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Pilot Design for Sparse Channel Estimation in
OFDM-Based Cognitive Radio Systems
Chenhao Qi, Member, IEEE, Guosen Yue, Senior Member, IEEE,
Lenan Wu, and A. Nallanathan, Senior Member, IEEE
Abstract—In this correspondence, sparse channel estimation is first
introduced in orthogonal frequency-division multiplexing (OFDM)-based
cognitive radio systems. Based on the results of spectrum sensing, the
pilot design is studied by minimizing the coherence of the dictionary
matrix used for sparse recovery. Then, it is formulated as an optimal
column selection problem where a table is generated and the indexes of the
selected columns of the table form a pilot pattern. A novel scheme using
constrained cross-entropy optimization is proposed to obtain an optimized
pilot pattern, where it is modeled as an independent Bernoulli random
process. The updating rule for the probability of each active subcarrier
selected as a pilot subcarrier is derived. A projection method is proposed
so that the number of pilots during the optimization is fixed. Simulation
results verify the effectiveness of the proposed scheme and show that it can
achieve 11.5% improvement in spectrum efficiency with the same channel
estimation performance compared with the least squares (LS) channel
estimation.
Index Terms—Cognitive radio (CR), compressed sensing (CS), orthogo-
nal frequency-division multiplexing (OFDM), pilot design, sparse channel
estimation.
I. INTRODUCTION
Traditionally, every wireless system is required to have an exclusive
spectrum license to avoid interference from other systems or users.
However, recent studies have shown that a large portion of the licensed
spectrum is underutilized. This has motivated studies on cognitive
radio (CR), which allows secondary users (SUs) to utilize the licensed
spectrum without interfering with licensed users or primary users
(PUs) and also improves spectrum utilization without allocating a new
spectrum resource [1], [2]. Orthogonal frequency-division multiplex-
Manuscript received March 25, 2013; revised June 18, 2013; accepted
August 6, 2013. Date of publication September 4, 2013; date of current
version February 12, 2014. This work was supported in part by the National
Natural Science Foundation of China under Grant 61302097, by the Ph.D.
Programs Foundation of the Ministry of Education of China under Grant
20120092120014, and by the Huawei Innovative Research Plan. The review
of this paper was coordinated by Prof. X. Wang.
C. Qi and L. Wu are with the School of Information Science and Engineer-
ing, Southeast University, Nanjing 210096, China (e-mail: qch@seu.edu.cn;
wuln@seu.edu.cn).
G. Yue is with NEC Laboratories America, Inc., Princeton, NJ 08540 USA
(e-mail: yueg@nec-labs.com).
A. Nallanathan is with the Center for Telecommunications, King’s College
London, London WC2R 2LS, U.K. (e-mail: nallanathan@ieee.org).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2013.2280655
ing (OFDM), which has been considered one of the best candidates for
the physical layer of CR systems, can efficiently avoid interference by
dynamically nulling corresponding subcarriers. Hence, the subcarriers
may be noncontiguous in OFDM-based CR systems, and the efficient
selection of pilot tones is crucial to the performance of pilot-assisted
channel estimation. In [3], the pilot design is formulated as an op-
timization problem minimizing an upper bound related to the mean
square error (MSE), where the pilot indexes are obtained by solving
a series of 1-D low-complexity subproblems. In [4], a pilot design
scheme using convex optimization together with the cross-entropy
optimization is proposed to minimize the MSE. In [5], parameter
adaptation for wireless multicarrier-based CR systems is investigated,
where the cross-entropy method is demonstrated to outperform the
genetic algorithm and particle swarm optimization. However, all of
them are based on the least squares (LS) channel estimation.
Recently, applications of compressed sensing (CS) to channel es-
timation, i.e., sparse channel estimation, have shown that improved
channel estimation performance and reduced pilot overhead can be
achieved by exploring the sparse nature of wireless multipath channels.
The sparse channel estimation for OFDM systems has been inten-
sively studied [6], [7], and many CS algorithms, including orthogonal
matching pursuit (OMP), compressive sampling matching pursuit, and
basis pursuit, have been applied. Therefore, it is natural to extend this
technique to OFDM-based CR systems, which can further improve
the data rate and flexibility of SUs. However, it also brings new
challenges to the pilot design. To the authors’ best knowledge, so far,
there has been no study focused on the pilot design for sparse channel
estimation in OFDM-based CR systems. Although we can continue to
use the same pilot design schemes as LS, e.g., predesigning pilot tones
and deactivating those tones occupied by PUs and using the nearest
available subcarriers instead, apparently, it is not optimal since it does
not benefit from the sparse channel estimation.
In this correspondence, we first introduce sparse channel estimation
in OFDM-based CR systems. After spectrum sensing, we explore the
pilot design by minimizing the coherence of the dictionary matrix
used for sparse recovery. We then formulate it as an optimal column
selection problem where a table is generated and the indexes of the
selected columns of the table form a pilot pattern. A novel scheme
using constrained cross-entropy optimization is proposed to obtain an
optimized pilot pattern, where we model it as an independent Bernoulli
random process. The updating rule for the probability of each active
subcarrier being selected as a pilot subcarrier is derived. Moreover, a
projection method is proposed so that the number of pilot subcarriers
during optimization is fixed.
The remainder of this correspondence is organized as follows.
Section II formulates the pilot-assisted channel estimation in OFDM-
based CR systems as a sparse recovery problem. Section III proposes
a pilot design scheme using constrained cross-entropy optimization.
Simulation results are provided in Section IV, and finally, Section V
concludes this correspondence.
The notations used in this paper are defined as follows. Symbols
for matrices (uppercase) and vectors (lowercase) are in boldface. (·)
T
,
(·)
H
, diag{·}, I
L
, CN, |·|,and· denote the matrix transpose,
the conjugate transpose (Hermitian), the diagonal matrix, the identity
matrix of size L, the complex Gaussian distribution, the absolute value,
and the ceiling function, respectively.
II. P
ROBLEM FORMULATION
The OFDM-based CR system under consideration is shown in
Fig. 1, where we employ sparse channel estimation instead of the
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