Stochastic resonance and optimal detection of pulse trains by threshold devices

摘要

The nonlinear detection by a threshold device of a periodic train of soliton-like pulses embedded in arbitrarily distributed white noise is studied. A theoretical model is developed which provides expressions for the signal-to-noise ratio at the output of the detector and for the input-output gain in signal-to-noise ratio. We analyze the properties and conditions of optimality for these quantities as functions of the parameters of the process. Especially, specific nonlinear properties not shared by linear devices are established, among which are the possibility of an input-output amplification of the signal-to-noise ratio and the demonstration that through nonlinear coupling the noise can be beneficial to the signal detection and that adding noise may result in improved performance via a mechanism known as stochastic resonance.