Performance analysis of stochastic signal detection with compressive measurements

Compressed sensing (CS) enables the recovery of sparse or compressible signals from relatively a small number of randomized measurements compared to Nyquist-rate samples. Although most of the CS literature has focused on sparse signal recovery, exact recovery is not actually necessary in many signal processing applications. Solving inference problems with compressive measurements has been addressed by recent CS literature. This paper takes some further steps to investigate the potential of CS in signal detection problems. We provide theoretical performance limits verified by simulations for detection performance in arbitrary random signal detection with compressive measurements.

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

[2]  W. B. Johnson,et al.  Extensions of Lipschitz mappings into Hilbert space , 1984 .

[3]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

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

[5]  Richard G. Baraniuk,et al.  Detection and estimation with compressive measurements , 2006 .

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

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

[8]  Antonio Artés-Rodríguez,et al.  Compressive sensing detection of stochastic signals , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[9]  Zhu Han,et al.  Sparse event detection in wireless sensor networks using compressive sensing , 2009, 2009 43rd Annual Conference on Information Sciences and Systems.

[10]  J. Haupt,et al.  Compressive Sampling for Signal Classification , 2006, 2006 Fortieth Asilomar Conference on Signals, Systems and Computers.

[11]  Richard G. Baraniuk,et al.  Signal Processing With Compressive Measurements , 2010, IEEE Journal of Selected Topics in Signal Processing.

[12]  Robert D. Nowak,et al.  Compressive Sampling for Signal Detection , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[13]  Jingxian Wu,et al.  Approximating the Sum of Correlated Lognormal or, Lognormal-Rice Random Variables , 2006, 2006 IEEE International Conference on Communications.

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

[15]  R. DeVore,et al.  The Johnson-Lindenstrauss Lemma Meets Compressed Sensing , 2006 .