The Mean First Passage Time of the Stochastic Resonance Driven by Dual-Sequence-Frequency-Hopping Signal and Noise

Zhaorui Li,Guangkai Liu,Peizhang Cui,Xiaobei Wu

doi:10.1155/2020/8845160

Abstract

The mean first passage time (MFPT) represents the dynamic characteristic of stochastic resonance (SR). The study focuses on how can the Dual-Sequence-Frequency-Hopping (DSFH) signal influence the MFPT and any difficulty in solving the MFPT problem considering the DSFH signal. In this current study, the SR system driven by DSFH signal and Gaussian white noise is described with the parameters of the signal amplitude, the frequency of Intermediate Frequency (IF) of the receptive DSFH signal, the SR system parameter, scale transformation coefficient, the noise intensity, and the sampling multiple, firstly. Secondly, under the assumption that MFPT is small aqueous about the domain of 0, the nonautonomous differential equation with MFPT is transformed to a nonhomogeneous differential equation with one unknown variable coefficient of second order. Finally, the numerical solution of MFPT can be obtained by the method of Runge–Kutta. Theoretical and simulation results are shown as below: (1) the effect of the signal amplitude, the IF frequency, the noise intensity, the SR system parameter, and the scale transformation coefficient, for decrease the MFPT, are positive; however, the effect of the sampling multiple is negative; (2) the MFPT cannot follow the dynamic period of the SR controlled by the IF frequency, when SNR is low; (3) when SNR = −12 dB, the sampling multiple is 200, the IF frequency is 2100, and the duty cycle reaches 25% (available for DSFH signal detection with peek or valley decision Liu et al. (2019)), so we need to decrease the IF frequency or increase the SNR for further availability.

Highlights

Introduction e DualSequence-Frequency-Hopping (DSFH) communication mode draws lessons from “the medium is the message” [1, 2]
Its typical character is that the message is modulated in the radio frequency, which is the hopping frequency controlled by the PN sequence
When 0 is transmitted, the hopping frequency controlled by PN 0 is transmitted. e radio frequency of DSFH is combined by hopping frequency controlled by PN 1 and PN 0. e chosen medium is the communication channel; the unchosen one is the dual channel controlled by two PN sequences representing the symbol 0 or 1. en, the receptive symbol is decided by whether the channel is occupied or not [3,4,5]

Summary

The System Model of the SR Driven by DSFH Signal and Gaussian White Noise

2.1. e Transmitted Signal of the DSFH. e communication and dual carrier controlled by PN sequences are chosen by the transmitted symbol in the DSFH mode and described as Figure 1. E communication and dual carrier controlled by PN sequences are chosen by the transmitted symbol in the DSFH mode and described as Figure 1. When the send symbol is 0, the carrier f0,n controlled by PN sequences FS0 is transmitted. At the time of t, the sine carrier s0(t) with the frequency of f0,n is transmitted if the transmitted symbol is 0. En, the transmitted signal is the sine carrier with a frequency of We need to analyze the dynamic characteristic of SR driven by the receptive signal of DSFH and Gaussian white noise. E IF signal of the two receptive branches is the sine wave as depicted in equation (2). We will analyze the MFPT with time-vary item of equation (6)

The MFPT Influenced by DSFH Signal and Gaussian White Noise

Simulated Analysis