A nonlinear monostable filter for bipolar pulse signal detection

We investigate a nonlinear bistable system as a nonlinear filter for bipolar pulse signal detection. This nonlinear system usually shows the phenomenon of stochastic resonance (SR) by adding noise. To thoroughly discuss the detection performance of the nonlinear system, we tune the system parameters to obtain the optimal detection performance. In this case, the system in fact is a monostable system, so here it is named as a nonlinear monostable filter. For quantifying observations of the nonlinear system output, we define the probability of detection error, and give the theoretical and numerical results. To investigate the detection performance of the monostable filter, it is compared with SR and the matched filter, respectively. We find that (a) the detection performance of the nonlinear monostable filter is better than that of the system exhibiting SR, (b) the detection performance of the matched filter surpasses that of the monostable filter in perfect condition of synchronisation, and (c) as the desynchronisation is introduced, with increasing desynchronisation the monostable filter catches up and even is superior to the matched filter.