Fast communication
A sparse recovery algorithm for DOA estimation using weighted
subspace fitting
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Nan Hu
a,b
, Zhongfu Ye
a,b,
n
, Dongyang Xu
a,b
, Shenghong Cao
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, China, Hefei, Anhui 230027, People’s Republic of China
article info
Article history:
Received 18 October 2011
Received in revised form
22 March 2012
Accepted 25 March 2012
Available online 12 April 2012
Keywords:
Direction-of-arrival
Weighted subspace fitting
Sparse recovery
Second-order cone programming
abstract
A new algorithm involving sparse recovery is proposed to address the problem of
direction-of-arrival (DOA) estimation using weighted subspace fitting (WSF). The
proposed algorithm proves to be a modified version of ‘
1
-SVD by using an optimal
weighting matrix, wherein a scheme of regularization between sparsity penalty and
subspace fitting error is also given for all SNR range. Numerical simulations verify the
efficiency of the proposed algorithm and illustrate the performance improvement in
low SNR.
& 2012 Elsevier B.V. All rights reserved.
1. Introduction
Direction of arrival (DOA) estimation has been an
important topic during the last decades [1] due to its
wide application in radar, sonar, radio astronomy, etc. The
traditional way to solve this problem includes the max-
imum likelihood (ML) estimators [2] and subspace-based
approaches [3]. Recently, the techniques of sparse recov-
ery have provided a new perspective of DOA estimation
by exploiting the spatial sparsity in the array signal model
[4–6,8–9], and the super-resolution property and ability of
resolving coherent sources have attracted a lot of attention.
An early work of applying sparse recovery into DOA
estimation is the global matched filter (GMF) [4] which
exploited the beamformer samples for DOA estimation
based on uniform circular array. The most successful one
is ‘
1
-SVD [5] which employs ‘
1
-norm to enforce sparsity
and singular value decomposition to reduce complexity and
sensitivity to noise. The optimization problem in ‘
1
-SVD can
be deemed as a subspace fitting [7] procedure, whereas the
optimality of the weighting matrix is not preserved. Another
problem is that the scheme of regularization between
sparsity penalty and subspace fitting error is suboptimal
in low signal-to-noise ratio (SNR). Some recently proposed
methods including sparse iterative covariance-based esti-
mation (SPICE) [8] and sparse representation of array
covariance vectors (SRACV) [9] also employed ‘
1
-norm
penalty, while they addressed the problem in the correlation
domain instead of the data domain. Actually the rigorous
constraint to enforce sparsity should be ‘
1
-norm instead of
‘
1
-norm, whereas the optimization problem involving
‘
0
-norm is NP-hard. An alternative strategy named joint
‘
2,0
approximation (JLZA) was given in Ref. [10],wherea
class of Gaussian functions was used to approximate the ‘
0
-
norm constraint; however, it is difficult to choose the
appropriate parameters for all scenarios in real applications.
In this communication, sparse recovery is introduced
to solve the problem of weighted subspace fitting (WSF)
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/sigpro
Signal Processing
0165-1684/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.sigpro.2012.03.020
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This work is supported by the Science and Technology Plan Project
of Anhui Province of China (No. 11010202191), National Natural Science
Foundation of China (No. 61101236).
n
Corresponding author at: Department of Electronic Engineering and
Information Science, University of Science and Technology of China,
Hefei, Anhui 230027, People’s Republic of China. Tel.: þ86 551 3601314.
E-mail address: yezf@ustc.edu.cn (Z. Ye).
Signal Processing 92 (2012) 2566–2570