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

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。

[1]  S. Kirolos,et al.  Analog-to-Information Conversion via Random Demodulation , 2006, 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.

[2]  Ren-hong Wang,et al.  Robustness of orthogonal matching pursuit under restricted isometry property , 2014 .

[3]  J. Tropp,et al.  SIGNAL RECOVERY FROM PARTIAL INFORMATION VIA ORTHOGONAL MATCHING PURSUIT , 2005 .

[4]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[5]  Yonina C. Eldar,et al.  Xampling: Signal Acquisition and Processing in Union of Subspaces , 2009, IEEE Transactions on Signal Processing.

[6]  Yimin Zhang,et al.  Large-scale sparse reconstruction through partitioned compressive sensing , 2014, 2014 19th International Conference on Digital Signal Processing.

[7]  Kenneth E. Barner,et al.  Iterative algorithms for compressed sensing with partially known support , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Massimo Fornasier,et al.  Numerical Methods for Sparse Recovery , 2010 .

[9]  Braham Himed,et al.  Complex multitask Bayesian compressive sensing , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[10]  Lie Wang,et al.  Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise , 2011, IEEE Transactions on Information Theory.

[11]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[12]  Justin K. Romberg,et al.  Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals , 2009, IEEE Transactions on Information Theory.

[13]  Zongben Xu,et al.  Sparse SAR imaging based on L1/2 regularization , 2012, Science China Information Sciences.

[14]  David B. Dunson,et al.  Multitask Compressive Sensing , 2009, IEEE Transactions on Signal Processing.

[15]  Yonina C. Eldar,et al.  Sub-Nyquist Radar via Doppler Focusing , 2012, IEEE Transactions on Signal Processing.

[16]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[17]  Martin Vetterli,et al.  Compressed sensing of streaming data , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  Ioannis Kyriakides,et al.  Adaptive Compressive Sensing and Processing of Delay-Doppler Radar Waveforms , 2012, IEEE Transactions on Signal Processing.

[19]  Sergiy A. Vorobyov,et al.  Segmented Compressed Sampling for Analog-to-Information Conversion: Method and Performance Analysis , 2010, IEEE Transactions on Signal Processing.

[20]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[21]  Ran Tao,et al.  Compressed sensing SAR imaging based on sparse representation in fractional Fourier domain , 2012, Science China Information Sciences.

[22]  R. E. Cline Representations for the Generalized Inverse of a Partitioned Matrix , 1964 .

[23]  Chao Liu,et al.  Pulse-doppler signal processing with quadrature compressive sampling , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[24]  Emmanuel J. Candès,et al.  A Compressed Sensing Parameter Extraction Platform for Radar Pulse Signal Acquisition , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[25]  Emmanuel J. Candès,et al.  Templates for convex cone problems with applications to sparse signal recovery , 2010, Math. Program. Comput..

[26]  Zhong Liu,et al.  Quadrature Compressive Sampling for Radar Signals , 2014, IEEE Transactions on Signal Processing.

[27]  Guangming Shi,et al.  UWB Echo Signal Detection With Ultra-Low Rate Sampling Based on Compressed Sensing , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Justin K. Romberg,et al.  Sparse Recovery of Streaming Signals Using $\ell_1$-Homotopy , 2013, IEEE Transactions on Signal Processing.

[29]  Wei Huang,et al.  The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit , 2013, IEEE Signal Processing Letters.

[30]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[31]  Zhong Liu,et al.  Quadrature compressive sampling for radar echo signals , 2011, 2011 International Conference on Wireless Communications and Signal Processing (WCSP).

[32]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[33]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[34]  M. Salman Asif,et al.  Compressive Sensing for streaming signals using the Streaming Greedy Pursuit , 2010, 2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE.

[35]  Martin Vetterli,et al.  Recursive Compressed Sensing , 2013, ArXiv.

[36]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[37]  Stephen Becker,et al.  Practical Compressed Sensing: Modern data acquisition and signal processing , 2011 .

[38]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[39]  Yang Liu,et al.  Compressed sensing digital receiver and orthogonal reconstructing algorithm for wideband ISAR radar , 2014, Science China Information Sciences.