Optimum stochastic resonance detector of weak sinusoid signals in additive white Gaussian noise

Stochastic resonance (SR) is a phenomenon that appeal\´s in nonlinear systems whereby weak input signals can be amplified and optimized by the assistance of noise. In the field of signal detection, the fundamental question is whether SR could be used to construct better detectors than the Neyman-Pearson (NP) detectors. Many researchers have pointed out that no gain should be expected from using a SR signal preprocessor because of the unwanted nonlinearities along the signal processing chain. We studied the SNR and the symmetry-breaking characteristic of the output probability density function (PDF) at the output of the SR. In order to avoid the nonlinearities between the input and output signal waveforms, we translate the input to zero frequency then through the SR processor. We called this procedure the optimum SR detector (OSRD) for its maximum output SNR and its avoidance from the nonlinearities. Simulations show that by using this kind of detector in some SR systems, the detection performance may be "\´better" than the NP detector. An explanation is given and implies that the NP detector is still optimum.