MIMO-MC radar: A MIMO radar approach based on matrix completion

In a typical multiple-input and multiple-output (MIMO) radar scenario, the receive nodes transmit to a fusion center either samples of the target returns, or the results of matched filtering with the transmit waveforms. Based on the data it receives from multiple antennas, the fusion center formulates a matrix, referred to as the data matrix, which, via standard array processing schemes leads to target detection and parameter estimation. In this paper, it is shown that under certain conditions, the data matrix is low rank and thus can be recovered based on knowledge of a small subset of its entries via matrix completion (MC) techniques. Leveraging the low-rank property of the data matrix, we propose a new MIMO radar approach, termed, MIMO-MC radar, in which each receive node either performs matched filtering with a small number of randomly selected dictionary waveforms or obtains sub-Nyquist samples of the target returns at random sampling instants, and forwards the results to a fusion center. Based on the received samples, and with knowledge of the sampling scheme, the fusion center partially fills the data matrix and subsequently applies MC techniques to estimate the full matrix. MIMO-MC radars share the advantages of MIMO radars with compressive sensing, (MIMO-CS), i.e., high resolution with reduced amounts of data, but unlike MIMO-CS radars do not require grid discretization. The MIMO-MC radar concept is illustrated through a uniform linear array configuration, and its target estimation performance is demonstrated via simulations.

[1]  Qilian Liang,et al.  Radar Sensor Networks: Algorithms for Waveform Design and Diversity with Application to ATR with Delay-Doppler Uncertainty , 2007, EURASIP J. Wirel. Commun. Netw..

[2]  Emmanuel J. Candès,et al.  The Power of Convex Relaxation: Near-Optimal Matrix Completion , 2009, IEEE Transactions on Information Theory.

[3]  H. Vincent Poor,et al.  MIMO Radar Using Compressive Sampling , 2009, IEEE Journal of Selected Topics in Signal Processing.

[4]  Xin Wang,et al.  Low-rank matrix completion for array signal processing , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[5]  Jian Li,et al.  On Parameter Identifiability of MIMO Radar , 2007, IEEE Signal Processing Letters.

[6]  Jian Li,et al.  MIMO Radar with Colocated Antennas , 2007, IEEE Signal Processing Magazine.

[7]  Thomas Strohmer,et al.  High-Resolution Radar via Compressed Sensing , 2008, IEEE Transactions on Signal Processing.

[8]  P.K. Dutta,et al.  Towards radar-enabled sensor networks , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[9]  Andrea Montanari,et al.  Regularization for matrix completion , 2010, 2010 IEEE International Symposium on Information Theory.

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

[11]  Emmanuel J. Candès,et al.  Matrix Completion With Noise , 2009, Proceedings of the IEEE.

[12]  Athina P. Petropulu,et al.  Matrix Completion in Colocated MIMO Radar: Recoverability, Bounds & Theoretical Guarantees , 2013, IEEE Transactions on Signal Processing.

[13]  Emmanuel J. Candès,et al.  Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements , 2011, IEEE Transactions on Information Theory.

[14]  Andrea Montanari,et al.  Matrix completion from a few entries , 2009, 2009 IEEE International Symposium on Information Theory.

[15]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[16]  Bart Vandereycken,et al.  Low-Rank Matrix Completion by Riemannian Optimization , 2013, SIAM J. Optim..

[17]  Nikos D. Sidiropoulos,et al.  Tensor Algebra and Multidimensional Harmonic Retrieval in Signal Processing for MIMO Radar , 2010, IEEE Transactions on Signal Processing.

[18]  Olgica Milenkovic,et al.  A Geometric Approach to Low-Rank Matrix Completion , 2010, IEEE Transactions on Information Theory.

[19]  A. Robert Calderbank,et al.  Sensitivity to Basis Mismatch in Compressed Sensing , 2011, IEEE Trans. Signal Process..

[20]  Yonina C. Eldar,et al.  Identification of Parametric Underspread Linear Systems and Super-Resolution Radar , 2010, IEEE Transactions on Signal Processing.

[21]  L.J. Cimini,et al.  MIMO Radar with Widely Separated Antennas , 2008, IEEE Signal Processing Magazine.

[22]  Emmanuel J. Candès,et al.  Templates for convex cone problems with applications to sparse signal recovery , 2010, Math. Program. Comput..

[23]  Athina P. Petropulu,et al.  Robust beamforming via matrix completion , 2013, 2013 47th Annual Conference on Information Sciences and Systems (CISS).

[24]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[25]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[26]  P. P. Vaidyanathan,et al.  MIMO Radar Space–Time Adaptive Processing Using Prolate Spheroidal Wave Functions , 2008, IEEE Transactions on Signal Processing.

[27]  Volkan Cevher,et al.  Distributed bearing estimation via matrix completion , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[28]  Athina P. Petropulu,et al.  Target estimation in colocated MIMO radar via matrix completion , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.