大规模MIMO IQI抑制：宽线性预编码算法与性能
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"在无线通信领域，尤其是在大规模多输入多输出（MIMO）系统中，同相/正交相位（IQ）不平衡（IQI）是一个常见的问题，它会严重影响系统的性能。本文深入探讨了如何利用广泛线性预编码技术来缓解这一问题。作者Wence Zhang等人提出了一种实值信号模型，该模型充分考虑了发射机端的IQI影响，并基于此开发了四种不同的广泛线性预编码算法：宽线性零强迫（WL-ZF）、宽线性匹配滤波器、宽线性最小均方误差（WL-MMSE）以及宽线性块对角化（WL-BD）。这些算法不仅适用于单天线用户，也适用于多天线用户。
在无IQI情况下，WL-ZF的复用增益和功率偏移与传统的零强迫（ZF）预编码完全一致。然而，当存在IQI时，WL-ZF能保持与理想IQ分支下的ZF预编码相同的复用增益，但其功率损失相对较小，损失程度与系统规模及IQ参数有关。此外，文章还对比了WL-BD与传统块对角化（BD）预编码的性能。分析显示，理想IQ条件下，WL-BD的数据速率与BD相同；而在有IQI的情况下，WL-BD能保持与BD相同的复用增益，同时避免了由IQ失衡带来的问题。
通过数值模拟，作者验证了理论分析的结果，证实了提出的广泛线性预编码方法在处理IQI方面明显优于传统方法，并且在性能上接近于假设理想IQ分支的情况。这些发现对于优化大规模MIMO系统在实际环境中的性能，特别是在存在IQI的情况下，提供了重要的理论支持和技术解决方案。"
这篇研究论文深入剖析了IQI对大规模MIMO系统性能的影响，并提出了有效的广泛线性预编码策略，旨在改善系统效率并降低功耗。这些算法的创新之处在于它们能够在考虑实际IQI影响的同时，保持接近理想情况的性能，从而为无线通信领域的工程实践提供了有价值的理论指导。
3300 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 16, NO. 5, MAY 2017
The numerical results are given in Section V and conclusions
are drawn in Section VI.
Notation: C
N
and C
N×M
denote the sets of N-dimensional
complex vectors and N × M complex matrices, respectively;
R
N
and R
N×M
denote the sets of N-dimensional real vectors
and N × M real matrices, respectively; (·)
∗
is the complex
conjugate; I
N
denotes an N × N identity matrix; CN (θ , )
denotes circularly symmetric complex Gaussian distribution
with mean θ and covariance ; U(a, b) denotes the uniform
distribution and N (a, b) denotes the Gaussian distribution,
where a and b are the mean and variance, respectively;
diag{a
1
, ···, a
K
} denotes a diagonal matrix with diagonal
entries given by a
1
, ···, a
K
; E{·} denotes the mathematical
expectation and Tr[·] denotes the trace of a matrix A.
II. S
YSTEM MODEL
Consider the downlink of a large-scale MIMO system with
one BS and K users. The BS is equipped with N antennas, and
there are M
k
antennas at the k-th user. Define M =
K
k=1
M
k
as the total number of antennas at all the users. Consider
the IQI at all the N transmit antennas at BS,
1
and for the
n-th antenna, the transmit symbol x
n
is corrupted by IQI as
a
n1
x
n
+ a
n2
x
∗
n
,wherea
n1
and a
n2
are the IQ parameters of
the n-th antenna that are modeled as [6]:
a
n1
=
1
1 + σ
2
g
[cos(θ
n
/2) + jg
n
sin(θ
n
/2)],
a
n2
=
1
1 + σ
2
g
[g
n
cos(θ
n
/2) − jsin(θ
n
/2)], (1)
where θ
n
∼ U(0,σ
2
θ
) and g
n
∼ N (0,σ
2
g
) are the relative
phase and gain mismatches between the IQ branches of the
n-th transmit antenna, respectively. The IQ parameters are
normalized so that they do not change the average signal
power. A proof of the selection of the normalization factor
is given in Appendix A. In (1), θ
n
= 0
◦
and g
n
= 0represent
the ideal case with no IQI. Note that although the Gaussian
and uniform distributions are considered for modeling IQ
parameters, the proposed algorithms and the performance
analysis are valid for other distributions.
