## Design of detectors based on stochastic resonance.(English)Zbl 1144.94374

Summary: This paper presents a study of the phenomenon of stochastic resonance in quantizers, and discusses the use of this phenomenon for the detection of weak sinusoidal signals in noise. Stochastic resonance in 2-level, symmetric 3-level, and symmetric multilevel quantizers is investigated. Expressions are derived for the signal-to-noise ratio (SNR) gain of the quantizers driven by a small amplitude sinsuoidal signal and i.i.d. noise. The gain depends on the probability density function (PDF) of the input noise, and for a given noise PDF, the gain can be maximized by a proper choice of the quantizer thresholds. The maximum gain $$G_{SR}$$ is less than unity if the input noise is Gaussian, but several non-Gaussian noise PDFs yield values of $$G_{SR}$$ exceeding unity. Thus, the quantizers provide an effective enhancement in the SNR, which can be utilized to design a nonlinear signal detector whose performance is better than that of the matched filter. The nonlinear detector in consideration consists of a stochastically resonating (SR) quantizer followed by a correlator. An asymptotic expression for the probability of detection of the SR detector is derived. It is shown that the detection performance of the SR detector is better than that of the matched filter for a large class of noise distributions belonging to the generalized Gaussian and the mixture-of-Gaussian families.

### MSC:

 94A13 Detection theory in information and communication theory 93E10 Estimation and detection in stochastic control theory
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