Array Signal Processing via Sparsity-Inducing Representation of the Array Covariance Matrix

A method named covariance matrix sparse representation (CMSR) is developed to detect the number and estimate the directions of multiple, simultaneous sources by decomposing the array output covariance matrix under sparsity constraint. In CMSR the covariance matrix elements are aligned to form a new vector, which is then represented on an overcomplete spatial dictionary, and the signal number and directions are finally derived from the representation result. A hard threshold, which is selected according to the perturbation of the covariance elements, is used to tolerate the fitting error between the actual and assumed models. A computation simplification technique is also presented for CMSR in special array geometries when more than one pair of sensors has equal distances, such as the uniform linear array (ULA). Moreover, CMSR is modified with a blind-calibration process under imperfect array calibration to enhance its adaptation to practical applications. Simulation results demonstrate the performance of CMSR.

[1]  M.A. Jensen,et al.  Sparse Power Angle Spectrum Estimation , 2009, IEEE Transactions on Antennas and Propagation.

[2]  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).

[3]  Erdal Panayirci,et al.  Eigenanalysis for interference cancellation with minimum redundancy array structure , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Jian Li,et al.  Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares , 2010, IEEE Transactions on Aerospace and Electronic Systems.

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

[6]  Xavier Mestre,et al.  MUSIC, G-MUSIC, and Maximum-Likelihood Performance Breakdown , 2008, IEEE Transactions on Signal Processing.

[7]  Dmitry M. Malioutov,et al.  Homotopy continuation for sparse signal representation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[8]  Bhaskar D. Rao,et al.  An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem , 2007, IEEE Transactions on Signal Processing.

[9]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[11]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[12]  A. Moffet Minimum-redundancy linear arrays , 1968 .

[13]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[14]  A.A. Monakov,et al.  Resolution of signal sources via spectral moment estimation , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[15]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

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

[17]  Bhaskar D. Rao,et al.  Sparse Bayesian learning for basis selection , 2004, IEEE Transactions on Signal Processing.

[18]  D. Donoho,et al.  Sparse nonnegative solution of underdetermined linear equations by linear programming. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[19]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[20]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[21]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[22]  Michael Elad,et al.  L1-L2 Optimization in Signal and Image Processing , 2010, IEEE Signal Processing Magazine.

[23]  Anthony J. Weiss,et al.  Array shape calibration using sources in unknown locations-a maximum likelihood approach , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.

[24]  Kaushik Mahata,et al.  A Robust Algorithm for Joint-Sparse Recovery , 2009, IEEE Signal Processing Letters.

[25]  Arian Maleki,et al.  Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing , 2009, IEEE Journal of Selected Topics in Signal Processing.

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

[27]  Mashud Hyder,et al.  Direction-of-Arrival Estimation Using a Mixed � , 2010 .