If we consider the IQI at BS, the received signal y
k
∈ C
M
k
at the k-th user is given by
y
k
= H
k
A
1
x + H
k
A
2
x
∗
+ n
k
, (2)
where H
k
∈ C
M
k
×N
is the downlink channel matrix of
the k-th user, the elements of which are independent and
identically distributed (i.i.d.) Gaussian random variables with
zero-mean and unit variance; A
1
= diag{a
11
, ···, a
N1
} and
A
2
= diag{a
12
, ···, a
N2
}; n
k
∼ CN (0,σ
2
n
I
M
k
) is the noise
vector at the receiver; x ∈ C
N
is the transmit signal vector
after precoding. Here we consider a narrow-band single-
carrier system for simplicity and the extension to multi-carrier
systems remains open for future work.
1
The IQI at the user’s receiver only degrades its own signal and can be
addressed individually by IQI compensation techniques [8]. In contrast, the
IQI at the BS affects all the users and is severe in large-scale MIMO systems
due to the potential use of cheap hardware for cost issues. Therefore, we only
consider the IQI at the BS in this paper.
Let L
k
be the number of data streams of user k and
P
k
∈ C
N×L
k
, s
k
∈ C
L
k
be the precoder and the transmit
signal vector for the k-th user, respectively. Denote P =
[P
1
, ···, P
K
], s =[s
T
1
, ···, s
T
K
]
T
, and we have
x = Ps.
Note that in contrast to single-antenna users using ZF, MMSE
or MF, in the case of multiple-antenna users using BD type
precoders, a receive filter matrix is generally required to
decode the multiple streams which is designed together with
the precoder, as will be detailed later in Section III.
In this paper, we assume that the transmitter has perfect
channel state information and the transmit signals for different
users are i.i.d circularly symmetric Gaussian random variables
with zero-mean and unit variance, i.e., ∀k = j, E{s
k
s
H
j
}=0,
and E{s
k
s
H
k
}=I
L
k
. We also assume there is a transmit power
constraint, i.e.,
E{Ps
2
}=P
T
. (3)
It can be seen from (2) that the transmit signal vector is
corrupted by its complex conjugate. In the frequency domain,
a mirror frequency component is introduced due to the IQI.
One possible way of handling such IQI resorts to estimation
of the corresponding IQ parameters and pre-compensation
for the IQI [6], [7]. Since the signal model of (2) gives
rise to non-circular data which can be exploited by widely-
linear processing, IQI can also be tackled by widely-linear
approaches [5], [17].
In what follows, we will devise and carry out a performance
analysis of widely-linear precoding schemes, which are able
to mitigate the IQI without significantly increasing the com-
putational complexity.
III. P
ROPOSED WIDELY-LINEAR
PRECODING ALGORITHMS
In this section, we employ a useful transformation,
i.e., the T -transform from [36] and [37], which represents
complex-valued matrices and vectors using their real-valued
equivalents. Then we employ the T -transform to develop an
equivalent real-valued signal model, which helps to design
widely-linear precoding schemes. Several widely-linear pre-
coding algorithms such as WL-ZF, WL-MMSE, WL-BD,
WL-RBD and WL-S-GMI are then developed.
A. Real-Valued Signal Model
A mapping function of C
n
→ R
2n
and C
m×p
→ R
2m×2p
,
namely the T -transform, is defined as:
T (x) =
Re(x)
Im(x)
, T (X) =
Re(X) −Im(X)
Im(X) Re(X)
, (4)
where Re(·) and Im(·) represent the real and imaginary parts
of a vector or a matrix, respectively. The T -transform sets
up a relationship between the complex-valued matrices and
their real-valued counterparts. It is very useful for design
and performance analysis of widely-linear precoders. Some
properties of the T -transform are summarized in Lemma 1,
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