Abstract: We discuss the signal detection through nonlinear
threshold systems. The detection performance is assessed by the
probability of error Per . We establish that: (1) when the signal is
complete suprathreshold, noise always degrades the signal detection
both in the single threshold system and in the parallel array of
threshold devices. (2) When the signal is a little subthreshold, noise
degrades signal detection in the single threshold system. But in the
parallel array, noise can improve signal detection, i.e., stochastic
resonance (SR) exists in the array. (3) When the signal is predominant
subthreshold, noise always can improve signal detection and SR
always exists not only in the single threshold system but also in the
parallel array. (4) Array can improve signal detection by raising the
number of threshold devices. These results extend further the
applicability of SR in signal detection.
Abstract: Stochastic resonance (SR) is a phenomenon whereby
the signal transmission or signal processing through certain nonlinear
systems can be improved by adding noise. This paper discusses SR in
nonlinear signal detection by a simple test statistic, which can be
computed from multiple noisy data in a binary decision problem based
on a maximum a posteriori probability criterion. The performance of
detection is assessed by the probability of detection error Per . When
the input signal is subthreshold signal, we establish that benefit from
noise can be gained for different noises and confirm further that the
subthreshold SR exists in nonlinear signal detection. The efficacy of
SR is significantly improved and the minimum of Per can
dramatically approach to zero as the sample number increases. These
results show the robustness of SR in signal detection and extend the
applicability of SR in signal processing.