IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 4, NO. 5, OCTOBER 2015 493
Optimal and Suboptimal Full-Duplex Secure Beamforming Designs
for MISO Two-Way Communications
Yaping Wan, Quanzhong Li, Qi Zhang, Member, IEEE,andJiayinQin
Abstract—In this letter, we investigate full-duplex (FD) secure
beamforming design problem for multiple-input-single-output
two-way communication systems. Our objective is to maximize
sum secrecy rate under sum transmit power constraint. We pro-
pose a globally optimal solution which solves the optimization
problem by two-dimensional (2-D) search. In each iteration of
2-D search, a semidefinite programming is solved. To reduce
computational complexity, we propose a null-space based sub-
optimal solution which solves the optimization problem by one-
dimensional search. Furthermore, we also propose a closed-form
low-complexity suboptimal solution. Simulation results demon-
strate that all the proposed solutions for the FD secure beam-
forming achieve higher average sum secrecy rate than the
half-duplex one.
Index Terms—Full-duplex (FD), multiple-input-single-output
(MISO), security, two-way.
I. INTRODUCTION
R
ECENTLY, a lot of research works have shown that it
is possible to employ full-duplex (FD) transmission to
enhance capacity of wireless communication systems [1]–[3].
Because of openness of wireless transmission medium, wire-
less information is susceptible to eavesdropping [3]–[5]. Thus,
secure communication is a critical issue for FD communi-
cations. For the conventional half-duplex (HD) transmission,
secure beamforming problem was extensively investigated [6].
In [7], one-way secure communication scheme was investigated
where a full-duplex multi-antenna destination simultaneously
acts as a cooperative jammer and an information receiver. In [8],
Vishwakarma et al. studied the secure beamforming design in
single-input-single-output (SISO) full-duplex two-way secure
communication systems.
In this letter, we investigate FD secure beamforming design
problem for a multiple-input-single-output (MISO) two-way
communication system where two FD sources exchange infor-
mation with the existence of a single-antenna eavesdropper. The
Manuscript received March 21, 2015; accepted June 9, 2015. Date of
publication June 16, 2015; date of current version October 9, 2015. 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
the Guangdong Natural Science Foundation under Grant 2014A030311032,
Grant 2014A030313111, and Grant 2014A030310374; in part by the Funda-
mental Research Funds for the Central Universities under Grant 15lgzd10 and
Grant 15lgpy15; and in part by the Industry-University-Research Project of
Dongguan City under Grant 2013509102215. The associate editor coordinating
the review of this paper and approving it for publication was I.-M. Kim.
Y. Wan and Q. Zhang are with School of Information Science and Tech-
nology, Sun Yat-Sen University, Guangzhou 510006, China (e-mail: wanyp@
mail2.sysu.edu.cn; zhqi26@mail.sysu.edu.cn).
Q. Li is with the School of Advanced Computing, Sun Yat-Sen University,
Guangzhou 510006, China (e-mail: liquanzhong2009@gmail.com).
J. Qin is with School of Information Science and Technology, Sun Yat-Sen
University, Guangzhou 510006, China, and also with Xinhua College of Sun
Yat-Sen University, Guangzhou 510520, China (e-mail: issqjy@mail.sysu.
edu.cn).
Digital Object Identifier 10.1109/LWC.2015.2445822
MISO two-way communication system is of particular interest
because to achieve spatial suppression FD communications
requires at least two transmit antennas and one receive antenna
[1]. The scenario is typical for future device-to-device com-
munications where two FD portable devices, such as laptops,
exchange information with the existence of an eavesdropping
mobile phone [9], [10]. Our objective is to maximize sum
secrecy rate under sum transmit power constraint.
Our main contribution is summarized as follows. We trans-
form the aforementioned constrained optimization problem into
an unconstrained one and propose a globally optimal solution
which solves the optimization problem by two-dimensional
(2-D) search. In each iteration of 2-D search, a semidefinite pro-
gramming (SDP) is solved. Since the computational complexity
of the globally optimal solution is high, we propose a null-
space based suboptimal solution which solves the optimization
problem by the one-dimensional (1-D) search. To further reduce
computational complexity, we also propose a closed-form low-
complexity suboptimal solution.
Notations: Boldface lowercase and uppercase letters denote
vectors and matrices, respectively. The transpose, conjugate
transpose, Frobenius norm, rank, and trace of matrix A are
denoted as A
T
, A
†
, A,rank(A),andtr(A), respectively. The
⊗ denotes Kronecker product. vec(A) denotes to stack the
columns of the matrix A into a single vector while MAT(a)
denotes the reverse operation. By A 0, we mean that A is
positive semidefinite.
II. S
YSTEM MODEL AND PROBLEM FORMULATION
Consider an MISO two-way secure communication system,
which consists of two FD sources, S
1
and S
2
, and an eavesdrop-
per. Each of two FD sources is equipped with N + 1 antennas,
including N transmit antennas and one receive antenna. The
eavesdropper is equipped with a single antenna. Denote the
channel responses from source S
1
to source S
2
and the eaves-
dropper as h
12
∈ C
N×1
and h
1e
∈ C
N×1
, respectively. Denote
the channel responses from S
2
to S
1
and the eavesdropper as
h
21
∈ C
N×1
and h
2e
∈ C
N×1
, respectively. We assume that loop
interference (LI) mitigation schemes [1] are employed such that
the LI leakage from the FD sources output to their input through
the effective channel response h
ii
, i ∈{1, 2}.
Two sources, S
1
and S
2
, transmit signals s
1
∈ C
1×1
and
s
2
∈ C
1×1
, respectively, where E[|s
1
|
2
]=E[|s
2
|
2
]=1. The
received signals at S
1
, S
2
, and the eavesdropper are
y
1
= h
†
11
w
1
s
1
+ h
†
21
w
2
s
2
+ n
1
, (1)
y
2
= h
†
12
w
1
s
1
+ h
†
22
w
2
s
2
+ n
2
, (2)
y
e
= h
†
1e
w
1
s
1
+ h
†
2e
w
2
s
2
+ n
e
, (3)
respectively, where w
1
∈ C
N×1
and w
2
∈ C
N×1
denote the
beamforming vectors at S
1
and S
2
, respectively; n
1
∼
CN (0,σ
2
1
), n
2
∼ CN (0,σ
2
2
),andn
e
∼ CN(0,σ
2
e
) are the
2162-2337 © 2015 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.