Compressive CFAR radar detection

In this paper we develop the first Compressive Sensing (CS) adaptive radar detector. We propose three novel architectures and demonstrate how a classical Constant False Alarm Rate (CFAR) detector can be combined with l1-norm minimization. Using asymptotic arguments and the Complex Approximate Message Passing (CAMP) algorithm we characterize the statistics of the l1-norm reconstruction error and derive closed form expressions for both the detection and false alarm probabilities. We support our theoretical findings with a range of experiments that show that our theoretical conclusions hold even in non-asymptotic setting. We also report on the results from a radar measurement campaign, where we designed ad hoc transmitted waveforms to obtain a set of CS frequency measurements. We compare the performance of our new detection schemes using Receiver Operating Characteristic (ROC) curves.

[1]  Richard G. Baraniuk,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[2]  Daniel P. Meyer,et al.  Radar Target Detection: Handbook of Theory and Practice , 1973 .

[3]  Michael P. Friedlander,et al.  Probing the Pareto Frontier for Basis Pursuit Solutions , 2008, SIAM J. Sci. Comput..

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

[5]  Saleem A. Kassam,et al.  Analysis of CFAR processors in homogeneous background , 1988 .

[6]  Hermann Rohling,et al.  Radar CFAR Thresholding in Clutter and Multiple Target Situations , 1983, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Emre Ertin,et al.  Sparsity and Compressed Sensing in Radar Imaging , 2010, Proceedings of the IEEE.

[8]  Andrea Montanari,et al.  Message-passing algorithms for compressed sensing , 2009, Proceedings of the National Academy of Sciences.

[9]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[10]  Peter Hoogeboom,et al.  Detection performance of Compressive Sensing applied to radar , 2011, 2011 IEEE RadarCon (RADAR).

[11]  Richard G. Baraniuk,et al.  Design and Analysis of Compressive Sensing Radar Detectors , 2012 .

[12]  R. Baraniuk,et al.  Compressive Radar Imaging , 2007, 2007 IEEE Radar Conference.

[13]  Geert Leus,et al.  Direction estimation using compressive sampling array processing , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[14]  Athina P. Petropulu,et al.  Step-frequency radar with compressive sampling (SFR-CS) , 2009, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  Jigen Peng,et al.  Improved Bounds for Restricted Isometry Constants , 2012 .

[16]  Andrea Montanari,et al.  The Noise-Sensitivity Phase Transition in Compressed Sensing , 2010, IEEE Transactions on Information Theory.

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

[18]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[19]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[20]  Peter Hoogeboom,et al.  False alarm probability estimation for Compressive Sensing radar , 2011, 2011 IEEE RadarCon (RADAR).

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

[22]  Richard G. Baraniuk,et al.  The Compressive Matched Filter , 2006 .

[23]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[24]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[25]  Peter Hoogeboom,et al.  Compressive sensing for high resolution radar imaging , 2010, 2010 Asia-Pacific Microwave Conference.