NDLI: Detection of unknown and arbitrary sparse signals against noise

Content Provider	IET Digital Library
Author	Lei, Chuan Zhang, Jun Gao, Qiang
Abstract	The detection of sparse signals against background noise is difficult since the information in the signal is only carried by a small portion of it. Prior information is usually assumed to ease detection. This study considers the general unknown and arbitrary sparse signal detection problem when no prior information is available. Under a Neyman–Pearson hypothesis-testing problem model, a new detection scheme referred to as the likelihood ratio test with sparse estimation (LRT-SE) is proposed. The SE technique from the compressive sensing theory is incorporated into the LRT-SE to achieve the detection of sparse signals with unknown support sets and arbitrary non-zero entries. An analysis of the effectiveness of LRT-SE is first given in terms of the characterisation of the conditions for the Chernoff-consistent detection. A large deviation analysis is then given to characterise the error exponent of LRT-SE with respect to the signal-to-noise ratio and the angle between the sparse signal and its estimate. Numerical results demonstrate superior detection performance of the proposed scheme over existing asymptotically optimal sparse detectors for finite signal dimensions. In addition, the simulation shows that the error probability of the proposed scheme decays exponentially with the number of observations.
Starting Page	146
Ending Page	157
Page Count	12
ISSN	17519675
Volume Number	8
e-ISSN	17519683
Issue Number	Issue 2, Apr (2014)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/8/2
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2011.0125
Journal	IET Signal Processing
Publisher Date	2013-08-29
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Arbitrary Nonzero Entries Arbitrary Sparse Signal Detection Problem Background Noise Chernoff-consistent Detection Deviation Analysis Error Probability Error Statistics Likelihood Ratio Test-with-sparse Estimation LRT-SE Neyman-Pearson Hypothesis-testing Problem Model Numerical Analysis Numerical Method Signal Denoising Signal Detection Signal Processing Theory Statistical Testing Statistics Unknown Sparse Signal Detection Problem Unknown Support Sets
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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