GC •12 Workshop: Radar and Sonar Networks
Amplitude Based Compressive Sensing for UWB Noise Radar Signal ]i Wu, Qilian Liang
Xiuzhen Cheng
Dept of Electrical Engineering University of Texas at Arlington Arlington, TX 76019-0016, USA Email:
[email protected] [email protected]
Dept of Computer Science George Washington University Washington, DC 20052, USA Email:
[email protected]
Dechang Chen
Ram M. Narayanan
Dept of Preventive Medicine and Biometrics Uniformed Services University of the Health Science Bethesda, MD 20814-4799, USA Email:
[email protected]
Dept of Electrical Engineering The Pennsylvania State University University Park, PA 16802, USA Email:
[email protected]
Abstract-Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, subNyquist signal acquisition. Ultra-wideband (UWB) noise radar is one of the novel techniques which is widely used in various applications such as emergency rescues and military operations. One challenging problem in UWB noise radar operation is that a huge amount of data will be received which requires tremendous storage space. Compressive sensing could easily handle this problem since it captures all the information we need from far fewer samples. In this paper, we propose a novel amplitude based compressive sensing algorithm to compress data without any knowledge in advance. Simulation results indicate that only 1/5 of original measurements are sufficient to recover original data, which also achieves a higher compression ratio than the conventional compressive sensing.
I. INTRODUCTION Compressive sensing (CS) is a new method to capture and represent compressible Signals at a rate significantly below the Nyquist rate [1]- [8]. It employs nonadaptive linear projections that preserve the structure of the signal; the Signal is then reconstructed from these projections using an optimization process. This leads immediately to new Signal reconstruction methods that are successful with surprisingly few measurements, which in turn leads to Signal acquisition methods that effect compression as part of the measurement process (hence "compressive sensing"). These recent realizations (though built upon prior work exploiting Signal sparsity) have spawned an explosion of research yielding exciting results in a wide range of topics, encompassing algorithms, theory, and applications. Since the UWB Signal is usually in UHF range (500-1000 MHz) [9][10], the sampling rate should be more than 1 GHz/s (Nyquist rate) for alias-free Signal sampling which requires plenty of space to store the received Signal. In this paper, we apply amplitude based compressive sensing in UWB noise radar Signal [11][12], which asserts that one can recover it
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from far fewer samples than the traditional Nyquist rate. It also enhances the operational feasibility of UWB noise radar. The remainder of this paper is organized as follows. Section II presents a overview of compressive sensing. In Section III, linear programming is introduced to solve the compressive sensing problem. Our novel amplitude based compressive sensing algorithm is proposed in Section IV. Finally, numerical results and conclusions will be given in Section V and Section V. II. OVERVIEW OF COMPRESSIVE SENSING
A. Sparsity and undersampled signal recovery Many natural Signals have concise representations when expressed in the proper basis [1][3]. Mathematically speaking, consider a discrete Signal f E IR ri which can be expanded in an orthonormal basis W == ['l/Jl 'l/J2 ... 'l/Jn] as follows:
f(t) ==
L Xi'l/Ji(t), N
i=l
where x is the coefficient sequence of from the Signal f:
f
(1) that can be computed
xi==(f,'l/Ji),i==1,2,···,n.
(2)
It will be convenient to express f as Wx (where W is the n x n matrix with 'l/Jl 'l/J2 ... 'l/Jn as columns). We can say the discrete Signal f is K-sparse in the domain W, K « N, if only K out of n coefficients in the sequence x are nonzero. Sparsity of Signal is a fundamental principle used in the compressive sensing. Note that there are only K coefficients are nonzero, so we can remove this "sampling redundancy" by acquiring only m samples of the Signal f, where K < m
