大规模CSIT下的多小区虚拟MIMO协调传输优化与性能提升
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更新于2024-07-14
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本文主要探讨了"多小区分布式天线系统（Multi-Cell Distributed Antenna System, DAS）中的虚拟多输入多输出（Virtual Multiple Input Multiple Output, V-MIMO）技术在具有大规模通道状态信息（Channel State Information at the Transmitter, CSIT）条件下的协调传输策略"。随着V-MIMO技术在多小区环境中展现出强大的干扰抑制潜力，其性能提升的关键挑战之一是如何有效地获取和利用CSIT，特别是对于动态变化的快速小尺度信道信息。
传统的V-MIMO系统依赖于精确的CSIT，但其带来的系统开销巨大，特别是在大规模网络中。然而，本研究关注的是一个更实际的情景，即在传输过程中，只需要接收端处理的快速变化的小尺度CSIT，而发送端则主要依赖于相对稳定的大规模CSIT。这种情况下，优化重点转向了如何通过协调传输来最大化系统的有效率，例如通过联合优化所有移动终端（Mobile Terminals, MTs）的输入协方差矩阵。
作者们提出了一种协同传输策略，旨在在大规模CSIT的支持下，通过对MT们的信号处理进行优化，以实现更高的信道利用率和系统容量。他们考虑的是长期平均性能，也就是 Ergodic Sum Rate，这是一种衡量通信系统性能的重要指标，它考虑了时间上的随机性和空间上的多路径效应。
具体来说，文中可能包含了以下知识点：
1. **虚拟MIMO的优势与挑战**：阐述了V-MIMO如何通过分布式天线阵列改善系统性能，以及在多小区环境下如何利用大尺度CSIT来减少干扰。
2. **大规模CSIT的假设与意义**：讨论了为何仅需关注大尺度信道参数，这有助于降低系统开销，并在一定程度上简化了信道估计和反馈过程。
3. **协调传输策略**：提出了优化MTs输入协方差矩阵的方法，以提高信号的空间复用和频谱效率，即使在有限的CSIT条件下也能实现性能提升。
4. **目标函数与优化算法**：可能介绍了如何设计数学模型，如求解多用户优化问题，以找到最接近最大Ergodic Sum Rate的输入配置。
5. **仿真结果与分析**：展示了在所提策略下的性能对比，以及与其他传统方法如独立传输或不协调传输的比较，从而验证了大规模CSIT对虚拟MIMO协调传输的有效性。
6. **潜在的应用前景**：文章可能还探讨了这项研究对未来多小区网络、无线通信标准以及分布式天线系统的设计和实施的影响。
总结来说，这篇文章深入研究了如何在多小区分布式天线系统中通过大规模CSIT支持下的协调传输，优化无线网络性能，为解决实际通信场景中的复杂问题提供了理论基础和技术指导。
FENG et al.: VIRTUAL MIMO IN MULTI-CELL DISTRIBUTED ANTENNA SYSTEMS: COORDINATED TRANSMISSIONS WITH LARGE-SCALE CSIT 2069
Remote antenna (RA)
Mobile terminal (MT
)
Central processor (CP)
Intra-cell system backhaul
Inter-cell system backhaul
Fig. 1. Illustration of a multi-cell DAS.
II. SYSTEM MODEL
As illustrated in Fig. 1, the system model for a multi-cell
DAS consists of K cells (indexed with 1, ..., K), and in cell
k,thereareN
k
RAs and an MT
2
equipped with M
k
antennas.
A full-fledged intra-cell system backhaul (e.g., using optical
fibers [45]) is assumed to support the joint signal processing at
the CP within each cell. Moreover, a limited system backhaul
(e.g., using the standardized interface named X2 [45]) is
assumed across the cells so that the large-scale CSIT and some
control signaling needed for coordinated transmissions can be
shared among different CPs.
