Digital Signal Processing 67 (2017) 116–122
Contents lists available at ScienceDirect
Digital Signal Processing
www.elsevier.com/locate/dsp
Spatial smoothing based methods for direction-of-arrival estimation of
coherent signals in nonuniform noise
Jun Wen
a
, Bin Liao
b,∗
, Chongtao Guo
b
a
School of Computer and Electrical Information, Guangxi University, Nanning, China
b
College of Information Engineering, Shenzhen University, Shenzhen, China
a r t i c l e i n f o a b s t r a c t
Article history:
Available
online 12 May 2017
Keywords:
Direction-of-arrival
estimation
Nonuniform
noise
Coherent
signals
Spatial
smoothing
Spatial smoothing techniques have been widely used to estimate the directions-of-arrival (DOAs) of
coherent signals. However, in general these techniques are derived under the condition of uniform white
noise and, therefore, their performance may be significantly deteriorated when nonuniform noise occurs.
This motivates us to develop new methods for DOA estimation of coherent signals in nonuniform noise
in this paper. In our methods, the noise covariance matrix is first directly or iteratively calculated from
the array covariance matrix. Then, the noise component in the array covariance matrix is eliminated to
achieve a noise-free array covariance matrix. By mitigating the effect of noise nonuniformity, conventional
spatial smoothing techniques developed for uniform white noise can thus be employed to reconstruct
a full-rank signal covariance matrix, which enables us to apply the subspace-based DOA estimation
methods effectively. Simulation results demonstrate the effectiveness of the proposed methods.
© 2017 Elsevier Inc. All rights reserved.
1. Introduction
Direction-of-arrival (DOA) estimation using sensor arrays is an
important task in many applications such as radar, sonar, and
wireless communications. Usually, this problem is tackled by as-
suming
uniform white noise, i.e., the noise covariance matrix is a
scaled identity matrix. This assumption can reduce the number of
unknown parameters and, therefore, the computational complex-
ity [1].
In practice, the noise, however, could be colored [2–4] and
non-Gaussian [5]. Particularly, in certain applications, the sensor
noise is uncorrelated but variances across the array are not iden-
tical,
which leads to the so-called nonuniform noise. In this case,
DOA estimation approaches which rely on the assumption of uni-
form
white noise cannot perform satisfactorily due to the incorrect
noise model adopted [6].
Numerous
studies have been devoted to the problem of DOA
estimation in the presence of nonuniform noise. In [6], the
maximum-likelihood (ML) estimator [1] for uniform noise has been
extended to nonuniform noise through the stepwise concentra-
tion
of the log-likelihood function with respect to the signal and
noise nuisance parameters. Based on the similar scheme of step-
wise
concentration, a stochastic ML estimator is proposed in [7] for
*
Corresponding author.
E-mail
address: binliao@ymail.com (B. Liao).
stochastic signals and an improved version of this algorithm has
been reported in [8]. Madurasinghe [9] proposed a power domain
approach which can relieve the computational burden of nonuni-
form
ML estimators to some extent, since the DOA estimates are
achieved by solving a nonlinear problem without iterations or de-
termining
the noise variances. In [10], a computationally attractive
method which only needs a one-dimensional search is proposed.
In [11], the noise covariance matrix is estimated by exploiting
the relationship among the sub-matrices of the array covariance
matrix. In [12,13], a noise-free sparse representation for DOA es-
timation
is built by vectorizing the array covariance matrix and
removing the entries which include noise variances. In [14], two
optimization problems based on the ML and least-squares (LS) es-
timations
are formulated to estimate the signal subspace and noise
covariance matrix in an iterative manner. Unlike the nonuniform
ML estimators, the unknown variables are obtained in an analytical
form in each iteration. More recently, by assuming high signal-to-
noise
ratios (SNRs), improved subspace-based DOA estimators have
been studied in [15].
It
is worth noticing that the aforementioned methods are ap-
plicable
to cases with uncorrelated signals only or noncoherent
signals. As a matter of fact, even though algorithms such as [14]
are
theoretically able to handle any noncoherent signals, their per-
formance
would be significantly deteriorated when the signals are
highly correlated [16]. To deal with coherent signals, numerous
strategies using spatial smoothing [17–20] and higher-order statis-
http://dx.doi.org/10.1016/j.dsp.2017.05.002
1051-2004/
© 2017 Elsevier Inc. All rights reserved.
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