Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Segment-sliding reconstruction of pulsed radar echoes with sub-Nyquist sampling

欠采样脉冲雷达回波信号的分段滑动重构

Abstract

It has been shown that analog-to-information conversion (AIC) is an efficient scheme to perform sub-Nyquist sampling of pulsed radar echoes. However, it is often impractical, if not infeasible, to reconstruct full-range Nyquist samples because of huge storage and computational load requirements. Based on the analyses of AIC measurement system, this paper develops a novel segment-sliding reconstruction (SegSR) scheme to effectively reconstruct the Nyquist samples. The SegSR performs segment-by-segment reconstruction in a sliding mode and can be implemented in real time. An important characteristic that distinguishes the proposed SegSR from existing methods is that the measurement matrix in each segment satisfies the restricted isometry property (RIP) condition. Partial support in the previous segment can be incorporated into the estimation of the Nyquist samples in the current segment. The effect of interference introduced from adjacent segments is theoretically analyzed, and it is revealed that the interference consists of two interference levels with different impacts to the signal reconstruction performance. With these observations, a two-step orthogonal matching pursuit (OMP) procedure is proposed for segment reconstruction, which takes into account different interference levels and partially known support of the previous segment. The proposed SegSR scheme achieves near-optimal reconstruction performance with a significant reduction of computational loads and storage requirements. Theoretical analyses and simulations verify its effectiveness.

创新点

本文提出新的分段滑动重构方法, 并进行深入的理论分析和计算机仿真实验。主要创新点如下:1. 提出一个新的雷达回波信号分段方法, 该方法使得每段测量对应的测量矩阵满足约束等距特性, 从而确保每段信号的可重构性。 2. 深入地理论分析了相邻段对当前段重构性能影响, 揭示了前一段和下一段的干扰特征。3. 根据干扰特征和前一段估计信息, 提出一个两步正交匹配追踪算法, 有效地抑制不同干扰。除外, 我们开展了大量计算机实验, 验证了本文方法的有效性和正确性。

This is a preview of subscription content, log in to check access.

References

  1. 1

    Donoho D L. Compressed sensing. IEEE Trans Inf Theory, 2006, 52: 1289–1306

  2. 2

    Candès E J, Romberg J K, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory, 2006, 52: 489–509

  3. 3

    Candès E J, Tao T. Decoding by linear programming. IEEE Trans Inf Theory, 2005, 51: 4203–4215

  4. 4

    Tropp J A, Laska J N, Duarte M F, et al. Beyond Nyquist: efficient sampling of sparse bandlimited signals. IEEE Trans Inf Theory, 2010, 56: 520–544

  5. 5

    Becker S. Practical compressed sensing: modern data acquisition and signal processing. Dissertation for Ph.D. Degree. Pasadena: California Institute of Technology, 2011

  6. 6

    Mishali M, Eldar Y C, Elron A J. Xampling: signal acquisition and processing in union of subspaces. IEEE Trans Signal Process, 2011, 59: 4719–4734

  7. 7

    Xi F, Chen S, Liu Z. Quadrature compressive sampling for radar echo signals. In: Proceedings of the International Conference on Wireless Communications and Signal Processing (WCSP), Nanjing, 2011. 1–5

  8. 8

    Xi F, Chen S, Liu Z. Quadrature compressive sampling for radar signals. IEEE Trans Signal Process, 2014, 62: 2787–2802

  9. 9

    Bu H X, Bai X, Tao R. Compressed sensing SAR imaging based on sparse representation in fractional Fourier domain. Sci China Inf Sci, 2012, 55: 1789–1800

  10. 10

    Hou Q K, Liu Y, Fan L J, et al. Compressed sensing digital receiver and orthogonal reconstructing algorithm for wideband ISAR radar. Sci China Inf Sci, 2015, 58: 020302

  11. 11

    Zeng J S, Fang J, Xu Z B. Sparse SAR imaging based on L1/2 regularization. Sci China Inf Sci, 2012, 55: 1755–1775

