LFM宽带雷达信号的盲压缩感知模型
收稿日期: 2013-10-25
修回日期: 2014-03-10
网络出版日期: 2014-04-04
基金资助
国家“863”计划（2013AA7014061）
A Blind Compressed Sensing Model for Linear Frequency Modulated Wideband Radar Signals
Received date: 2013-10-25
Revised date: 2014-03-10
Online published: 2014-04-04
Supported by
National High-tech Research and Development Program of China (2013AA7014061)
在欠采样测量基础上，提出了一种基于盲压缩感知（BCS）的线性调频（LFM）宽带雷达信号欠采样与重构新框架。这一机制利用LFM雷达信号在分数阶傅里叶变换（FRFT）域上良好的能量聚集特性，将LFM及其延迟信号看做是未知p阶次FRFT域上的稀疏线性组合。首先通过时延相关解线调欠采样得到最佳稀疏FRFT域，再以此构造出原信号对应的p阶次离散FRFT（DFRFT）稀疏基字典，最后结合离散FRFT系数的块稀疏性利用块重构算法从测量值中估计出稀疏系数，同时论证了LFM信号单通道BCS问题解的唯一性，从而实现了稀疏基未知情况下针对LFM宽带雷达信号的盲压缩感知，为非合作条件下LFM信号欠采样采集与无源探测提供了一种新思路。
方标 , 黄高明 , 高俊 . LFM宽带雷达信号的盲压缩感知模型[J]. 航空学报, 2014 , 35(8) : 2261 -2270 . DOI: 10.7527/S1000-6893.2014.0020
A novel framework of sub-Nyquist sampling and reconstruction for linear frequency modulation (LFM) radar signals based on the theory of blind compressed sensing (BCS) is proposed. This mechanism takes LFM signals as a sparse linear combination under an unknown order p of fractional Fourier transform (FRFT) domain. Firstly, we make use of the scheme of delays correction dechirp and good energy concentration of LFM signal in proper FRFT domain to determine the optimal order, which meets the convergence conditions. Secondly, we construct discrete FRFT (DFRFT) basis dictionary according to the specific sparse FRFT domain dominated by p. To reconstruct the sources, group sparse reconstruction algorithms are chosen with less data storage and lower computational complexity. Finally, the results are provided to verify the uniqueness of the proposed framework, realizing the undersampling and reconstruction without the knowledge of priori sparse basis for LFM radar signals under the theory of BCS. The novel framework can bring a new solution concerned about the under-sampling and detection for LFM signals under the environment of non-collaboration.
[1] Candes E J. Compressive sampling//Proceedings of the International Congress of Mathematicians, 2006, 3: 1433-1452.
[2] Candes E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[3] Shi G M, Lin J, Chen X Y, et al. UWB echo signal detection with ultra-Low rate sampling based on compressed sensing[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2008, 55(4): 379-383.
[4] Gleichman S, Eldar Y C. Blind compressed sensing[J]. IEEE Transactions on Information Theory, 2011, 57(10): 6958-6975.
[5] Gleichman S, Eldar Y C. Latent varible analysis and signal separation-blind compressed sensing: theory[M]. Berlin: Springer, 2010: 386-393.
[6] Tao R, Deng B, Wang Y. Fractional Fourier transform and its evolution in signal processing[J]. Science in China Science E: Information Sciences, 2006, 36(2): 113-136.
[7] Tao R, Deng B, Wang Y. Fractional Fourier transform and its application[M]. Beijing: Tsinghua University Press 2009, 12-50. (in Chinese) 陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用[M]. 北京: 清华大学出版社, 2009: 12-50.
[8] Namias V. The fractional order Fourier transform and its application to quantum mechanics[J]. IMA Journal of Applied Mathematics, 1980, 25(3): 241-265.
[9] Donoho D L, Elad M. Maximal sparsity representation via l1 minimization[J]. Proceeding of National Academic Science, 2003, 100(3): 2197-2202.
[10] Shen X X, Ye R Q, Tang B, et al. An algorithm for estimation of wideband LFM signal parameters based on subsampling[J]. Chinese Journal of Radio Sciece, 2007, 22(1): 43-46. (in Chinese) 沈显祥, 叶瑞青, 唐斌, 等. 基于欠采样的宽带线性调频信号参数估计[J]. 电波科学学报, 2007, 22(1): 43-46.
[11] Pei S C, Ding J J. Closed-form discrete fractional and affine Fourier transform[J]. IEEE Transactions on Signal Processing, 2000, 48(5): 1338-1353.
[12] Eldar Y C, Kuppinger P, Bolcskei H. Block-sparse signals: uncertainty relations and efficient recovery[J]. IEEE Transactions on Signal Processing, 2010, 58(6): 3042-3054.
[13] Tropp J, Gilbert A. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666.
[14] Majumdar A, Ward R K. Fast group sparse classification[J]. Canadian Journal of Electrical and Computer Engineering, 2009, 34(4): 136-144.
[15] Blumensath T, Davies M E. Gradient pursuits[J]. IEEE Transactions on Signal Processing, 2008, 56(6): 2370-2382.
/
| 〈 |
|
〉 |
CJA