Stochastic Resonance in Nonlinear Signal Detection

Authors: Youguo Wang, Lenan Wu

Abstract:

Stochastic resonance (SR) is a phenomenon whereby the signal transmission or signal processing through certain nonlinear systems can be improved by adding noise. This paper discusses SR in nonlinear signal detection by a simple test statistic, which can be computed from multiple noisy data in a binary decision problem based on a maximum a posteriori probability criterion. The performance of detection is assessed by the probability of detection error Per . When the input signal is subthreshold signal, we establish that benefit from noise can be gained for different noises and confirm further that the subthreshold SR exists in nonlinear signal detection. The efficacy of SR is significantly improved and the minimum of Per can dramatically approach to zero as the sample number increases. These results show the robustness of SR in signal detection and extend the applicability of SR in signal processing.

Keywords: Probability of detection error, signal detection, stochastic resonance.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331655

References:

[1] B. McNamara, K. Wiesenfeld, Theory of stochastic resonance, Physical review A, 39(1989) 4854-4869.
[2] A. Restrepo, L. F. Zuluaga, L. E. Pino, Optimal noise levels for stochastic resonance, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 3(1997) 1617-1620.
[3] B. Kosko, S. Mitaim, Stochastic resonance in noisy threshold neurons, Neural networks 16(2003) 755-761.
[4] A. Saha, G.V. Anand, Design of detectors based on stochastic resonance, Signal processing 83(2003) 1193-1212.
[5] S. Zozor, P.-O.Amblard, On the use of stochastic in signal detection, Signal Processing 82(3) (2002) 353-367.
[6] S. Kay, Can detecability be improved by adding noise? IEEE Signal processinging letters 7(2000) 8-10.
[7] Hu Gang, Gong De-chun, Wen Xiao-dong, Yang Chun-yun, Qing Guang-rong, and Li Rong, Stochastic resonance in a nonlinear system driven by an a-periodic force, Physical review A, 46(1992) 3250-3254.
[8] M. E. Inchiosa, A. R. Bulsara, Signal detection statistics of stochastic resonators, Physical review E, 53(1996) 2021-2024.
[9] F. Chapeau-Blondeau, Stochastic resonance for an optimal detector with phase noise, Signal processing, 83(2003) 665-670.
[10] B. Kosko, S. Mitain; Robust stochastic resonance: signal detection and adaptation in impulsive noise, Physical review E 64(2001) 051110,1-11.
[11] V.Galdi, V. Pierro, I. M. Pinto, Evaluation of stochastic-resonance-based detectors of weak harmonic signals in additive white Gaussian noise, Physical review E 57(1998) 6470-6479.
[12] F.Chapeau-Blondeau, Nonlinear test statistic to improve signal detection in non-Gaussian noise, IEEE Signal Processing Letters, 7(2000) 205-207.