A simple optimum nonlinear filter for stochastic-resonance-based signal detection

Stochastic resonance (SR) is a physical phenomenon through which system performance is enhanced by noise. Applications of SR in signal processing are expected to realize the detection of a weak signal buried in strong noise. Extraction of the effect of SR requires the design of an effective nonlinear system. Although a number of studies have investigated SR, most have employed conventional nonlinear filters. The present study proposes simple optimum nonlinear characteristics that maximize the performance enhancement, which is measured by the signal-to-noise ratio. The mathematical expression is simple, and the obtained performance is beyond that of linear systems. Surprisingly, the proposed nonlinear method can obtain the Cramér-Rao bounds and is equivalent to the maximum likelihood estimator. In addition, such optimization demonstrates systematically that the applications of SR to signal detection is effective only in non-Gaussian noise environments.