JOINTDODANDDOAESTIMATIONUSING2-DUNITARY
ESPRITFORBISTATICMIMORADAR
Yali Wang
1, 2
, Zhiguo Liu
3*
1
Faculty of Science, Air Force Engineering University, Xi’an 710051, China,
2
Faculty of air defense anti-missile, Air Force Engineering University, Xi’an 710051, China,
3
Xi’an Research Institute of Navigation Technology, Xi’an, 710068, China
yayahope@163.com, liu_zhiguo2013@163.com
Keywords: Bistatic MIMO radar, angle estimation, 2-D
unitary ESPRIT
Abstract
It is shown how bistatic MIMO radar with uniform linear may
be used with the data extension technique and 2-D unitary
ESPRIT algorithm to estimate the joint direction of departure
(DOA) and direction of arrival (DOD). First, channel matrix
is estimated from the receive data matrix by a match filtering
process. Second, to improve the performance, the forward-
backward averaging technique is exploited to extend the
reconstructed Hankel matrix which is constructed using virtue
of the shift-invariant structure of the spatial channel matrix.
Third, after real process, a closed-form solution of DOA and
DOD of targets is obtained. Then, the RCS of targets are
estimated by exploiting the solution of DOA and DOD.
Finally, simulation results are presented to validate the
proposed method.
1 Introduction
Active target localization is one of the most important radar
applications frequently encountered in practice. Many
direction of departure (DOD) and direction of arrival (DOA)
estimation algorithms for MIMO radar have been investigated
[1-6]. It has been proved that two-dimension MUSIC (2D-
MUSIC) algorithm [1] and two-dimension Capon (2D-Capon)
algorithm [4] can be used for DOD and DOA estimation in
MIMO radar; however, the requirement of 2D search renders
much higher computational complexity. [6] presents a
reduced-dimension MUSIC (RD-MUSIC) algorithm and [5]
derives a reduced-dimension Capon (RD-Capon) which
reduce the complexity for angle estimation in a bistatic
MIMO radar system. Unfortunately, the RD algorithms fail to
estimate angle when some targets have same receive angle.
Estimation method of signal parameters via rotational
invariance technique (ESPRIT) in [2] algorithm has exploited
the invariance property for angle estimation in MIMO radar
systems, while [3] has presented another ESPRIT algorithm
which automatically paired DOD and DOA using the
interrelationship between the two one-dimensional ESPRIT,
whose complexity can be lower than that of [2], but the
performance of angle estimation within both methods appears
to be almost the same. In the presence of same DOA or DOD
in signal model, searching pair in [2] may result in wrong
pairing, and the performance of angle estimated by Step. 5 in
[3] will degrade.
In this paper, we present a closed-form joint DOD and DOA
estimation method for bistatic MIMO radar by 2-D unitary
ESPRIT [7]. By virtue of the shift-invariant structure of the
spatial channel matrix, a Hankel matrix
H
A
is constructed.
To improve the performance of the estimation, a data
extension techniques i.e., forward-backward averaging [7] is
applied to the matrix
H
A
. In addition, the application of
combing Hankel matrix construction with forward-backward
averaging techniques can overcome performance
degradations caused by the fact that some targets have same
DOA or DOD. To use the 2-D unitary ESPRIT to perform the
joint diagonalization [8] for the joint DOD and DOA
estimation, we exploit real process to transform a complex
matrix to a real one so that the eigenvalues of the matrix are
real, which reduce the computational complexity
simutaneously.
2 MIMOradarsignalmodel
Assume a MIMO radar system with two uniform linear arrays
of
M
antennas at the transmitter and
N
antennas at receiver.
t
d
denotes the inter element space at the transmitter and
r
d
denotes the inter element space at the receiver. We assume in
the following a spacing of
/ 2
r
d
to enable unambiguous
direction finding. Assume also
P
independent point targets
locate in a far field. Each target is assumed to have isotropic
reflectivity modeled by zero-mean, unit-variance per
dimension, independent and identically distributed (i.i.d.)
Gaussian complex random variables denoted by
p
, which
involving the reflection coefficients and path loses of the pth
target. Here we define
p
as the RCS of the pth target.
With
1 2
, ,ζ
P
, the target is then modeled by the
diagonal matrix
1
2
ζ
diag
P
.The transmitted baseband
coded signal of the mth transmitter within one repetition
interval is denoted
by
1
1 , 2 , , , 1, 2, ,
s
L
m m m m
s s s L m M
,
where
1 L
denotes the set of complex matrices with the size
of
1 L
.
H
s s
m m
L
, where
H
denotes the Hermitian
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