Noise-Improved Signal Detection in Nonlinear Threshold Systems

We discuss the signal detection through nonlinear threshold systems. The detection performance is assessed by the probability of error Per . We establish that: (1) when the signal is complete suprathreshold, noise always degrades the signal detection both in the single threshold system and in the parallel array of threshold devices. (2) When the signal is a little subthreshold, noise degrades signal detection in the single threshold system. But in the parallel array, noise can improve signal detection, i.e., stochastic resonance (SR) exists in the array. (3) When the signal is predominant subthreshold, noise always can improve signal detection and SR always exists not only in the single threshold system but also in the parallel array. (4) Array can improve signal detection by raising the number of threshold devices. These results extend further the applicability of SR in signal detection.




References:
[1] B. McNamara, K. Wiesenfeld, "Theory of stochastic resonance," Physical
Review A, vol. 39, pp. 4854-4869, 1989.
[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, vol. 3, pp. 1617-1620, 1997.
[3] B. Kosko, S. Mitaim, "Stochastic resonance in noisy threshold neurons,"
Neural Networks, vol. 16, pp. 755-761, 2003.
[4] A. Das, N. G. Stocks, A. Nikitin, and E. L. Hines, "Quantifying stochastic
resonance in a single threshold detector for random aperiodic signals,"
Fluctuation and Noise Letters, vol. 4, no. 2, L247-L265, 2004.
[5] N. G. Stocks, "Supra-threshold stochastic resonance in multilevel
threshold systems," Physical Review Letters, vol. 84, pp. 2310-2313,
2000.
[6] N. G. Stocks, "Information transmission in parallel threshold arrays:
supra-threshold stochastic resonance," Physical Review E, vol. 63, pp.
041114, 2001.
[7] N. G. Stocks, "Supra-threshold stochastic resonance: an exact result for
uniformly distributed signal and noise," Physics Letters A, vol. 279, pp.
308-312, 2001.
[8] D. Rousseau, F. Duan, and F. Chapeau-Blondeau, "Supra-threshold
stochastic resonance and noise-enhanced Fisher information in an arrays
of threshold devices," Physical Review E, vol. 68, pp. 031107, 2003.
[9] D. Rousseau, F. Chapeau-Blondeau, "Supra-threshold stochastic
resonance and signal-to-noise ratio improvement in arrays of
comparators," Physics Letters A, vol. 321, pp. 280-290, 2004.
[10] Mark D. Mcdonnell, Derek Abbott, "A characterization of
supra-threshold stochastic resonance in an array of comparators by
correlation coefficient," Fluctuation and Noise Letters, vol. 2, no. 3, pp.
213-228, 2002.
[11] N. G. Stocks, R. Mannella, "Generic noise-enhanced coding in neuronal
arrays," Physical Review E, vol. 64, pp. 030902(R), 2001.
[12] N. G. Stocks, Optimizing information transmission in model neuronal
ensembles: the role of internal noise, Stochastic Processes in Physics,
Chemistry, and Biology, Edited by J. A.. Freund, Th, Pöschel, Lecture
Notes in Physics, 557(2000)150.
[13] S. Zozor, P.-O.Amblard, "On the use of stochastic in sine detection,"
Signal Processing, vol. 82, no. 3, pp. 353-367, 2002
[14] S. Kay, "Can detectability be improved by adding noise?" IEEE Signal
Processing Letters, vol. 7, pp. 8-10, 2000.
[15] 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, vol. 46, pp. 3250-3254,
1992.
[16] M. E. Inchiosa, A. R. Bulsara, "Signal detection statistics of stochastic
resonators," Physical Review E, vol. 53, pp. 2021-2024, 1996.
[17] F. Chapeau-Blondeau, "Stochastic resonance for an optimal detector with
phase noise," Signal Processing, vol. 83, pp. 665-670, 2003.
[18] B. Kosko, S. Mitain; "Robust stochastic resonance: signal detection and
adaptation in impulsive noise," Physical Review E, vol. 64, pp.
051110,1-11, 2001.
[19] 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, vol. 57, pp. 6470-6479, 1998.
[20] A. Saha, G.V. Anand, "Design of detectors based on stochastic
resonance," Signal Processing, vol. 83, pp. 1193-1212, 2003
[21] Youguo Wang, Lenan Wu, "Stochastic resonance in nonlinear signal
detection," to be published.