TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
Trans. Emerging Tel. Tech.
2014; 25:1020–1027
Published online 7 April 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2816
RESEARCH ARTICLE
A robust and distributed design for coordinated
downlink beamforming for secure MISO
interference channels
Zesong Fei
*
, Jiqing Ni, Niwei Wang, Chengwen Xing and Jingming Kuang
School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, China
ABSTRACT
In this paper, we address the optimization problems of downlink coordinated beamforming over the K-user multiple-
input single-output interference channel with confidential messages. Our design objective is to minimise the total transmit
power subject to the constraints of individual signal-to-interference plus noise ratio and equivocation rates. For the case
with perfect channel state information (CSI), by deriving the equivalent forms for the signal-to-interference plus noise
ratio and the secrecy constraints, the optimization problem is reformulated as a second-order cone programme prob-
lem. Then, an optimal distributed algorithm using the partial Lagrangian duality is discussed. In addition we extend the
analysis to the imperfect CSI scenario with bounded ellipsoidal errors, the centralised algorithm has been proposed by
solving a semi-definite programme with the help of rank relaxation, whereas the distributed robust algorithm is devised
by using ADMM. Finally, the simulation results have shown that with perfect CSI, the centralised and distributed algo-
rithms have nearly the same performance, but in the case of imperfect CSI, the centralised algorithm shows a slightly better
performance. Copyright © 2014 John Wiley & Sons, Ltd.
*Correspondence
Zesong Fei, School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, China.
E-mail: feizesong@bit.edu.cn
Received 10 August 2013; Revised 28 December 2013; Accepted 9 Februar y 2014
1. INTRODUCTION
Instead of using passwords or keys, security that has drawn
great attention of researchers [1, 2], can be provided in the
physical layer where signal processing techniques can be
used to degrade an eavesdropper’s channel so that mean-
ingful detection at the eavesdropper is difficult or even
impossible. Later in [3], the author studied a more general
wiretap channel model and showed that secure commu-
nication is in fact possible without using key encryption
in the presence of the eavesdropper. Literature [4] char-
acterised the performance tradeoffs and derived upper and
lower bounds on the secrecy capacity both for finite-size
systems and in the large system limit. For cooperative com-
munication employing relays, [5] established the utility
of cooperation for secret communication and derived an
outer bound on the optimal rate-equivocation region based
on a four-terminal relay-eavesdropper channel. Recently,
[6] examined the optimization of cooperative jamming to
enhance the physical layer security of a wiretap fading
channel via distributed relays.
The focus of this paper is on the K-user interference
channel with confidential messages (IFC-CM) in which
each receiver decodes its own message but could also
eavesdrop t he messages intended for other users. In the
information-theoretic sense, the secrecy rate region and an
outer bound for the IFC-CM were presented in [7], whereas
[8] derived the inner and the outer bounds of a one-
sided IFC-CM and analysed their gap. Recently, in [9], the
K-user Gaussian many-to-one IFC was investigated, in
which the achievable secrecy sum rate over all users was
shown to be achievable by using nested lattice codes.
From the signal-processing perspective, secure (or
secret) communications has also received much attention.
In [10], the power control problem over the two-user
symmetric IFC-CM was addressed. Most recently, the
multiple-input multiple-output Gaussian IFC-CM was
investigated in [11] where a game-theoretic approach was
proposed to permit the two transmitters to compromise to
an operating point that better balances the network perfor-
mance. Nevertheless, secrecy optimization for more than
two users is much less known, which motivates the work
of this paper.
In most existing works of physical security, the channel
state information (CSI) is assumed to be perfectly known.
Unfortunately, such an assumption generally does not hold
1020 Copyright © 2014 John Wiley & Sons, Ltd.