  12. 12

    Bar-Ilan O, Eldar Y C. Sub-Nyquist radar via Doppler focusing. IEEE Trans Signal Process, 2014, 62: 1796–1811

  13. 13

    Yoo J, Turnes C, Nakamura E B, et al. A compressed sensing parameter extraction platform for radar pulse signal acquisition. IEEE J Emerg Sel Topics Circ Syst, 2012, 2: 626–638

  14. 14

    Liu C, Xi F, Chen S, et al. Pulse-doppler signal processing with quadrature compressive sampling. IEEE Trans Aerosp Electron Syst, 2015, 51: 1217–1230

  15. 15

    Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans Inf Theory, 2007, 53: 4655–4666

  16. 16

    Needell D, Tropp J A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl Comput Harmon Anal, 2009, 26: 301–321

  17. 17

    Yin W, Osher S, Goldfarb D, et al. Bregman iterative algorithm for ℓ1-minimization with applications to compressive sensing. SIAM J Imaging Sci, 2008, 1: 143–168

  18. 18

    Becker S R, Candès E J, Grant M C. Templates for convex cone problems with applications to sparse signal recovery. Math Program Comput, 2011, 3: 165–218

  19. 19

    Ji S, Dunson D, Carin L. Multitask compressive sensing. IEEE Trans Signal Process, 2009, 57: 92–106

  20. 20

    Wu Q, Zhang Y D, Amin M G, et al. Complex multitask Bayesian compressive sensing. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Florence, 2014. 3375–3379

  21. 21

    Fornasier M. Numerical methods for sparse recovery. Radon Series Comp Appl Math, 2010, 9: 1–110

  22. 22

    Shi G, Lin J, Chen X, et al. UWB echo signal detection with ultra-low rate sampling based on compressed sensing. IEEE Trans Circ Syst Express Briefs, 2008, 55: 379–383

  23. 23

    Freris N M, Öçal O, Vetterli M. Compressed sensing of streaming data. In: Proceedings of the 51st Annual Allerton Conference on Communication, Control, and Computing, Monticello, 2013. 1242–1249

  24. 24

    Freris N M, Öçal O, Vetterli M. Recursive compressed sensing. ArXiv:1312.4895, 2013

  25. 25

    Petros T B, Asif M S. Compressive sensing for streaming signals using the streaming greedy pursuit. In: Proceedings of the Military Communications Conference (MILCOM), San Jose, 2010. 1205–1210

  26. 26

    Asif M S, Romberg J. Sparse recovery of streaming signals using ℓ1-homotopy. IEEE Trans Signal Process, 2014, 62: 4209–4223

  27. 27

    Qin S, Zhang Y D, Wu Q, et al. Large-scale sparse reconstruction through partitioned compressive sensing. In: Proceedings of the 19th International Conference on Digital Signal Processing, Hong Kong, 2014. 837–840

  28. 28

    Carrillo R E, Polania L F, Barner K E. Iterative algorithms for compressed sensing with partially known support. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Dallas, 2010. 3654–3657

  29. 29

    Cai T T, Wang L. Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Trans Inf Theory, 2011, 57: 4680–4688

  30. 30

    Wu R, Huang W, Chen D. The exact support recovery of sparse signals with noise via orthogonal matching pursuit. IEEE Signal Process Lett, 2013, 20: 403–406

  31. 31

    Dan W, Wang R. Robustness of orthogonal matching pursuit under restricted isometry property. Sci China Math, 2014, 57: 627–634

Download references

Author information

Correspondence to Zhong Liu.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Xi, F., Chen, S. et al. Segment-sliding reconstruction of pulsed radar echoes with sub-Nyquist sampling. Sci. China Inf. Sci. 59, 122309 (2016). https://doi.org/10.1007/s11432-015-0602-9

Download citation

Keywords

  • compressed sensing
  • analog-to-information conversion
  • orthogonal matching pursuit (OMP)
  • segment-sliding reconstruction
  • restricted isometry property (RIP)

关键词

  • 压缩感知
  • 模拟信息转换
  • 正交匹配追踪算法
  • 分段滑动重构
  • 约束等距特性