IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 5, MAY 2015 847
Distributed Energy Efficiency Optimization for MIMO
Cognitive Radio Network
Xiaohui Zhang, Hongxiang Li, Yanhui Lu, and Bing Zhou
Abstract—This paper considers a multiple-input-multiple-
output (MIMO) cognitive radio network, where secondary users
(SUs) equipped with multiple antennas coexist with a primary
user (PU). Joint power allocation and transmission beamform-
ing design is proposed to optimize the network energy efficiency
under power constraint and interference temperature constraint.
Distributed algorithm that maximizes energy efficiency of each
individual node is derived through fractional programming. Sim-
ulation results are presented to validate the convergence and
effectiveness of the proposed algorithm.
Index Terms—Multiple-input-multiple-output (MIMO),
cognitive radio, energy efficiency, fractional programming,
beamforming.
I. INTRODUCTION
C
OGNITIVE radio (CR) is a promising approach to en-
hance radio spectrum utilization, in which secondary users
can opportunistically access the licensed spectrum of a primary
user [1]. In particular, the underlay mode of the CR allows
multiple SUs to simultaneously share the PU’s spectrum as
long as the interference from SUs to PU is under certain
threshold [2]. Meanwhile, with the fast development of multi-
antenna technique, the multiple-input-multiple-output (MIMO)
communication has shown its potential on interference suppres-
sion in cognitive network [3]. Particularly, CR nodes equipped
with multiple antennas can leverage communication in the
space dimension and adjust its radiation pattern to manage
the network interference in a multi-user setting. This kind of
cognitive MIMO system is usually modeled as cognitive MIMO
interference channel, which is the major concern of this paper.
On the other hand, increasing energy demand and soaring
energy related operating cost call for new design of energy
efficient communication networks. The energy efficiency of
a communication network can be measured in terms of bit-
per-joule capacity, which is the maximum amount of bit that
can be delivered by per joule energy consumed by the commu-
nication network [4]. In the literature, most previous works for
MIMO-CR over interference channels have focused on capacity
maximization [5], [6], with few work available on optimizing
energy efficiency. In [7], the energy efficient spectrum sharing
Manuscript received October 31, 2014; revised March 8, 2015; accepted
March 10, 2015. Date of publication March 18, 2015; date of current ver-
sion May 7, 2015. This work was partially supported by NASA EPSCoR
research infrastructure development grant (RIDG) and Kentucky Science and
Engineering Foundation (KSEF-148-502-14-331). The research was also par-
tially supported by Program for New Century Excellent Talents in University
(Grant No. NCET-12-0699) and National Science Foundation of China, under
Grants. 61379079. The associate editor coordinating the review of this paper
and approving it for publication was T. J. Oechtering.
X. Zhang and H. Li are with the Department of Electrical and Computer
Engineering, University of Louisville, Louisville, KY 40292 USA (e-mail:
zhangxh1985@gmail.com; h.li@louisville.edu).
Y. Lu and B. Zhou are with the School of Information Engineering,
Zhengzhou University, Zhengzhou 450001, China.
Digital Object Identifier 10.1109/LCOMM.2015.2414415
Fig. 1. Network model.
in MIMO-CR under interference channel is studied through
a game-theoretic approach. However, the spectrum sharing
algorithm proposed is actually to find an optimal selection of
transmission beamforming matrix from an existing codebook.
The study of energy efficiency optimization under MIMO
interference channel in [8] is not under the scenario of CR
network and the algorithm proposed can not protect the PU’s
transmission in CR network.
In this paper, we study the joint power allocation and beam-
forming strategy to optimize the energy efficiency of MIMO-
CR network over interference channel. Specifically, distributed
algorithm is proposed to maximize the energy efficiency of each
individual node. Since the optimization problem is non-convex
fractional programming problem, we use Dinkelbach’s method
to relax it into parametric subproblem for practical solutions. To
the best of our knowledge, it is the first time that Dinkelbach’s
method [9] is used in the energy efficiency optimization of
MIMO-CR network over interference channel. Throughout the
paper, we use (.)
∗
to denote the conjugate matrix, (.)
H
to denote
the Hermitian matrix transpose, tr(.) for the trace of a matrix,
E(.) for the expectation and det(.) for the determinant.
II. S
YSTEM MODEL
We consider a CR network shown in Fig. 1, which consists
of I pairs of transmitters and receivers (i.e., I CR links) s haring
the same frequency channel with PU. We assume each CR
node is equipped with M antennas so that the transmitter of
each CR link can send up to M independent data s treams. On
the i
th
CR link (i ∈ Φ
I
= {1, 2, ···,I}), we denote source
information as an M × 1 vector x
i
and E(x
i
x
H
i
)=I, which is
multiplied by an M × M precoding matrix T
i
before sending
out to its desired receiver d(i). The received complex baseband-
equivalent signal vector y
i
at i
th
receiver can be expressed as:
y
i
= H
d(i),i
T
i
x
i
+
j∈{Φ
I
\i}
H
d(i),j
T
j
x
j
+ N, (1)
where the first term in the right side of (1) is the desired signal
component with H
d(i),i
being the M × M channel gain matrix
of the i
th
link. The second term represents the interference
from other CR transmissions; N is an M × 1 complex Gaussian
noise vector with covariance matrix σ
2
N
I, representing the floor
noise plus other interference (e.g., PU transmission on the s ame
channel).
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