EVALUATION OF A NONLINEAR BISTABLE FILTER FOR BINARY SIGNAL DETECTION

We consider the nonlinear bistable dynamic system that is the archetypal system giving way to the phenomenon of stochastic resonance for noise-improved signal processing. Independently of a strict stochastic resonance effect, we use this bistable system as a nonlinear filter for a detection task on a binary signal. We expose a methodology to tune the nonlinear filter at its best performance that minimizes its probability of detection error. The optimally tuned nonlinear filter is then compared to the ideal matched filter, which is the optimal filter for the detection with Gaussian noise. We show that the performance of the nonlinear filter, although (expectedly) not as good, comes close to that of the ideal matched filter operating in its strict nominal conditions. We next examine several possible departures, quite plausible in practical operation, from the nominal conditions of the ideal matched filter. We demonstrate that in such degraded conditions, the nonlinear filter can catch up and surpass the performance of the matched filter. This reveals a robustness superiority of the nonlinear filter, compared to the matched filter operating outside its strict nominal conditions.