Frequency-domain adaptive sparse signal reconstruction at sub-Nyquist rate

Sub-Nyquist sparse signal reconstruction technique can significantly reduce the cost of hardware design. Many sub-Nyquist reconstruction algorithms (e.g., greedy relax and convex optimization) have been developed to reconstruct the real frequency-sparse signal by utilizing its sparsity. However, greedy algorithms require a large memory size and convex optimization algorithms exhaust a long calculation time. Unlike previous schemes, in this paper, we propose a frequency-domain adaptive sparse signal reconstruction scheme under sub-Nyquist to achieve better performance and lower computational time. Specifically, discrete Hartley transform (DHT) is adopt to find a sparse representation in frequency domain accompanying with sub-Nyquist random demodulation sampling rate and £0-NLMS algorithm is utilized to reconstruct sparse signal. Experiment results are conducted to confirm the advantages of the proposed method in terms of computational time and mean square error.

[1]  Wotao Yin,et al.  Iteratively reweighted algorithms for compressive sensing , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[2]  Yuantao Gu,et al.  A Stochastic Gradient Approach on Compressive Sensing Signal Reconstruction Based on Adaptive Filtering Framework , 2010, IEEE Journal of Selected Topics in Signal Processing.

[3]  Nanning Zheng,et al.  Generalized Correntropy for Robust Adaptive Filtering , 2015, IEEE Transactions on Signal Processing.

[4]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

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

[6]  Bernhard Schölkopf,et al.  Use of the Zero-Norm with Linear Models and Kernel Methods , 2003, J. Mach. Learn. Res..

[7]  J. A. Wepman,et al.  Analog-to-digital converters and their applications in radio receivers , 1995, IEEE Commun. Mag..

[8]  Richard G. Baraniuk,et al.  Random Filters for Compressive Sampling and Reconstruction , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[9]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[10]  Edoardo Amaldi,et al.  On the Approximability of Minimizing Nonzero Variables or Unsatisfied Relations in Linear Systems , 1998, Theor. Comput. Sci..

[11]  Yonina C. Eldar,et al.  From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals , 2009, IEEE Journal of Selected Topics in Signal Processing.

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

[13]  Badong Chen,et al.  Quantized Kernel Least Mean Square Algorithm , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Wentao Ma,et al.  Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments , 2015, J. Frankl. Inst..

[15]  S. Kirolos,et al.  Random Sampling for Analog-to-Information Conversion of Wideband Signals , 2006, 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.

[16]  Tom Diethe,et al.  Compressed Sampling for pulse Doppler radar , 2010, 2010 IEEE Radar Conference.

[17]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.