Theory of the stochastic resonance effect in signal detection - Part II: Variable detectors

In Part I of this paper [Theory of the Stochastic Resonance Effect in Signal Detection: Part I-Fixed Detectors, IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol. 55, no. 7, pt. 1, pp. 3172-3184], the mechanism of the stochastic resonance (SR) effect for a fixed detector has been examined. This paper analyzes the stochastic resonance (SR) effect under the condition that the detector structure or its parameters can also be changed. The detector optimization problem with SR noise under both Neyman-Pearson and Bayesian criteria is examined. In the Bayesian approach when the prior probabilities are unknown, the minimax approach is adopted. The form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined. The developed theory is then applied to a general class of weak signal detection problems. Under the assumptions that the sample size N is large enough and the test statistics satisfies the conditions of central limit theorem, the optimal SR noise is shown to be a constant vector and independent of the signal strength for both Neyman-Pearson and Bayesian criteria. Illustrative examples are presented where performance comparisons are made between the original detector and the optimal SR noise modified detector for different types of SR noise.