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1
Joint Precoding and Artificial Noise Design for
Cognitive MIMOME Wiretap Channels
Bing Fang, Zuping Qian, Wei Shao, and Wei Zhong
Abstract—In this paper, we study the secrecy precoding prob-
lem for a cognitive multiple-input multiple-output multiple-
eavesdropper (MIMOME) wiretap system. The problem is studied
with an artificial noise (AN)-aided precoding scheme. First,
we place AN in the null space of the legitimate receiver’s
channel matrix and formulate a secrecy rate maximization (SRM)
problem, which subjects to both an interference power constraint
imposed to protect the primary user (PU) and a maximum
transmit power constraint available for the secondary transmitter.
Second, we drop the null space constraint and reformulate the
SRM problem. Because the formulated SRM problems naturally
constitute difference convex (DC)-type programming problems,
we solve them by employing a successive convex approximation
(SCA) method, where the nonconvex parts of each problems are
approximated by their first-order Taylor expansion. Thus, the
SRM problems can be iteratively solved through successive convex
programming of their convexified versions. Results show that our
algorithms can achieve a satisfactory solution with guaranteed
convergence.
Keywords—MIMOME wiretap channel, physical layer security,
cognitive radio, artificial noise, successive convex approximation.
I. INTRODUCTION
C
OGNITIVE radio network (CRN) is a novel approach
to enhance spectrum utilization. One common model in
this context is the underlay approach where the secondary
users (SUs) are allowed to transmit concurrently on the same
frequency bands with the licensed primary users (PUs) as
long as the resulting interference power is kept below the
maximum threshold that can be tolerated by the licensed
PUs [1]. Along with multiple-input multiple-output (MIMO)
becoming a dominating technology for the next-generation
cellular networks, the researches with regard to cognitive
MIMO radio have gained increasing interests [2].
Similar to any wireless networks, security against malicious
eavesdropping is one of the important issues rising in CRNs
[3]. Recently, physical layer security has gained much attention
due to its dramatic ability to establish security using only the
physical properties of wireless channel and become a promis-
ing complement to the traditional cryptographic technology
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 by the Natural Science Foundation of China under
Grants 61201218 and 61201241, and by the Natural Science Foundation of
Jiangsu Province under Grant BK2012056.
B. Fang, Z. Qian, W. Shao, and W. Zhong are with the College of
Communications Engineering, PLA University of Science and Technology,
Nanjing, 210007, China. (Email: {bingfang ch@163.com, qzp811@sina.com,
swlxssz@126.com, weizhong@ieee.org}).
for wireless communication. Physical layer security is studied
from an information-theoretic perspective, where the secrecy
capacity is defined as the maximum achievable rate from
the transmitter to the legitimate receiver while keeping the
eavesdroppers ignorant of the transmitted massages. Generally,
there are two kinds of physical layer secrecy problems on
CRNs considered in the literature: one is to enhance secrecy
between the PUs in presence of the SUs’ transmission, and
the other is to achieve secrecy among the SUs subject to the
constraints set by the PUs [3] [4] [5].
In this work, we study the secrecy precoding problem for a
cognitive multiple-input multiple-output multiple-eavesdropper
(MIMOME) wiretap channel [6] [7], where a secondary trans-
mitter sends confidential messages to a legitimate receiver in
the presence of multiple eavesdroppers and on the licensed
spectrum band of a PU. The problem is studied with an
artificial noise (AN)-aided precoding scheme [8]. First, we
place AN in the null space of the legitimate receiver’s channel
matrix, and formulate the problem as a secrecy rate maximiza-
tion (SRM) problem, which subjects to both an interference
power constraint and a maximum transmit power constraint.
Second, we drop the null space constraint and reformulate
the SRM problem. Because the formulated SRM problems
naturally constitute difference convex (DC)-type programming
problems, we solve them by employing a successive convex
approximation (SCA) method [1] [9]. With the SCA method,
the nonconvex parts of each SRM problems are approximated
by their first-order Taylor expansion. Then, relying on solving a
series of convexified optimization problems, two novel iterative
precoding algorithms, under different AN-aided precoding
schemes, are developed. Moreover, a proximal point-based
regularization approach is pursued to ensure the convergence
of the proposed algorithms without requiring any special
restrictions on the channel ranks. Numerical simulations are
further provided to demonstrate the proposed algorithms.
Notations: Bold uppercase letters denote matrices and bold
lowercase letters denote vectors; C
m×n
defines the space of
all m × n complex matrices; A ≽ 0 means that matrix A
is positive semidefinite; Hermitian transpose of matrix A is
represented by A
H
; |A|, ||A||
F
and Tr(A) means the deter-
minant, Frobenius norm, and trace of matrix A, respectively;
and log(·) denotes the natural logarithm.
II. SYSTEM MODEL
In this paper, we study the secrecy precoding problem for
a cognitive MIMOME wiretap channel. As shown in Fig. 1,
the system model considered here consists of a primary user
(PU), a secondary transmitter (Alice), a secondary legitimate