| Stochastic resonance proposed a new non-linear weak signal detection method in recent years, which can be used to enhance the useful signal by using noise, to achieve the purpose of detecting weak signals. This article focuses on the theory of stochastic resonance under strong noise background of non-periodic signal detection methods. This research is subsidized by the project"Research on nonlinear filter theory and technology based on Stochastic Resonance theory", which is supported by National Natural Science Funding.This paper first give a brief introduction for classical Bi-stable Langevin model, then study the potential function of the Bi-Stable Langevin model, explain the causes of stochastic resonance and introduce the classical theory of stochastic resonance: adiabatic approximation theory. And we also studied the signal output SNR for the output signals of the Bi-Stable Langevin model when change the noise intensity and the system parameters , and give the definition of the output bit error rate (BER) for nonlinear system, while the input signals is aperiodic signal such as baseband binary pulse amplitude modulation (PAM) signal. All these are to provide a theoretical basis for the follow-up study. Then for the Bi-Stable Langevin model, the system output probability density progressive steady-state solution and system response time were studied. And we study the detection of input signal as single-frequency cosine signal and the baseband binary pulse amplitude modulation (PAM) signal while changing noise intensity, as well as the detection on a binary aperiodic signal through system parameter adjustment. We found that changing the noise intensity and change system parameters have the same effect, there is an optimum value so that the effect of stochastic resonance in the best, for the aperiodic input signals submerged at different noise intensity can be obtained the appropriate system output signal by continuous changing system parameters, but noise adjusting stochastic resonance is not feasible, we can adjust parameters to achieve the stochastic resonance.In this paper, the piecewise linear model was used for non-periodic signal detection research, and for the binary aperiodic signal as the input signals for the piecewise linear model, the probability characteristics of the output signal and the output of sub-linear model signal to noise ratio were studied. And the detection on binary aperiodic signals based on the piecewise linear model, we found that through an appropriate adjustment to the noise intensity and system parameters, there is an optimum value can be achieved for non-periodic signal detection. Then analyzes how the potential well locations and other system parameters of piecewise linear model system effect the stochastic resonance. We obtain that the potential well location and the output signal amplitude is related, system parameters affect the signal transitions between potential wells.Then we detect aperiodic signal based on a two-dimensional multistable nonlinear model, and discuss the relationship to the Bi-Stable Langevin Model. By regulating the non-linear system input noise intensity and system parameters, we discuss to the impact of aperiodic signal detection on two-dimensional multistable nonlinear model for noise intensity and system parameters. Finally, we summarize the emphases of this paper, and discuss the lack of research. In order to consummate this subject, further work needs to be done in the fields of adaptive parameter stochastic resonance (PSR), stochastic resonance under colored noise and more accurate methodology for the evaluation of communication system's performance. Innovation points: (1) binary aperiodic signal detection researchs based on the theory of stochastic resonance on the piecewise linear model; (2) binary aperiodic signal detection researchs based on the theory of stochastic resonance on the two-dimensional multistable nonlinear model. |
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