424 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 7, NO. 3, JUNE 2018
Secure Beamforming Designs for Secrecy MIMO SWIPT Systems
Zhengyu Zhu , Zheng Chu , Fuhui Zhou , Hehao Niu, Zhongyong Wang ,andInkyuLee , Fellow, IEEE
Abstract—In this letter, secure beamforming designs are
investigated in a multiple-input multiple-output secrecy chan-
nels with simultaneous wireless information and power transfer.
In order to achieve fairness among different multiple energy
harvesting receivers, the minimum harvested energy is maxi-
mized under the secrecy rate requirements. In particular, in
order to reduce the computational complexity of the semidefi-
nite programming problem, a successive convex approximation
(SCA) iterative algorithm is proposed in the perfect channel state
information (CSI) case to obtain a near-optimal rank-one solu-
tion. Moreover, the original problem is extended to the imperfect
CSI case by incorporating a norm-bounded error model, where
an SCA-based iterative algorithm is also proposed. Simulation
results reveal that the SCA-based iterative algorithm achieves
the same performance as the semidefinite relaxation method with
reduced complexity.
Index Terms—SWIPT, MIMO system, secure beamforming,
successive convex approximation, semidefinite relaxation.
I. INTRODUCTION
S
IMULTANEOUS wireless information and power transfer
(SWIPT) which harvests energy for wireless devices and
increases the durability of wireless networks [1]. Meanwhile,
because of the openness of wireless networks, the informa-
tion security is a key issue for SWIPT system. Physical-layer
security (PLS), has become more crucial in 5G wireless
networks to increase the security of wireless channels [2]–[5].
Moreover, PLS has recently been pursued in different SWIPT
systems, such as relay network [6], multiple-input-multiple-
output (MIMO) channel [7], cognitive radio network [8], and
multiple-input-single-output (MISO) systems [9], [10].
In many investigations [7]–[12], with the help of the
semidefinite relaxation (SDR) method, a rank relaxation
method has widely employed in various PLS-SWIPT design
problems, where a semi-definite programming (SDP) problem
Manuscript received November 12, 2017; accepted November 28, 2017.
Date of publication December 7, 2017; date of current version June 19, 2018.
This work was supported in part by the National Nature Science Foundation
of China under Grant 61571402, Grant 61301150, Grant 61571401, Grant
61640005, Grant 61701214, and Grant 61401401, and in part by the National
Research Foundation funded by the Ministry of Science, ICT and Future
Planning of Korea Government under Grant 2017R1A2B3012316. The asso-
ciate editor coordinating the review of this paper and approving it for
publication was I. Krikidis. (Corresponding author: Zhongyong Wang.)
Z. Zhu and Z. Wang are with the School of Information
Engineering, Zhengzhou University, Zhengzhou 450001, China (e-mail:
zhuzhengyu6@gmail.com; iezywang@zzu.edu.cn).
Z. Chu is with the 5G Innovation Center, Institute of Communication
Systems, University of Surrey, Guildford GU2 7XH, U.K. (e-mail:
zheng.chu@surrey.ac.uk).
F. Zhou is with the School of Information Engineering, Nanchang
University, Nanchang 330031, China (e-mail: zhoufuhui@ncu.edu.cn).
H. Niu is with the College of Communications Engineering,
PLA Army Engineering University, Nanjing 210007, China (e-mail:
niuhaonupt@foxmail.com).
I. Lee is with the School of Electrical Engineering, Korea University,
Seoul 136-713, South Korea (e-mail: inkyu@korea.ac.kr).
Digital Object Identifier 10.1109/LWC.2017.2780830
was generated. Unfortunately, SDP problem can not be guaran-
teed to get a rank-one solution, which serve as a performance
upper bound of the original problem in general. Specifically,
since the proof of rank-two solution was presented, the
works [9], [10] have generated a suboptimal rank-one solu-
tion by applying a Gaussian randomization (GR) method,
which may not be correct. In addition, if SDP returns a
high-rank solution, the GR method may give rise to poor
performance or even may not obtain the optimal beamforming.
Besides, solving a SDP problem requires higher computational
complexity [15].
It is worth noting that these previous works referring to
PLS-SWIPT were either focus on transmit power minimization
or secrecy rate maximization problem. As another impor-
tant issue of PLS-SWIPT, the research of the max-min fair
energy harvesting (EH) problem still remains infrequent,
which brought extensive attention of academia. So far, only
several literatures [11], [12] studied the max-min fair EH
problem. However, [11] and [12] only considered the signal-to-
interference and noise ratio (SINR) constraint at the informa-
tion receiver. Also, Khandaker and Wong [12] only studied the
case with single-antenna energy harvesting receivers (EHR). In
addition, the SDR method is applied to some works [11], [12],
which results of the higher complexity.
Motivated by these issues, in this letter, the energy harvested
by EH receivers under the rule of a max-min fairness criterion
is optimized while guaranteing the secrecy transmission. The
contributions of this letter are summarized as follows:
• For the perfect channel state information (CSI) case, to
solve a non-convex problem, we present a novel secrecy
rate reformulation as a second-order cone (SOC), and
utilize a first-order Taylor approximation to convert the
minimum harvested energy into a linear constraint. To cir-
cumvent rank relaxation, a novel iterative algorithm based
on successive convex approximation (SCA) is proposed
to obtain a near-optimal beamforming.
• For the imperfect CSI case, we extend the max-min EH
fairness problem with deterministic channel uncertain-
ties. According to the SCA method, a robust problem
can be relaxed as a second order cone programming
(SOCP). Thus, a SCA-based iterative algorithm is applied
to compute the near-optimal secure beamforming vector.
Simulation results demonstrate that our proposed algorithms
can achieve the same secrecy performance as the SDR method
with much low complexity.
Notation: {·} stands for the real part of a complex num-
ber. The operator ⊗ is the Kronecker product. [x]
+
represents
max{x, 0}. A 0 indicates that A is positive semi-definite, tr
(A), A
F
and vec(A) means the trace, Frobenius norm and a
column vector where elements of A are stacked, respectively.
II. S
YSTEM MODEL
Considering a secrecy MIMO system with SWIPT which
include one legitimate transmitter (named Alice) equipped
2162-2345
c
2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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