Fast communication
DOA estimation based on fourth-order cumulants in the
presence of sensor gain-phase errors
Shenghong Cao
a,b
, Zhongfu Ye
a,b,
n
, Nan Hu
a,b
,XuXu
a,b
a
Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, Anhui 230027,
People’s Republic of China
b
National Engineering Laboratory for Speech and Language Information Processing, Hefei, Anhui 230027, People’s Republic of China
article info
Article history:
Received 8 April 2012
Received in revised form
10 December 2012
Accepted 7 March 2013
Available online 15 March 2013
Keywords:
Array signal processing
Direction-of-arrival estimation
Fourth-order cumulants
Gain-phase errors
abstract
A method based on fourth-order cumulants (FOC) for direction-of-arrival (DOA) estima-
tion in the presence of sensor gain-phase errors is presented. This method can be applied
in the scenario that the signals are non-Gaussian and the noises are Gaussian. The DOAs
are estimated from the Hadamard product of an FOC matrix and its conjugation. The
advantage of the proposed method is that it performs independently of the phase errors.
Moreover, it is practicable when the noise is spatially colored. Simulation results
demonstrate the effectiveness of the proposed method.
& 2013 Elsevier B.V. All rights reserved.
1. Introduction
In the fields of radar, sonar and mobile communication,
the problem of determining the directions-of-arrival
(DOAs) of plane waves impinging on a sensor array has
been an important topic. Many high-resolution methods
have been proposed [1–3] in the past decades, and their
performance is critically dependent on the knowledge of
the array manifold [4–6]. However, the array manifold is
often affected by unknown array characteristics such as
sensor gain-phase errors.
In recent decades, the problem of DOA estimation with
unknown gain-phase errors has been studied in numerous
papers [6–10]. The methods proposed in [6–8] are limited
to the special array geometries: linear arrays. The method
proposed in [9] is applicable to non-linear arrays. However
it is an alternative iterative algorithm which does not
guarantee the optimal convergence from arbitrary initial
estimation. Liu et al. proposed an eigenstructure DOA
estimation method for nonlinear arrays which is based
on the dot product of the array output vector and its
conjugate [10]. This method has the advantage that DOA
estimates are independent of phase errors, whereas it
requires that at least two signals are spatially far separated
from each other.
All the above-mentioned methods are based on second-
order statistics and many assume that the noise are spatiall y
white [8–10]. In many practical situations, the additive noises
between sensors are correlated and estimating the cov ar-
iancematrixofnoisesisnotavailable. Non-Gaussian signals
contain valuable statistical information in their high-order
statistics, while all cumulants of order greater than two for
Gaussian processes are identically zero. Owing to this prop-
erty of high order cumulants, many effective DOA estimation
algorithms based on cumulants ha v e been proposed [11–15].
Unfortunat ely, these FOC based methods do not consider the
effect of sensor gain-phase errors.
In this communication, a novel method based on FOC is
proposed for DOA estimation in the presence of sensor gain-
phase errors. It can be applied when the non-Gaussian signals
received at the array are corrupted by additive Gaussian
noises. Being similar to the method in [10], the proposed
method also has the advantage that the performance of DO A
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/sigpro
Signal Processing
0165-1684/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.sigpro.2013.03.007
n
Corresponding author at: Department of Electronic Engineering and
Information Science, University of Science and Technology of China,
Huangshan Road, Hefei, Anhui 230027, China. Tel.: þ86 551 3601314.
E-mail address: yezf@ustc.edu.cn (Z. Ye).
Signal Processing 93 (2013) 2581–2585
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