Application of L1 reconstruction of sparse signals to ambiguity resolution in radar

A novel approach for range-Doppler ambiguity resolution in pulse Doppler radars is presented. The new technique makes use of the sparse measurement structure of the post-detection data in multiple pulse repetition frequency radars and the resulting L0/L1 equivalence. The ambiguity resolution problem is cast as a linear system of equations which is solved for the unique sparse solution. Numerical results show that the ambiguities can be effectively resolved even with the number of measurements much less than the number of unknowns. The proposed technique reduces the number of PRFs required to resolve multiple targets in some cases compared to conventional techniques.

[1]  V. Chandar.  A Negative Result Concerning Explicit Matrices With The Restricted Isometry Property , 2008 .

[2]  A. G. Thomas,et al.  Medium PRF set selection: an approach through combinatorics , 1994 .

[3]  Piotr Indyk,et al.  Sparse Recovery Using Sparse Random Matrices , 2010, LATIN.

[4]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[5]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[6]  A. Ferrari,et al.  Doppler ambiguity resolution using multiple PRF , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[7]  C. M. Alabaster,et al.  Novel PRF schedules for medium PRF radar , 2003, 2003 Proceedings of the International Conference on Radar (IEEE Cat. No.03EX695).

[8]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

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

[10]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

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

[12]  E. J. Hughes,et al.  Medium PRF set selection using evolutionary algorithms , 2002 .

[13]  I. Loris.  On the performance of algorithms for the minimization of ℓ1-penalized functionals , 2007, 0710.4082.

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

[15]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[16]  D. Donoho,et al.  Thresholds for the Recovery of Sparse Solutions via L1 Minimization , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[17]  Emmanuel J. Candès,et al.  NESTA: A Fast and Accurate First-Order Method for Sparse Recovery , 2009, SIAM J. Imaging Sci..

[18]  Mark A. Richards,et al.  Fundamentals of Radar Signal Processing , 2005 .

[19]  Hamish Meikle,et al.  Modern Radar Systems , 2001 .

[20]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[21]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[22]  Deanna Needell,et al.  Noisy signal recovery via iterative reweighted L1-minimization , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[23]  Yaakov Tsaig,et al.  Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution , 2006, Signal Process..

[24]  Alexandros G. Dimakis,et al.  Sparse Recovery of Nonnegative Signals With Minimal Expansion , 2011, IEEE Transactions on Signal Processing.

[25]  Alexandros G. Dimakis,et al.  Explicit matrices for sparse approximation , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[26]  Piotr Indyk,et al.  Combining geometry and combinatorics: A unified approach to sparse signal recovery , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[27]  T Talaky,et al.  Interior Point Methods of Mathematical Programming , 1997 .

[28]  Teng Long,et al.  Resolution of range and velocity ambiguity for a medium pulse Doppler radar , 2000, Record of the IEEE 2000 International Radar Conference [Cat. No. 00CH37037].

[29]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.