A robust detector of known signal in non-Gaussian noise using threshold systems

Authors:
Gencheng Guo;Mrinal Mandal;Yindi Jing
Affiliations:
Department of Electrical and Computer Engineering, 2nd Floor, ECERF Building, University of Alberta, Edmonton, AB, Canada T6G 2V4;Department of Electrical and Computer Engineering, 2nd Floor, ECERF Building, University of Alberta, Edmonton, AB, Canada T6G 2V4;Department of Electrical and Computer Engineering, 2nd Floor, ECERF Building, University of Alberta, Edmonton, AB, Canada T6G 2V4
Venue:
Signal Processing
Year:
2012

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Abstract

In this paper, we propose a threshold-system-based detector (TD) for detecting a known deterministic signal in independent non-Gaussian noise whose probability density function (pdf) is unknown but is symmetric and unimodal. The optimality of the proposed TD is proved under the assumptions of white noise, small signal, and a large number of samples. While previous TD designs need accurate information of the noise pdf, the proposed TD is independent of the noise pdf, and thus is robust to the noise pdf. The detection probability and the receiver operating characteristic (ROC) of the proposed TD are analyzed both theoretically and numerically. It is shown that even without knowing the noise pdf, the proposed TD has close performance to the optimal detector designed with the noise pdf information. It also performs significantly better than the matched filter (MF) when the noise pdf has heavy tails. The practical implementation, robustness to both the noise pdf and the signal, and region of validity of the proposed TD are also investigated.