Joint multi-target DOD and DOA estimation in bistatic MIMO
radar exploiting 2-level nested arrays
Han Qi, Hong Jiang, Shunyou Yao
College of Communication Engineering, Jilin University, Changchun, 130012, China
Keywords: MIMO radar, DOD and DOA estimation, nested
array, virtual sensors, spatial resolution.
Abstract
In this paper, we investigate joint estimation of direction-of-
departure (DOD) and direction-of-arrival (DOA) of multiple
targets in bistatic MIMO radar exploiting nested arrays. By
configuring 2-level nested arrays in the transmit and receive
arrays, a large number of virtual array apertures are
introduced. Therefore, the spatial resolution of the MIMO
radar system is significantly enhanced. Moreover, the
maximum number of the identifiable targets is enlarged to a
higher degree compared with traditional uniform linear arrays.
The signal model is formulated by the exploitation of the
nested arrays. A novel row extraction method is proposed to
construct an observed data vector for joint angle estimation.
The simulation results validate the theoretical algorithm.
1 Introduction
Since the concept of the multiple input multiple output
(MIMO) radar was developed [1], it has drawn considerable
research [2][3]. Specifically, the problem of joint estimation
of the direction-of-departure (DOD) and direction-of-arrival
(DOA) is widely investigated for colocated bistatic MIMO
radar systems. In [4], a two-dimensional (2D) Capon-based
method is addressed to jointly estimate the DOD and DOA.
The 2D multiple signal classification (MUSIC) algorithm [5]
and its reduced dimension version [6] are proposed by
searching through the 2D space to estimate the DOD and
DOA. By exploiting rotational invariance technique of the
transmitter and receiver arrays, the ESPRIT-like methods [7]-
[9] are investigated for joint estimation of DOD and DOA.
Besides, a polynomial root finding approach and a combined
ESPRIT-MUSIC approach are proposed in [10][11] to
achieve joint angles estimation and automatic pairing. In
these algorithms, the uniform linear array (ULA) is used.
Based on the concept of coarray [12], the non-uniform
linear array (NLA) has drawn a lot of attention recently. The
non-uniform indicates that the sensor positions normalized by
half carrier wavelength are not a series of consecutive
integers. The typical NLAs include the minimum redundancy
array [13], coprime array [14] and nested array [12]. The
DOA estimation exploiting coprime array has been addressed
in [14] by utilizing the MUSIC algorithm and spatial
smoothing technique. By exploiting a variety of angle
estimation algorithms, the joint estimation of DOD and DOA
based on the minimum redundancy arrays and the coprime
arrays is presented in [15]. In this paper, we elaborate a joint
multi-target DOD and DOA estimation algorithm using a
bistatic MIMO radar configured with 2-level nested arrays at
both the transmit and receive sites. Furthermore, we propose a
novel row extraction method to construct a data vector based
on the configuration of the nested arrays. From the acquired
data vector, the 2D ESPRIT algorithm is applied to perform
angle estimation and achieve automatic pairing.
2 Signal model
We assume that the bistatic MIMO radar is configured with 2-
level nested arrays at both the transmit and receive sites. As
shown in Fig. 1, the sensor positions of the transmit array are
denoted by a set
{
}
()
{
}
11 2
,1,2,, 1 , 1,2,,
t
Sndn N N mdm N== ∪+ =
,
where
1
N
and
2
N
are arbitrary positive integers,
d
is a
fundamental spacing that halved by the carrier wavelength
λ
to avoid the spatial aliasing, i.e.
/2d
λ
=
. Similarly, the
sensor positions of the receive array can be denoted by a set
{
}
(
)
{
}
33 4
,1,2,, 1 , 1,2,,
r
Sndn N N mdm N== ∪+ =
, where
3
N
and
4
N
are arbitrary integers.
Figure 1: 2-level nested array with parameters N
1
and N
2
Furthermore, let us denote the elements of a set
{
}
12
1
,,
tNN
Xx x
+
=
as the sensor positions in
t
S
which are
arranged in order, i.e.
1
,
x
d
=
and
(
)
12
21
1
NN
x
NN d
+
=+
. Also,
we denote the elements of a set
{
}
34
1
,,
rNN
Yy y
+
=
as the
sensor positions in
r
S
which are arranged in order, i.e.
1
yd
=
and
(
)
34
43
1
NN
yNNd
+
=+
.
Assume that there are
P
targets in the same range-bin
The DOD and DOA of the pth target are denoted by
p
θ
and
p
φ
, respectively,
Pp ,...,2,1
=
. The output of the matched
filters at the receive array is given by
() ( , ) () ()ttt
θ
φ
=
+
z
Csn
(1)
The total steering matrix
12 34
()()
(,)
N
NNN P
θφ
++×
∈C
can be
given by
(
)
(
)
(
)()()
11
,,,
PP
θφ ϕ θ ϕ θ
=⊗ ⊗
⎡
⎤
⎣
⎦
Cbaba
, where
⊗
denotes the Kronecker product. The transmit and receive
steering vectors of the pth target are respectively given by
()
1
12
2( /)sin
2( /)sin
,,
NN p
p
T
jx
jx
p
ee
πλθ
πλθ
θ
+
−
−
⎡
⎤
=
⎣
⎦
a
and
(
)
p
ϕ
=
b
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