Research on Stochastic Resonance Detection Method for Periodic Signals under Low SNR and α-Stable Noise

Abstract

In Dual Sequence Frequency Hopping (DSFH) communication mode, aiming at improving the detection performance to weak signal under low signal-to-noise ratio (SNR) conditions, stochastic resonance (SR) detection method is proposed. First, the α-stable distribution is used as the impulsive noise model and the influence of α value on the properties of α-stable noise is analyzed. Second, the transmitting and receiving signal model of DSFH communication system is introduced. The SR method is used to detect DSFH signal. In order to analyze the output signal, the fractional Fokker–Planck equation (FFPE) is established, and a new simplified solution method based on sampling decision time is proposed to solve the time-varying fractional differential equation. Base on the theoretical solution of FFPE, a binary hypothesis test statistic is constructed to quantify the signal detection probability and false alarm probability, and the detection performance is analyzed. Finally, simulation experiments verify the theoretical conclusions. The minimum effective SNR for SR detection is obtained, and it is about −20 dB, which provides a theoretical basis for the application of SR in the DSFH communication system.