Noise-Induced Resonance and Particle Swarm Optimization-Based Weak Signal Detection

Abstract

The noise always plays a key role in different science and engineering applications. Here, we study the effect of the addition of external noise (i.e., stochastic resonance (SR) noise) in weak signal detection application. We also explore the conditions of improvability and non-improvability for a particular SR noise. We analyze both symmetric and asymmetric SR noises in our example. With certain equality and inequality constraints, we discuss the penalty function method which is used to design a single objective function. Furthermore, the particle swarm optimization technique has been used to maximize the probability of detection ( $$P_\mathrm{D}$$ ) at a constant value of the probability of false alarm ( $$P_\mathrm{FA}$$ ). With a numerical example, we have exhibited the performance of the proposed detector. We compare our proposed detection technique with the state-of-the-art techniques, and it is observed that the optimum $$P_\mathrm{D}$$ is comparable at a constant value of $$P_\mathrm{FA}$$ . The proposed detection technique is also used for watermark detection application to show the practicality of the proposed technique.