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RESEARCH PAPER

Special Issue

SCIENCE CHINA

Information Sciences

August 2012 Vol. 55 No. 8: 1852–1859

doi: 10.1007/s11432-012-4604-9

 Science China Press and Springer-Verlag Berlin Heidelberg 2012 info.scichina.com www.springerlink.com

Sparse synthetic aperture radar imaging with

optimized azimuthal aperture

ZENG Cao

∗

, WANG MinHang, LIAO GuiSheng & ZHU ShengQi

National Lab of Radar Signal Processing, Xidian University, Xi’an 710071,China

Received November 28, 2011; accepted April 21, 2012; published online June 22, 2012

Abstract To counter the problem of acquiring and processing huge amounts of data for synthetic aperture

radar (SAR) using traditional sampling techniques, a method for sparse SAR imaging with an optimized az-

imuthal aperture is presented. The equivalence of an azimuthal match ﬁlter and synthetic array beamforming

is shown so that optimization of the azimuthal sparse aperture can be converted to optimization of synthetic

array beamforming. The azimuthal sparse aperture, which is composed of a middle aperture and symmetrical

bilateral apertures, can be obtained by optimization algorithms (density weighting and simulated annealing

algorithms, respectively). Furthermore, sparse imaging of spectrum analysis SAR based on the optimized sparse

aperture is achieved by padding zeros at null samplings and using a non-uniform Taylor window. Compared

with traditional sampling, this method has the advantages of reducing the amount of sampling and alleviating

the computational burden with acceptable image quality. Unlike periodic sparse sampling, the proposed method

exhibits no image ghosts. The results obtained from airborne measurements demonstrate the eﬀectiveness and

superiority of the proposed method.

Keywords sparse SAR, aperture optimization, beamforming, density weighting, simulated annealing

Citation Zeng C, Wang M H, Liao G S, et al. Sparse synthetic ap erture radar imaging with optimized azimuthal

aperture. Sci China Inf Sci, 2012, 55: 1852–1859, doi: 10.1007/s11432-012-4604-9

1 Introduction

As an all-day, all-weather, long-distance active sensor, a synthetic aperture radar (SAR) [1,2] installed

on an airborne or a space-borne platform acquires real-time remote-sensing information for many civil

and military applications. With faster platform velocities and smaller antenna apertures, the azimuth

bandwidth becomes much broader, thus requiring a higher pulse repetition frequency (PRF). According

to the Nyquist sampling theory, the PRF must be greater than two times the azimuthal bandwidth to

avoid azimuth ambiguity. Thus a dual challenge of obtaining considerable amounts of data with the

associated heavy burden of signal processing is created.

There may be three ways to overcome the challenge. The ﬁrst way is through uniform or periodic

azimuthal down-sampling [3]; however the former is limited by azimuthal bandwidth and the latter leads

to beamforming grating lobes. A second way, which has received a lot of attention recently [4,5], is by

compressive sensing (CS), i.e., extracting useful information with less sampling data using the sparse

characteristic. CS applied to SAR requires further research in the following areas: (1) how to obtain

∗

Corresponding author (email: czeng@mail.xidian.edu.cn)

Zeng C, et al. Sci China Inf Sci August 2012 Vol. 55 No. 8 1853

−M −M+1 −2 −10 1 2 M−1

Figure 1 Geometry of side-looking, strip-mode SAR.

an eﬀective sparse representation; (2) how to reduce the complexity of the recovery algorithm; and (3)

how to improve robustness in the presence of model mismatch. A third way to meet the data acquisition

and signal processing challenge is by way of sparse sampling optimization via intelligent algorithms

such as the genetic algorithm (GA) [6,7], the particle swarm optimization (PSO) algorithm [8], and the

simulated annealing (SA) algorithm [9,10]. GA is a parallel random-search algorithm based on concepts

in natural heredity and Darwin’s theory of evolution, and has the capability of global optimization. PSO

is a bionics algorithm based on a speed-displacement model, and has the merits of simple computation

and fast convergence. SA is a heuristically random-search algorithm based on Monte Carlo iteration by

perturbation; SA requires only one initial state, while both GA and PSO need a large initial population.

Adopting the third approach, a method with acceptable image quality is presented for sparse SAR

that is based on an optimized azimuthal sparse aperture. The equivalence of the azimuthal match ﬁlter

and synthetic array beamforming is demonstrated, whereby the point-spread function is shown to be

equivalent to the beamforming pattern. Also, the sparse sampling aperture, which consists of a middle

aperture and bilateral apertures, is attained by optimization of the beamforming pattern. The former

aperture is optimized by a density-weighting algorithm [11] to reduce dimensions and to suppress the

levels of side lobes; and the latter aperture is optimized by the SA algorithm that maximizes the ratio

of the main lobe to the second side lobe. Finally, sparse imaging of a spectrum analysis (SPECAN)

SAR, based on the optimized sparse aperture, is achieved by padding zeros at null samplings and using

a non-uniform Taylor window [12].

2 Equivalence of an azimuthal match ﬁlter and synthetic array beamforming

The geometry of side-looking, strip-mode SAR is depicted in Figure 1. The synthetic array consists

of 2M + 1 virtual sensors (i.e. sampling positions) along the azimuth that are placed at a distance

d = V /PRF apart where V is the platform velocity. Without loss of generality, consider a scattering

point T located at R

and X

where R

is the slope distance between T and the center of the synthetic

array and X

is the azimuthal oﬀset between T and the center of the scene P . The direction of arrival

of T is denoted as θ

2.1 Match ﬁl ter along azimuth

Neglecting the quadratic component of the range cell migration (RCM), the signal after compensation of

the RCM linear component and the range pulse compression can be expressed as



t, t

; R

)=A

sinc







t −



)exp



−j

4π

R(t

; R

)



, (1)

where



t is the fast time; t

is the slow time, t

= m/PRF and m ∈ [−M : M − 1]; A

is the amplitude

response after range compression; B

is the bandwidth of the chirp signal; c and λ are the speed of light and

the wavelength of carrier, respectively; a

) is the window along the azimuth; sinc(z)=sin(πz)/(πz); j

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