DVB-S系统下的Laplace-SLIM算法：稀疏无源雷达成像新方法

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"基于Laplace-SLIM算法的基于DVB-S的稀疏无源雷达成像" 在本文中，作者探讨了如何利用数字卫星视频广播（DVB-S）系统进行稀疏图像重建，特别是在无源雷达成像领域。无源雷达成像是一种利用非专用发射信号（如DVB-S信号）进行目标探测的技术，它具有成本效益高和隐蔽性强等优点。然而，由于信号的复杂性和目标响应的特性，传统的稀疏恢复方法可能无法达到理想的成像效果。 Swerling I模型被引入来描述目标的散射行为。这个模型指出，目标的散射系数在不同的频率下可能存在共振现象，导致信号的非均匀性。这种非线性的响应使得基于固定模型的恢复算法表现不佳，尤其是在处理稀疏数据时。为了解决这个问题，作者提出了Laplace-SLIM（Laplace先验的迭代最小化）算法。该算法是针对联合稀疏恢复问题设计的，它采用了拉普拉斯分布作为先验信息，以适应Swerling I模型中的频率依赖性散射特性。Laplace-SLIM可以视为一种重新加权的l1-norm算法，l1-norm常用于促进稀疏解，而重新加权策略则有助于更好地捕捉目标的频率响应变化。在Laplace-SLIM算法中，每一轮迭代都包括对观测数据的拟合以及对稀疏系数的更新。通过迭代优化，算法能够逐步逼近真实的目标图像，从而提高重建质量。此外，通过与传统方法的对比，仿真结果证实了Laplace-SLIM算法的有效性，显示其在处理Swerling I模型下的DVB-S信号时，能获得更精确的成像结果。本研究工作得到了中国国家自然科学基金和中国高技术研究发展计划的支持。该研究对于提升无源雷达成像技术的性能具有重要意义，特别是在应对复杂散射环境和资源有限的条件下。通过采用Laplace-SLIM，未来的研究可以进一步探索如何在实际应用中优化无源雷达系统的效能，提高目标检测和识别的准确率。

The work in this paper is supported by National Natural Science Foundation

of China under Grant No. 61172155 and the Hi-Tech Research and Development

Program of China under Grant Project No. 2013AA122903.

Sparse Passive Radar Imaging Based on DVB-S

using the Laplace-SLIM Algorithm

Xiaofei Yu, Tianyun Wang*, Xinfei Lu, Chang Chen, Weidong Chen

Key Laboratory of Electromagnetic Space Information, Chinese Academy of Sciences

University of Science and Technology of China, Hefei, Anhui, P.R. China

*China Satellite Maritime Tracking and Control Department, Jiangyin, 214431, China

Email: {yuxfagn, wangty, lxfei}@mail.ustc.edu.cn, {chench, wdchen}@ustc.edu.cn

Abstract—This paper studies sparse image reconstruction

based on digital video broadcasting-satellites (DVB-S) system. The

signal model is slightly different from our previous research [1-2],

i.e. we consider the Swerling I model to characterize the target

response, which means the scattering coefficients of the target

resonate at different frequencies. Due to this effect, the

performance of the conventional sparse recovery methods would

decrease considerably. By utilizing the sparse learning via iterative

minimization (SLIM) with the Laplace priors, we propose an

effective algorithm named Laplace-SLIM to deal with the

aforementioned joint sparse recovery problem, which can be seen

as a kind of reweighted l

-norm algorithm. Simulation results

verify the effectiveness of the proposed method and related

analysis.

Keywords—Sparse passive radar imaging, DVB-S, Swerling I

model, Laplace-SLIM.

I. INTRODUCTION

Passive radar, which is a subset of bistatic radar, uses non-

cooperative illuminator of opportunity as a transmitter. Because

of containing no transmitter, passive radar is virtually

undetectable and there is also no constraint in spectrum

allocation. In the past few years, passive radar systems based on

digital video broadcasting-satellites (DVB-S), FM and GNSS,

etc.[1][2][3] have developed in target detection, tracking and

imaging with numerous advantages, such as low cost, good

accuracy, strong survivability and robustness against deliberate

directional interference.

Compared with terrestrial illuminators, the DVB-S spread

more widely in space and have broader beam coverage. What’s

more, those satellites are geostationary, therefore, there is no

Doppler clutter caused by relative motion. This paper continues

our previous research on imaging for passive radar system based

on DVB-S [1] [2]. As shown in our previous work, we choose 7

available Ku-band DVB satellites which can cover the area of

China. Because there are not enough transmitters due to the

practical limitation, the wavenumber domain coverage is usually

sparse, which directly leads to poor inversion performance using

traditional imaging methods like matched filter (MF) [1].

Nevertheless, considering the fact that most space-borne targets

have limited number of strong scatterers, thus we utilize the

sparse recovery techniques to obtain better imaging performance

from the poor wavenumber coverage.

As shown in our previous work, we assume the scattering

coefficients of the target are the same under the different

frequencies, which is not appropriate according to the radar

target characteristics. In this paper, we generalize our signal

model in [1][2], and consider the Swerling I model to

characterize the target response, which means the scattering

coefficients of the target resonate at different frequencies [4].

Because of neglecting this change, conventional sparse imaging

methods such as BP, OMP etc., cannot reconstruct the target

correctly when snapshots are limit, i.e., would decrease in

performance.

Under the aforementioned assumption of the scattering

coefficients, firstly, we reestablish the receiving signal model

termed as a joint sparse recovery problem, which can be

considered as a generalized multiple measurement vectors

(MMV) case. Then, inspired by the wideband SLIM algorithm

proposed in [5], we introduce an effective algorithm called

Laplace-SLIM to deal with sparse image reconstruction problem

in passive radar system, which is based on the technique of

sparse learning via iterative minimization (SLIM) [6] combined

with the Laplace priors [7]. Our algorithm is based on three

different hierarchical Bayesian statistical models, which gives a

more accurate description of signals and noise similar as the

Bayesian compressive sensing (BCS) denoted in [8]. What’s

more, as shown in the following part of this paper, our algorithm

can been seen as a kind of reweighted l

-norm algorithm, which

may have many advantages over wideband SLIM algorithm

proposed in [6], which using reweighted l

-norm. In [9], the

authors have presented that the number of iterations of the

reweighted l

-norm required is generally much less than the

reweighted l

-norm. A second advantage of the reweighted l

norm algorithm is that it is often much easier to incorporate

additional constraints, e.g., bounded activation or non-negativity

of unknown [10], which exhibits the superior of our method

compared with the existing sparse recovery approaches.

The paper is organized as follows. Section II describes the

modified signal model, including the new DVB-S receiving

echo equation and the novel Bayesian model establishment.

Section III provides a full description of the proposed Laplace-

SLIM Algorithm. In Section IV, we will offer numerical

simulations to demonstrate the performance improvement of our

algorithm compared with several popular sparse imaging

algorithms. Section V draws the conclusions.

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