Linearly-coupled sigmoid bistable stochastic resonance for weak signal detection

The paper focuses on developing a stochastic resonance (SR) system designed for the detection of weak signals under alpha-stable-distributed noises. Initially, in view of the strong impulsive characteristics of noises, a linearly-coupled sigmoid bistable stochastic resonance (LSBSR) system is proposed, which is constructed by potential function and sigmoid function. Through formula derivation, it is theoretically proved that the output signal-to-noise ratio (SNR) of the LSBSR system is superior to that of the classical bistable SR system. Then, a new signal processing strategy based on the LSBSR system is introduced. Simulation experiments have demonstrated that under the input SNR = −20 dB, the detection probability of the LSBSR system exceeds 95% for the alpha-stable-distributed noise with α = 1.5. When α is reduced to 0.1, the detection probability approaches 80%, significantly outperforming other detection methods. Finally, the LSBSR system is applied to detect sea-trial signals with an SNR improvement of 22.5 dB, which further validates the practicability of the proposed system.