Diagonal Loading for STAP and Its Performance
Analysis
Liu Xiaojun Liu Congfeng Liao Guisheng
National Lab of Radar Signal Processing, Xidian University, Xian Shaanxi 710071, China
xjliu001@163.com cfliu@mail.xidian.edu.cn gsliao@xidian.edu.cn
Abstract—For the moving target detection with space-time
adaptive processing (STAP), the non- homogeneity will cause the
covariance matrix estimation error, which substantially results in
the STAP performance degradation. Diagonal loading has long
been used as a means to improve the robustness of the spatial
filter against mismatches in both the desired spatial signature
and the spatial correlation matrix. In this paper, we consider the
application of diagonal loading to improve the detection
performance for STAP, especially for the covariance matrix
mismatch (statistical mismatch) in STAP, namely, there is a
mismatch between the actual covariance matrix of interest and
the presumed one. For the diagonal loading, the key problem is
the choice of the loading level, and the method for selecting the
loading level is given, and the particular performance analysis
indicates that the diagonal loading can improve the detection
probability and the output signal-to-noise ratio. Numerical
simulations attest the validity of the analysis.
Keywords—- Array signal processing; Space-Time Adaptive
Processing; Diagonal Loading; Performance analysis
I. INTRODUCTION
The surveillance radar whose mission is the detection of
moving targets, either airborne or ground-based, is commonly
referred to as the Moving Target Indication (MTI) radar. The
key challenge to an MTI system is the suppression of
interference, either due to other transmitted radar signals, such
as jamming or incidental, or from the ground reflections of the
MTI radars own signal, known as clutter. The fundamental
problem with ground clutter interference is that, despite the
fact that it is not physically movement, it does have a non-zero
Doppler frequency due to the platform motion of the MTI
radar. As a result, the detection of moving targets that share
the same Doppler frequency with ground clutter is severely
impaired without adaptive clutter mitigation. One physical
characteristic that can be exploited, however, is the fact that
ground clutter with the same Doppler frequency as a moving
target has a different angle of incidence. The array elements
allow the radar to determine angle, while a series of pulses
provides a measurement of Doppler frequency. Thus, by
adaptively combining elements and pulses, clutter can be
canceled by placing a null in angle and Doppler. Two-
dimensional adaptive processing of elements and pulses is
commonly referred to as Space-Time Adaptive Processing
(STAP)
[1][2]
.
We know that non-homogeneity will cause the
covariance matrix estimation error, which substantially results
in the STAP performance degradation. The adaptive algorithm
generates a pattern with distorted mainbeam and high
sidelobes, Distortion beam shapes and high sidelobes may not
be acceptable for reasons of clutter rejection, the need to avoid
sidelobe target detection, and inaccuracy in target parameter
estimation.
Diagonal loading (i.e., adding a constant to all the
elements of the diagonal of the sample correlation matrix) has
long been used as a means to improve the robustness of the
spatial filter against mismatches in both the desired spatial
signature and the spatial correlation matrix
[3]
. It is a method to
reduce the adaptive capability against small interference
sources. When the elements are at half-wavelength spacing,
adding the diagonal matrix to the true covariance matrix can
be thought of as adding many small false jammers with all
possible angles of arrival to the matrix for purposes of antenna
weight computation
[4]
.
In this paper, we consider the application of diagonal
loading to improve the detection performance, especially in the
case of “statistical mismatch” for STAP, i.e. when there is a
mismatch between the actual covariance matrix of interest and
the presumed one. For the diagonal loading, the key matter is
the selection of the loading level, the selecting method of the
loading level is given. The impact of diagonal loading on
detection probability and output signal-to-noise ratio is
analyzed detailedly, namely, it can improve the detection
probability and the output signal-to-noise ratio. Numerical
simulations attest the validity of the analysis, it improves the
performance greatly, such as, the diagonal loading is an
effective method for improving the detective performance for
low velocity target, it can raises up the signal power of
mainlobe, and depresses the sidelobe power and clutter, noise
power. Especially it has favourable performance for “statistical
mismatch” between the ideal covariance matrix and its
estimation.
II. P
ROBLEM STATEMENTS
Consider the MVDR-SMI STAP, Diagonal loading is
added to STAP as follows. Diagonal loading solves the
following constrained minimization:
()
{}
wRwwIRww
swsw
u
H
Lu
Hdl
HH
~
minarg
ˆ
minarg
11 ==
=+=
σ
(1)
where
IRR
2
ˆ
Luu
σ
+=
(2)
is the diagonal loading covariance matrix, and
I
is the identity
matrix, and
2
L
σ
is the loading factor which controls the amount
of loading. Therefore diagonally loaded MVDR-SMI weight
vector are computed as follows:
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