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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)

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

0000

()r

()

mmmm

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

, r

, and

= r

(cos θ

sin ϕ

, cos θ

cos ϕ

, sin θ

)

= r

(cos θ

sin ϕ

, cos θ

cos ϕ

, sin θ

)

(2)

Assume the transmitted signal of the m-th illuminator as

(t)=u

(t)e

j(2πf

t+ψ

)

(3)

where u

(t),f

,ψ

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

(t)=

⎧

⎨

⎩



n=0

jυ

g(t − nT

), 0 <t<NT

0,else

(4)

where g(t) represents the impulse response of the square

root raised cosine ﬁlter, T

is the symbol width, N is the

number of the symbols, and υ

(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

(t)=u

(t − τ

j(2πf

(t−τ

)+ψ

)

(5)

where τ

= r

/c, r

is the distance between the m-

th illuminator and the receiver, i.e. r



− r



, and c

denotes the speed of the light.

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