Sparse Imaging for Passive Radar System Based on
Digital Video Broadcasting Satellites
Changchang Liu, Tianyun Wang, Li Ding, Weidong Chen
Department of Electronic Engineering and Information Science
University of Science and Technology of China
Hefei, Anhui, 230027, P.R. China
Email:{cccliu, wangty, lilyding}@mail.ustc.edu.cn, wdchen@ustc.edu.cn
Abstract—This paper studies passive radar imaging system
based on digital video broadcasting (DVB) satellites. Firstly, the 3-
dimensional (3-D) imaging model which consists of multiple DVB
satellites and one receiver is established. After analyzing in the
wavenumber domain, we consider to exploit the sparsity of the
target to realize high-resolution imaging from the undersampled
wavenumber domain coverage. However, traditional compressive
sensing (CS) radar imaging methods require the imaging scene
to be pre-discretized into finite grids and all scatterers to be
located exactly on the grid. And they are likely to be severely
affected by the off-grid scatterers. Therefore, based on the
theories of Xampling and the finite rate of innovation (FRI),
we propose the analog sparse imaging (ASI) method to deal with
arbitrarily-located scatterers, which utilizes the estimating signal
parameters through rotational invariance techniques (ESPRIT)
and the plane matching technique (PMT). Simulation results
show the effectiveness of the proposed method and the related
analysis.
Index Terms—Sparse passive radar imaging, DVB satellites,
Analog compressive sensing, ESPRIT.
I. MODEL ESTABLISHMENT
Consider the 3-dimensional (3-D) passive radar imaging
model which is composed of M DVB satellites and one
receiver as shown in Fig. 1 (taking the center of the target
as origin). Assume that one scatterer of the target is located
at r =(x, y, z)
T
and
x = r cos θ sin ϕ, y = r cos θ cos ϕ, z = r sin θ (1)
where r, θ, ϕ represent the radial range, the elevation angle
and the azimuth angle of the scatterer, respectively.
(, , )r
TM
r
r
T
0000
,,
()r
TM
r
,,
()
mmmm
r
TM
r
M
Fig. 1. 3-D passive radar imaging model
Further, denote the positions of the m-th (for m =
1, 2, ··· ,M) DVB satellite and the receiver as r
m
, r
0
, and
r
m
= r
m
(cos θ
m
sin ϕ
m
, cos θ
m
cos ϕ
m
, sin θ
m
)
T
,
r
0
= r
0
(cos θ
0
sin ϕ
0
, cos θ
0
cos ϕ
0
, sin θ
0
)
T
.
(2)
Assume the transmitted signal of the m-th illuminator as
s
m
(t)=u
m
(t)e
j(2πf
m
t+ψ
m
)
(3)
where u
m
(t),f
m
,ψ
m
are the complex envelop, the carrier
frequency and the initial phase of the signal, respectively.
Considering that the DVB satellites utilize the quadrature
phase shift keying (QPSK) modulation mode, and the trans-
mitted signal is filtered by the square root raised cosine
filter before modulation in order to suppress the out-of-band
radiation, therefore we have
u
m
(t)=
⎧
⎨
⎩
N
n=0
e
jυ
n
g(t − nT
s
), 0 <t<NT
s
0,else
(4)
where g(t) represents the impulse response of the square
root raised cosine filter, T
s
is the symbol width, N is the
number of the symbols, and υ
n
(for n =0, 1, ··· ,N)
is considered to be independently and uniformly distributed
among {π/4, 3π/4, 5π/4, 7π/4} for rather large N.
There are two receiving channels in our system, the direct
wave channel and the target echo channel, as shown in Fig. 1.
Since different illuminators are located at different directions
for the receiver, the direct waves of different illuminators can
be straightforwardly separated. Further, for different illumina-
tors, we consider to choose the signals that occupy different
bands so that the corresponding target echoes can be separated
directly in the frequency domain. Therefore, here we simply
assume that the direct waves and the target echoes with respect
to different illuminators have already been separated.
For the m-th illuminator, the direct wave can be represented
as
s
md
(t)=u
m
(t − τ
md
)e
j(2πf
m
(t−τ
md
)+ψ
m
)
(5)
where τ
md
= r
md
/c, r
md
is the distance between the m-
th illuminator and the receiver, i.e. r
md
=
r
m
− r
0
, and c
denotes the speed of the light.
978-1-4673-5829-3/12/$26.00 ©2012 IEEE
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