IEICE TRANS. FUNDAMENTALS, VOL.Exx–A, NO.xx XXXX 200x
1
LETTER
Wideband DOA estimation based on co-prime arrays with
sub-Nyquist sampling
∗
Wanghan LV
†
, Huali WANG
††
, Feng LIU
†
, Nonmembers, and Zheng DAI
†
, Student Member
SUMMARY In this letter, a method of wideband direction
of arrival (DOA) estimation based on co-prime arrays with sub-
Nyquist sampling is proposed. Previous works have employed co-
prime arrays for wideband DOA estimation, which can increase
the degrees of freedom (DOFs) in the spatial domain. However,
they are all based on Nyquist sampling. Different from existing
methods, we incorporate a sub-Nyquist sampling scheme called
multicoset sampling for DOA estimation to relax hardware con-
dition. Simulation results show the correctness and effectiveness.
key words: co-prime array, direction of arrival estimation, sub-
Nyquist sampling, wideband
1. Introduction
Recently, the co-prime array technique has been a re-
search focus due to its superior detection performance.
A co-prime array utilizes two uniform linear subarrays,
where one uses M sensors with an inter-element spac-
ing of N units, and the other uses N elements with an
inter-element spacing of M units, where M and N are
chosen to be co-prime. Such co-prime array can resolve
O(MN) sources with M + N − 1 sensors [1]. To further
enhance the degrees of freedom (DOFs), another co-
prime array structure was proposed in [2] by doubling
the number of sensors in one subarray, where a larger
number of consecutive virtual sensors can be achieved.
Various methods have been proposed to exploit the
increased DOFs of co-prime arrays for DOA estima-
tion. In [2], the subspace-based spatial smoothing MU-
SIC algorithm was implemented and showed that an
increased number of sources can be detected. Howev-
er, this MUSIC-like algorithm requires a consecutive
difference coarray lag and the application of spatial s-
moothing implies significant reduction of the obtained
virtual array aperture. To fully utilize the virtual aper-
ture achieved in the difference coarray, sparsity-based
DOA estimation methods are exploited in [3] and [4].
This kind of technique can overcome the disadvantages
of the MUSIC-like methods. Based on the sparsity-
based estimation technique, a class of low-complexity
†
The authors are with School of Electronic and Optical
Engineering, Nanjing University of Science and Technology,
Nanjing, China
††
The author is with College of Communications Engi-
neering, PLA University of Science and Technology, Nan-
jing, China
∗
This work is supported by National Natural Science
Foundation of China (No. 61271354)
DOI: 10.1587/transfun.E0.A.1
DOA estimation method for wideband co-prime arrays
is proposed in [5]. It utilizes a group sparsity concept.
The aforementioned methods are all designed under the
frame of Nyquist sampling, which may be too expensive
to perform, especially for wideband signal.
In this letter, we present a wideband DOA estima-
tion method employing a sub-Nyquist sampling scheme
called multicoset sampling [6], based on co-prime ar-
rays. The proposed method not only can detect more
sources than the number of sensor elements but al-
so makes it possible to capture the target information
under relaxed hardware conditions. Simulation result-
s show that our proposed metho d has the estimation
performance approximate to that in case of Nyquist
sampling.
Notation: ⊗ denotes the Kronecker product. vec(.)
is the vectorization operator that turns a matrix into
a vector by stacking all columns on top of the anoth-
er. (.)
T
, (.)
H
and (.)
∗
denote the transpose, conjugate
transpose and complex conjugation of a matrix. E{.}
is the mathematical expectation operator. blkdiag{.}
is used to construct a block diagonal matrix from input
arguments.
2. Data Model
Consider a co-prime linear array consisting of two uni-
form linear subarrays with 2M and N sensor elements
where M and N are co-prime integers. One has the
position set S
1
= {Mnd, 0 ≤ n ≤ N − 1} and the other
has the position set S
2
= {Nmd, 0 ≤ m ≤ 2M − 1},
where d = λ
min
/2. λ
min
denotes the wavelength cor-
responding to the highest frequency of interest. Since
that these two subarrays share the first sensor, namely
reference sensor, there are N + 2M − 1 sensors totally.
Such array configuration allows most adjacent elements
to be spaced father apart, which is attractive when it
is necessary to reduce mutual coupling between sen-
sor elements. Assume that there are K uncorrelated
wideband signals with the same bandwidth impinging
on the array from θ
i
, i = 1, . . . , K. Then the received
signal at the k-th (k = 1, . . . , N + 2M − 1) sensor is
expressed as
x
k
(t) =
K
∑
i=1
s
i
[t + τ
k
(θ
i
)] + n
k
(t) (1)
Copyright
c
200x The Institute of Electronics, Information and Communication Engineers