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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 1
Joint Beamforming and Antenna Subarray
Formation for Non-Regenerative MIMO Relay
Networks
Qi Zhang, IEEE Member, Xinpeng Zeng, Quanzhong Li, and Jiayin Qin
Abstract—Antenna subarray formation (ASF) is a complexity
reducing technique for multiple-input-multiple-output (MIMO)
receivers. For non-regenerative MIMO relay networks, we pro-
pose a joint beamforming and ASF scheme in this correspondence
which maximizes the achievable rate subject to transmit power
constraints at the source and the relay, and limited number of
nonzero elements in the ASF matrix. By relaxing the constraint
of limited number of nonzero elements in the ASF matrix, we
decouple the joint beamforming and ASF design problem into
three problems and propose to alternatively optimize beamform-
ing matrices at the source and the relay, and the ASF matrix. We
also propose a gradient projection algorithm to solve non-linear
programming of relay beamforming design problem. Simulation
results demonstrate that the proposed joint beamforming and
ASF scheme outperforms antenna selection scheme.
Index Terms—Antenna subarray formation (ASF), antenna
selection (AS), beamforming, multiple-input-multiple-output
(MIMO), relay networks.
I. INTRODUCTION
M
Ultiple-input-multiple-output (MIMO) relay networks
were proposed to improve the overall end-to-end
throughput [1]–[6]. However, MIMO technique significantly
increases hardware cost because each antenna requires a radio
frequency (RF) chain which is expensive. One way to reduce
the number of required RF chains in MIMO system is to
employ antenna selection (AS) scheme [6]–[8]. The key idea
of AS is selecting the most advantageous antennas to transmit
or receive signals given the number of available RF chains.
The AS scheme exploits only partial array gain while the
MIMO system with full complexity exploits full array gain.
To exploit more array gain at MIMO receivers, the AS scheme
is further developed into an antenna subarray formation (ASF)
scheme [9]–[11]. Unlike the AS scheme where each RF chain
is allocated to a single antenna, the ASF scheme allocates
Copyright (c) 2015 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
This work was supported in part by the National Natural Science Foundation
of China under Grant 61472458, Grant 61202498, and Grant 61173148, in part
by Guangdong Natural Science Foundation under Grant 2014A030311032,
2014A030313111, and 2014A030310374, and in part by the Fundamental
Research Funds for the Central Universities under Grant 15lgzd10 and Grant
15lgpy15.
Q. Zhang, X. Zeng, and Jiayin Qin are with the School of Information
Science and Technology, Sun Yat-Sen University, Guangzhou 510006, Guang-
dong, China (e-mail: zhqi26@mail.sysu.edu.cn, zxinp@mail2.sysu.edu.cn,
issqjy@mail.sysu.edu.cn). Q. Li is with the School of Advanced Computing,
Sun Yat-Sen University, Guangzhou 510006, Guangdong, China (e-mail:
liquanzhong2009@gmail.com).
each RF chain to a subarray of antennas. For the ASF
scheme, each antenna output in a subarray is complexly
weighted using a variable gain low noise amplifier (vg-LNA)
and a programmable phase shifter. The complex weighted
antenna outputs in a subarray are constructively combined to
exploit the array gain. Compared to the MIMO system with
full complexity, the ASF scheme achieves decreased receiver
hardware complexity, since less downconverters and analog-to-
digital converters (ADCs) are needed [9]–[11]. In [11], a joint
beamforming and ASF scheme for MIMO cognitive radios
was proposed. However, to our best knowledge, the research
on joint beamforming and ASF scheme for non-regenerative
MIMO relay networks is missing.
In this correspondence, we propose a joint beamforming and
ASF scheme for non-regenerative MIMO relay networks. At
the multi-antenna destination, we apply the relaxed-structured
ASF technique as in [9], [10]. Our objective is to maximize
the achievable rate subject to transmit power constraints at the
source and the relay, and limited number of nonzero elements
in the ASF matrix.
Our main contribution is summarized as follows. We pro-
pose to apply the relaxed-structured ASF technique on non-
regenerative MIMO relay networks which provides an ideal
tradeoff between system complexity and performance. By
relaxing the constraint of limited number of nonzero elements
in the ASF matrix, we decouple the joint beamforming and
ASF design problem into three problems and propose to
alternatively optimize beamforming matrices at the source and
the relay, and the ASF matrix. We also propose a gradient
projection (GP) algorithm to solve non-linear programming of
relay beamforming design problem.
Notations: Boldface lowercase and uppercase letters denote
vectors and matrices, respectively. The conjugate, transpose,
conjugate transpose, Frobenius norm and trace of the matrix
A are denoted as A
∗
, A
T
, A
†
, ∥A∥
F
, and tr(A), respectively.
By A ≽ 0, we mean that A is positive semidefinite. CN (0, I)
denotes the distribution of a circularly symmetric complex
Gaussian vector with mean 0 and covariance I.
II. SYSTEM MODEL
Consider a non-regenerative MIMO relay network which
consists of a source, a relay and a destination. The source,
relay and destination are equipped with N
s
, N
r
and N
d
anten-
nas, respectively. We assume that N
r
≥ N
s
and N
r
≥ N
d
. To
reduce hardware cost, the destination has only L (L ≤ N
d
) RF