3480 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 9, NO. 11, NOVEMBER 2010
MSE-Based Transceiver Designs for the
MIMO Interference Channel
Hui Shen, Member, IEEE, Bin Li, Member, IEEE, Meixia Tao, Member, IEEE, and Xiaodong Wang, Fellow, IEEE
Abstract—Interference alignment (IA) has evolved as a pow-
erful technique in the information theoretic framework for
achieving the optimal degrees of freedom of interference channel.
In practical systems, the design of specific interference alignment
schemes is subject to various criteria and constraints. In this
paper, we propose novel transceiver schemes for the MIMO
interference channel based on the mean square error (MSE)
criterion. Our objective is to optimize the system performance
under a given and feasible degree of freedom. Both the total
MSE and the maximum per-user MSE are chosen to be the
objective functions to minimize. We show that the joint design
of transmit precoding matrices and receiving filter matrices
with both objectives can be realized through efficient iterative
algorithms. The convergence of the proposed algorithms is proven
as well. Simulation results show that the proposed schemes out-
perform the existing IA schemes in terms of BER performance.
Considering the imperfection of channel state information (CSI),
we also extend the MSE-based transceiver schemes for the MIMO
interference channel with CSI estimation error. The robustness
of the proposed algorithms is confirmed by simulations.
Index Terms—MIMO interference channel, transceiver de-
signs, interference alignment, MSE criterion, robustness.
I. INTRODUCTION
W
ITH the rapid d evelopment of wireless communica-
tions, more and more attention is paid to the distributed
multiple-input multiple-output (MIMO) communication sys-
tems. Ear lier studies have determined the degrees of freedom
for various distributed MIMO systems [1-4]. It is shown in
[1] that for a two-user (𝑀
1
,𝑁
1
,𝑀
2
,𝑁
2
) MIMO interference
channel (i.e., a MIMO interference channel with 𝑀
1
,𝑀
2
antennas at the two transmitters and 𝑁
1
,𝑁
2
antennas at the
two receivers), the maximum degree of freedom (DoF) is equal
to 𝑚𝑖𝑛(𝑀
1
+ 𝑀
2
,𝑁
1
+ 𝑁
2
,𝑚𝑎𝑥(𝑀
1
,𝑁
2
),𝑚𝑎𝑥(𝑀
2
,𝑁
1
)).
The network sum capacity for the K-user interference channel
is given by 𝐶
Σ
(𝑆𝑁𝑅)=
𝐾
2
log(𝑆𝑁𝑅)+𝑂(log(𝑆𝑁𝑅)) when
the channel coefficients are random, time-varying and drawn
from a continuous distribution [4].
Manuscript received December 22, 2009; revised May 2, 2010 and August
8, 2010; accepted August 8, 2010. The associate editor coordinating the review
of this paper and approving it for publication was K. K. Wong.
The partial material in this paper was presented in the Proceedings of IEEE
WCNC 2010.
H. Shen and B. Li are with the Department of Corporate Research, Huawei
Technologies Co. Ltd., Shenzhen, P.R. China (e-mail: nickshenhui@sina.com,
binli@huawei.com).
M. Tao is with the Dept. of Electronic Engineering, Shanghai Jiao Tong
University, P.R. China (e-mail: mxtao@sjtu.edu.cn). The w ork of M. Tao
is supported in part by the Shanghai Pujiang Taleng Program under grant
09PJ1406000, and the Shanghai Educational Development Foundation under
grant 2008CG14.
X. Wang is with the Dept. of Electrical Engineering, Columbia University,
Ne w York, USA (e-mail: wangx@ee.columbia.edu).
Digital Object Identifier 10.1109/TWC.2010.091510.091836
Recently, interference alignment has been proposed to
achieve the optimal degree of freedom in single-input single-
output (SISO) interference channel (IC) [4]. Some studies
propose the alignment of multi-user interference at each
receiver based on carefully constructed signal structures [5-7],
which is referred to as interference alignment in signal scale.
Other studies achieve the interference alignment in signal
space [8-12]. For the interference alignment in signal space,
transmit precoding technique is used to align the multi- user
interferences, namely, to restrict all interference to the same
signal space which is separate from the desired signal space
at each receiver.
Interference alignment schemes are p resented in [1] in
the form of the transmit precoding matrices with closed-
form expressions. However, these closed form solutions are
only available in certain cases, such as three-user MIMO
interference channel with the equal number of antennas at each
node and two-user MIMO X channel. Distributed interference
alignment algorithms [8], which require only local channel
knowledge at each node, achieve the interference alignment
by iteratively minimizing leakag e interference or maximizing
signal-to-interference-plus-noise ratio (SINR). An interference
alignment scheme with a linear system of equations based on
least square approach is proposed in [11]. The iterative pre-
coder optimization algorithm using gradient descent method
is proposed in [12] to maximize the sum rate of the K-user
interference channel system.
Interfere nce alignment has the potential application in mit-
igating the inter-cell interference and improving the cell-edge
throughput in wireless system, such as the application to
CoMP (Coordinated Multi-Point Transmission) [13] with con-
strained backhaul connection. But in practical wireless system,
the SNR, especially SNR at the cell edge, is not so high. So
the performance in the low and intermediate SNR region is
essential to the most potential applicability of IA in practical
wireless system. Although the Max-SINR algorithm [8] also
offers improved performan ce compar ed with the distr ibuted IA
[8] in the low and inter mediate SNR region, its convergence
is not guaranteed. Motivated by the imperative performance
improvement in the low and intermediate SNR region, MSE-
based transceiver designs for the MIMO interference channel
are investigated in this paper.
Joint transmitter and receiver desig ns have been well-
studied in the literature [14 -30]. The joint transceiver schemes
for the single-user point-to-point MIMO channel were pro-
posed in [14-18]. The joint transceiver schemes for the MIMO
multiple access ( MAC) channel (uplink) were proposed in
[19,20]. The uplink/downlink MSE duality under a total
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