Transmission waveform design for compressive sensing active sonar using the matrix projection from Gram matrix to identity matrix and a constraint for bandwidth

Sehyun Lee; Keunhwa Lee; Jun-Seok Lim; Myoung-Jun Cheong

doi:10.7776/ASK.2019.38.5.522

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2019 Vol.38, Issue 5 Preview Page Next Page

Research Article

Transmission waveform design for compressive sensing active sonar using the matrix projection from Gram matrix to identity matrix and a constraint for bandwidth 대역폭 제한 조건과 Gram 행렬의 단위행렬로의 사영을 이용한 압축센싱 능동소나 송신파형 설계

30 September 2019. pp. 522-533

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Abstract

The compressive sensing model for range-Doppler estimation can be expressed as an under-determined linear system y = Ax. To find the solution of the linear system with the compressive sensing method, matrix A should be sufficiently incoherent and x to be sparse. In this paper, we propose a transmission waveform design method that maintains the bandwidth required by the sonar system while lowering the mutual coherence of the matrix A so that the matrix A is incoherent. The proposed method combines two methods of optimizing the sensing matrix with the alternating projection and suppressing unwanted frequency bands using the DFT (Discrete Fourier Transform) matrix. We compare range-Doppler estimation performance of existing waveform LFM(Linear Frequency Modulated) and designed waveform using the matched filter and the compressive sensing method. Simulation shows that the designed transmission waveform has better detection performance than the existing waveform LFM.

Keywords

Compressive sensing

Waveform optimization

Range-Doppler estimation

Active sonar

Mutual coherence

Matched filter

거리-도플러 추정을 위한 압축센싱(Compressive Sensing,CS) 모델은 과소결정계인 y=Ax 선형시스템으로 표현할 수 있다. 압축센싱 기법으로 위 선형시스템의 해를 찾으려면 행렬 A가 충분히 비간섭적이고 x가 희소해야한다. 본 연구는 행렬 A가 비간섭적이도록 행렬 A의 상호간섭성을 낮추는 동시에 소나시스템에서 요구하는 대역폭을 유지하는 송신파형 설계 방법을 제안하였다. 제안한 방법은 행렬사영으로 센싱행렬을 최적화하는 방법과 DFT (Discrete Fourier Transform) 행렬을 이용하여 원하지 않은 주파수밴드를 억압하는 두 가지 방법을 결합한 것이다. 정합필터와 압축센싱 기법을 이용하여 기존파형 LFM(Linear Frequency Modulated)과 설계한 파형의 거리-도플러 추정 성능을 비교하였다. 시뮬레이션을 통해 설계한 송신파형이 기존파형(LFM)보다 탐지성능이 우수함을 보인다.

키워드

압축센싱

파형 최적화

거리-도플러 추정

능동소나

상호간섭성

정합필터

References

P. Stoica, J. Li, and X. Zhu, "Waveform synthesis for diversity-based transmit beampattern design," IEEE Trans. on Signal Processing, 56, 2593-2598 (2009).

10.1109/TSP.2007.916139

P. Stoica, H. He, and J. Li, "New algorithm for designing unimodular sequences with good correlation properties," IEEE Trans. on Signal Processing, 57, 1415-1425 (2011).

10.1109/TSP.2009.2012562

P. Stoica, H. He, and J. Li, "Waveform design with stopband and correlation constraints for cognitive radar," in 2nd International Workshop on Cognitive Information Processing, 344-349 (2010).

J. Zhang, "Adaptive compressed sensing radar oriented toward cognitive detection," IEEE Trans. on Signal Processing, 60, 1718-1729 (2012).

10.1109/TSP.2012.2183127

J. A. Tropp, I. S. Dhillon, R. W. Heath, and T. Strohmer, "Designing structured tight frames via an alternating projection method," IEEE Trans. on Information Theory, 51, 188-209 (2005).

10.1109/TIT.2004.839492

L. Zegov, Waveform optimization for compressive-sensing radar systems, (M.S. thesis, TUDelft, 2013).

J. A. Tropp and A. C. Gilbert, "Signal recovery from partial information by orthogonal matching pursuit," IEEE Trans. on Information Theory, 53, 4655-4666 (2008).

10.1109/TIT.2007.909108

S. S. Chen, D. Donoho, and M.A. Saunders, "Atomic decomposition by basis pursuit," SIAM Review, 52, 489-509 (2001).

Y. E. Nesterov and A. S. Nemirovski, "Interior Point Polynomial Algorithms in Convex Programming," SIAM, 13 (1994).

10.1137/1.9781611970791

E. J. Candes and M. B. Wakin, "An introduction to compressive sampling," IEEE, Signal Trans. on Signal Processing, 57, 2275-2284 (2009).

10.1109/TSP.2009.2014277

Y. C. Eldar and G. Kutyniok, Compressed Sensing: Theory and Applications (Cambridge University Press, London, 2012), pp. 1-166.

O. Bar-Ilan and Y. C. Eldar, "Sub-nyquist radar via doppler focusing," IEEE Trans. on Signal Processing, 62, 1796-1811 (2014).

10.1109/TSP.2014.2304917

Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 38
No :5
Pages :522-533
Received Date : 2018-10-24
Revised Date : 2018-11-22
Accepted Date : 2019-06-18
DOI :https://doi.org/10.7776/ASK.2019.38.5.522

The Journal of the Acoustical Society of Korea ISSN:1225-4428(Print) 2287-3775(Online) 한국음향학회지

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