Wideband Sparse Signal Acquisition With Dual-rate Time-Interleaved Undersampling Hardware and Multicoset Signal Reconstruction Algorithms

A new undersampling-based dual-rate signal acquisition technique for measuring a wideband sparse signal (i.e., a multiband signal) is presented in this paper. The proposed architecture employs a combination of dual-rate time-interleaved undersampling hardware and associated multicoset back-end signal processing algorithms. In dual-rate sampling hardware, a pair of uniform samplers is used to acquire a common incoming wideband sparse signal while the operation frequencies of the two samplers have a small frequency offset. Due to the sampling frequency offset, the time grids of the samples obtained from the two samplers are irregularly spaced. These nonuniform periodic samples are then digitally re-sequenced and applied as input to a multicoset signal reconstruction algorithm. The multicoset signal reconstruction algorithm uses the re-sequenced nonuniform periodic samples to achieve a perfect reconstruction of the original wideband signal with an enhanced time resolution beyond the sampling hardware's capability. Compared to the conventional multi-channel sampling approach commonly used with multicoset algorithms, the proposed method uses fewer sampling channels and does not require their accurate clock phase adjustment.

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

[2]  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.

[3]  Y. Bresler Spectrum-blind sampling and compressive sensing for continuous-index signals , 2008, 2008 Information Theory and Applications Workshop.

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

[5]  Yoram Bresler,et al.  Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals , 2001, IEEE Trans. Signal Process..

[6]  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.

[7]  Richard G. Baraniuk,et al.  Recovery of frequency-sparse signals from compressive measurements , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[8]  Vladimir Stojanovic,et al.  Design and Analysis of a Hardware-Efficient Compressed Sensing Architecture for Data Compression in Wireless Sensors , 2012, IEEE Journal of Solid-State Circuits.

[9]  Abhijit Chatterjee,et al.  Low Cost Sparse Multiband Signal Characterization Using Asynchronous Multi-Rate Sampling: Algorithms and Hardware , 2015, J. Electron. Test..

[10]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[11]  Amir Rosenthal,et al.  Multirate Synchronous Sampling of Sparse Multiband Signals , 2008, IEEE Transactions on Signal Processing.

[12]  Geert Leus,et al.  Power Spectrum Blind Sampling , 2011, IEEE Signal Processing Letters.

[13]  Yoram Bresler,et al.  Perfect reconstruction formulas and bounds on aliasing error in sub-nyquist nonuniform sampling of multiband signals , 2000, IEEE Trans. Inf. Theory.

[14]  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.

[15]  Emmanuel J. Candès,et al.  A Nonuniform Sampler for Wideband Spectrally-Sparse Environments , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[16]  J. Kruskal Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .

[17]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[18]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[19]  H. Carfantan,et al.  A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data , 2007, IEEE Journal of Selected Topics in Signal Processing.

[20]  Jesus Selva Regularized Sampling of Multiband Signals , 2010, IEEE Transactions on Signal Processing.

[21]  Amir Rosenthal,et al.  Multirate Synchronous Sampling of Sparse Multiband Signals , 2008, IEEE Transactions on Signal Processing.

[22]  F. Herrmann,et al.  Simply denoise: Wavefield reconstruction via jittered undersampling , 2008 .

[23]  Yonina C. Eldar,et al.  Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals , 2007, IEEE Transactions on Signal Processing.

[24]  Yonina C. Eldar,et al.  Xampling: Analog to digital at sub-Nyquist rates , 2009, IET Circuits Devices Syst..

[25]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[26]  D. Donoho,et al.  Basis pursuit , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.