the relay have the perfect cross
CSI, i.e., H
S
i
R
and H
RS
i
.
After the self-interference cancellation, the received signal
at the user node S
i
becomes (5), shown at the top of this page.
In (5), the first term
1
is the desired received signal,
the second term
2
is inter-pair interference, the third term
3
is intra-group interference, the fourth term
4
is the propagated
residual self-loop interference from the relay node, the fifth
term
5
is the residual self-loop interference at the user node
S
i
, the sixth term
6
is the propagated noise from the relay,
and the last term
7
is the noise at the user node S
i
.
B. Channel Model
Due to insufficient antenna spacing and scattering, spatial
correlation among antennas generally occurs and is considered
in this paper. Following the Kronecker model [20], [30],
the channels can be generally expressed as
H
AB
= R
1
2
B
W
AB
T
1
2
A
, A, B = R, S
i
, S
j
. (6)
In (6), W
AB
consists of independent and identically distrib-
uted (i.i.d.) Gaussian random entries with zero mean. When
A = B and neither A nor B equals to R, W
AB
is associated
with the channel from the user A to the user B and the variance
of its elements is μ
2
.WhenA = B and one of A and B equals
to R, W
AB
is associated with the cross channel between users
and the relay and the variance of its elements is γ
2
, while
when A = B, W
AB
is corresponding to the self-loop channel
at the node and the variance of its elements is α
2
.Onthe
other hand, R
B
and T
A
are deterministic nonnegative definite
matrices, characterizing the receiving antenna correlation at
the node B and the transmitting antenna correlation at the
node A, respectively. Without loss of generality, we assume
the correlation matrices R
B
and T
A
are normalized such
that tr(R
S
i
) = N
u
,tr(T
S
i
) = M
u
,fori = 1, 2, ···, 2K ,
and tr(R
R
) = N
R
,tr(T
R
) = M
R
. Moreover, the relay’s
antenna correlation matrices R
R
and T
R
have uniformly
bounded spectral norms, i.e., lim sup
N
R
R
R
≤R < ∞
and lim sup
M
R
T
R
≤T < ∞ [31]. These assumptions
are practical and have been widely adopted in [32] and [33].
Notice that the Kronecker model in (6) is valid for MIMO
channels with arbitrary number of antennas when there is a
physical separation between the transmitting antennas and the
receiving antennas as shown in [20], [30], and [34]. Since we
assume different sets of antennas are used for transmission
and reception respectively at each node, i.e., the transmitting
antennas are physically separated from the receiving antennas
at each node, the Kronecker model is also applicable to the
self-loop channel [20].
C. Amplifying Matrix F
In the considered system, the relay amplifies the received
signal and forwards it to all users simultaneously. One popular
AF scheme with low complexity, i.e., maximum ratio combin-
ing and maximum ratio transmission (MRC/MRT), is adopted
here. Notice that the amplifying matrix F can also be designed
based on other criteria, e.g., zero-forcing and minimum mean
square error, etc.. The analysis of other schemes can be easily
extended from our work. With the CSI corresponding to
the links between the users and the relay, H
RS
i
and H
S
i
R
,
i = 1, 2, ···, 2K , the MRC/MRT amplifying matrix is
designed as
F = β
F, (7)
where β is the amplification factor which is set to satisfy the
relay’s transmission power constraint tr(E(x(n)x
†
(n))) = P
R
and
F is given as [15]
F = H
H
H
†
BC
PH
H
H
†
MAC
. (8)
In (8), H
H
H
BC
=
H
T
RS
1
H
T
RS
2
... H
T
RS
2K
T
∈ C
(2KN
u
)×M
R
denotes the broadcast channel (BC) response from the relay
to all users, while H
H
H
MAC
=
H
S
1
R
H
S
2
R
... H
S
2K
R
∈
C
N
R
× (2KM
u
)
denotes the multiple access channel (MAC)
response from users to the relay node, P is a block permutation
matrix as P = diag(P
1
, P
2
,...,P
K
),inwhichP
k
has the form
of
P
k
=
0
N
u
,M
u
P
2k−1
P
2k
0
N
u
,M
u
(9)
where
P
2k−1
,
P
2k
∈ C
N
u
×M
u
are general permutation matri-
ces with binary elements and characterize the information
exchange between the kth pair of users (2k − 1, 2k).
With (1), (2), and the knowledge of cross CSI (i.e., H
RS
i
and
H
S
i
R
), the relay’s power constraint tr(E(x(n)x
†
(n))) = P
R
can
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