Noise improvements in stochastic resonance: From signal amplification to optimal detection

It is demonstrated that benefits from the noise can be gained at various levels in stochastic resonance. Raising the noise can produce signal amplification as well as signal-to-noise ratio improvement, input-output gain exceeding unity in signal-to-noise ratio, and enhanced performance in optimal processing. This series of benefits is successively exhibited in the processing of a periodic signal coupled to a white noise through essentially static nonlinearities. Especially, it is established that noise benefits in stochastic resonance can extend up to optimal processing, by considering an optimal Bayesian detector whose performance is improvable by raising the level of the noise.