The received signal of the MT in cell k in the downlink
can be written as
y
(k)
= H
(k,k)
x
(k)
+
K
i=1,i=k
H
(k,i)
x
(i)
+ n
(k)
, (1)
where H
(k,i)
∈ C
M
k
×N
i
denotes the channel matrix between
the RAs in cell i and the MT in cell k, x
(i)
∈ C
N
i
×1
is
the transmit signal for the MT in cell i,andn
(k)
represents
the additive white Gaussian noise with independent entries
distributed according to CN(0,σ
2
). Assuming a total transmit
power constraint for each cell, we have that
tr
E[x
(k)
x
(k)
H
]
= tr(Φ
(k)
) ≤ P
(k)
, (2)
where Φ
(k)
0 denotes the input covariance for the MT in
cell k,andP
(k)
is the transmit power constraint for cell k.
For all k, i =1, ..., K, H
(k,i)
can be modeled as [22][23]
H
(k,i)
= S
(k,i)
L
(k,i)
, (3)
where S
(k,i)
and L
(k,i)
represent the small-scale and the
large-scale fading effects, respectively. The entries of S
(k,i)
are independent and identically distributed (i.i.d.) according
to CN(0, 1). L
(k,i)
is a diagonal matrix, i.e., L
(k,i)
=
2
There can be multiple MTs in each cell that are served in orthogonal
resource blocks, e.g., different subcarriers for an orthogonal frequency di vi-
sion multiplexing access (OFDMA) system [44], and this work focuses on a
particular resource block.
diag
l
(k,i)
1
, ..., l
(k,i)
N
i
, the entries of which can be expressed
as
l
(k,i)
n
=
D
(k,i)
n
−γ
F
(k,i)
n
,n=1, ..., N
i
, (4)
where D
(k,i)
n
and γ represent the distance and the path-
loss exponent, respectively, and F
(k,i)
n
denotes the shadowing
effect.
III. T
HE COORDINAT ED TRANSMISSION PROBLEM
In this section, we first formulate the coordinated transmis-
sion problem in Section III-A. The problem comes out to be
a quite challenging non-convex problem with a complicated
non-closed-form objective function. In Section III-B, we recast
the problem equivalently as a Max-Min problem, which is
more tractable, allowing us to find a solution via optimization
techniques.
A. Problem Formulation
Base on (1), the interference plus noise suffered by the MT
in cell k can be expressed as
z
(k)
=
K
i=1,i=k
H
(k,i)
x
(i)
+ n
(k)
. (5)
Then, combining (2) and (5), we conclude that the following
sum rate is achievable [13][46]-[49]
R(Φ)=
K
k=1
log
2
det
H
(k,k)
Φ
(k)
H
(k,k)
H
+ Z
(k)
det
Z
(k)
, (6)
where Φ = diag
Φ
(1)
, ..., Φ
(K)
,and
Z
(k)
=
K
i=1,i=k
H
(k,i)
Φ
(i)
H
(k,i)
H
+ σ
2
I
M
k
, (7)
is the covariance matrix of z
(k)
.
When only the large-scale CSIT {L
(k,i)
|k, i =1, ..., K} is
available, the achievable ergodic sum rate, i.e., the achievable
sum rate averaged over the random small-scale CSIT S =
{S
(k,i)
|k, i =1, ..., K}, is of great interest for the system
performance [26][50]. Based on (6) and (7), the achievable
ergodic sum rate can be expressed as (8) on the top of the
next page.
It can be seen from (8) that the input covariances for all
the MTs, i.e., Φ
(1)
, ..., Φ
(K)
, should be jointly optimized so
as to maximize the achievable ergodic sum rate. Under the
transmit power constraint for each cell as expressed in (2),
the coordinated transmission problem can be formulated as
(P1) max
Φ
¯
R(Φ) (9a)
s.t. tr(Φ
(k)
) ≤ P
(k)
, (9b)
Φ
(k)
0,k =1, ..., K. (9c)
It is easy to observe from (8) that
¯
R(Φ) is neither concave
nor convex with respect to {Φ
(k)
|k =1, ..., K} because of
the strong coupling between different cells caused b y ICI. In
addition, due to the expectation operator,
¯
R(Φ),asshown
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