Stochastic Resonance in Nonlinear Signal Detection

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.

Authors:

• Youguo Wang
• Lenan Wu

Keywords:

• Probability of detection error
• signal detection
• stochastic resonance.

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.