1. INTRODUCTION
In array signal processing, it is a major task to estimate the
2-D DOAs of signals impinging on a passive sensor array.
Therefore, many high-resolution algorithm, such as 2-D
MUSIC [1] and 2-D ESPRIT [2,3] etc have been
developed. Recently, several DOA estimation method
based on blind source separation have been addressed
throughout literature [4]~[6]. The basic function is to
recover combined source signals and their DOA as they
propagate across an array. The “blind” aspect naturally
implies that no knowledge of the source direction or signals
is available. However, in most situations at least some
practical assumptions can be made.
In this paper, we make use of the blind source separation
method based on the second-order identification [7, 8] to
obtain the estimation of the array response matrix. Via the
rotational invariance techniques [9] for the array response
matrix, the 2-D DOAs are estimated. The estimated
elevation angle and azimuth angle is automatically
determined.
The outline of the paper is organized as follows. Section 2
briefly introduces the data model. The 2-D DOA estimation
method based on blind source separation is proposed in
Section 3. In Section 4, simulation results are presented to
verify the performance of the proposed approach. Section 5,
provides a concluding remark to summarize the paper.
2. DATA MODEL
We consider the receiving system with 2M isotropic
sensors in the directions along the x-axis and along the
y-axis with an equal spacing of d, as shown in Fig. 1.
Assume that there are
q narrowband source ()
i
t
(1,,)iq= " with same wavelength
impinging on the
array, such that the kth source has an elevation angle
k
and an azimuth angle
k
. In this paper, we describe the 2-D
This work is supported by National Nature Science Foundation under
Grant
60874108
DOA of the kth signal with (, )
kk
α
that
k
α
denotes the
angle between the kth incident signal and the x-axis,
k
represents the angle between the kth incident signal and the
y-axis. It is easily shown that
cos sin cos
kkk
α
=×,
cos sin sin
kkk
=×.
Fig 1. Illustration of the array geometry.
The baseband signals received at this array are given by
() () ()ttt=+yAsn (1)
The matrices and vectors in (1) have the following forms:
T
12
( ) [ ( ), , ( )]
M
tyt yt= "y
T
1
( ) [ ( ), , ( )]
q
tst st= "s
T
12
() [ (), , ()]
M
tnt nt= "n
1
[, , ]
q
= "Aa a
21 1T
[1,,,, ,, , ]
MM
kkkkkkkkk
aa a ba b a b
−−
=××""a
exp{ 2 ( / ) cos }
kk
ajd
πλ α
=− ×
exp{ 2 ( / ) cos }
kk
bjd
πλ
=− ×
where ()
k
t and ()
k
nt denote the output and the additive
noise of the kth sensor, respectively, and the superscript
T
()⋅ presents the transpose operation. The common
assumptions are listed first.
A 2-D DOA Estimation Method Based on Blind Source Separation
Fulai Liu, Jinkuan Wang, Ruiyan Du, Bin Wang
Engineering Optimization & Smart Antenna Institute Northeastern University, Qinhuangdao, 066004
E-mail: fulailiu@126.com,
wjk@mail.neuq.edu.cn, ruiyandu@126.com, wangbin_neu@yahoo.com.cn
Abstract: A new two-dimensional direction of arrival (2-D DOA) estimation method is proposed, in this paper. The
presented method makes using of blind source separation method based on the second-order identification to estimate the
array response matrix. Via the rotational invariance techniques, we can estimate the 2-D DOA from the array response
matrix estimation. The estimated elevation angles and azimuth angles is automatically determined. Simulation results are
presented verifying the efficiency of the proposed method.
Key Words: Blind Source Separation, Two-Dimensional Direction of Arrival (2-D DOA), Second-Order Identification,
Array Response Matrix.
2875
978-1-4244-2723-9/09/$25.00
c
2009 IEEE