Array aperture extrapolation using sparse reconstruction

In this paper we present some preliminary results on antenna array extrapolation for Direction Of Arrival (DOA) estimation using Sparse Reconstruction (SR). The objective of this study is to establish wether it is possible to achieve with an array of a given physical length the performance (in terms of accuracy, resolution and sidelobe level) of an equivalent larger array by using SR. The difference between our work and previous publications on DOA estimation using SR lies in the fact that we do not use SR as a beamformer, but instead we use the sparse solution for aperture extrapolation. We adopt an approach similar to the one of Swingler and Walker in [1], where the extrapolated sensor data are first tapered and then beamformed to suppress sidelobes of strong interfering targets, resulting in improved detection of weak targets.

[1]  J. Capon High-resolution frequency-wavenumber spectrum analysis , 1969 .

[2]  David N. Swingler,et al.  Line-array beamforming using linear prediction for aperture interpolation and extrapolation , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Yonina C. Eldar,et al.  Direction of Arrival Estimation Using Co-Prime Arrays: A Super Resolution Viewpoint , 2013, IEEE Transactions on Signal Processing.

[4]  Keith Q. T. Zhang Probability of resolution of the MUSIC algorithm , 1995, IEEE Trans. Signal Process..

[5]  Christian Jutten,et al.  A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm , 2008, IEEE Transactions on Signal Processing.

[6]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[7]  Adriaan van den Bos,et al.  Resolution: a survey , 1997 .

[8]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[9]  Geoffrey F Edelmann,et al.  Beamforming using compressive sensing. , 2011, The Journal of the Acoustical Society of America.

[10]  Jean-Jacques Fuchs,et al.  On the application of the global matched filter to DOA estimation with uniform circular arrays , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[11]  Johann F. Böhme,et al.  On the direction estimation Cramér-Rao bounds in the presence of uncorrelated unknown noise , 1999 .

[12]  D. Brandwood Topics in the accuracy and resolution of superresolution systems , 2009 .

[13]  Shefeng Yan,et al.  Single snapshot DOA estimation by compressive sampling , 2013 .

[14]  Emmanuel J. Cand Towards a Mathematical Theory of Super-Resolution , 2012 .

[15]  Raffaele Grasso,et al.  Single-snapshot DOA estimation by using Compressed Sensing , 2014, EURASIP Journal on Advances in Signal Processing.

[16]  Richard G. Baraniuk,et al.  Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP) , 2011, IEEE Transactions on Information Theory.