On The Use Of Stochastic Resonance And Bistable Systems In Signal Detection

As a counterintuitive phenomenon of nonlinear systems, since its concept being proposed and experimentally verified, stochastic resonance (SR) has been a new focus of academic research in the almost past thirty years, and has attracted lots of interests of researchers from diverse scientific fields. Recently, the application of the theories and techniques of SR in signal processing, especially in signal detection, has been an interesting and attractive research subject, and in this thesis, we attempt to do some new researches in this subject.First, a frequently questioned problem is whether the output signal-to-noise ratio (SNR) can be greater than the input SNR, namely, whether the SNR gain can exceed unity with the help of SR system. It has been proved impossible under the conditions of linear response theory. However, beyond the limits of linear response theory, some researches showed that the fact of the SNR gain exceeding unity can be easily observed. Based on the prototype SR model, an overdamped bistable system, we derived the theoretical method for calculating the output SNR via the solutions of related Fokker-Planck equations (FPE) when the system is fed by a periodic signal and white Gaussian noise. Numerical simulations are carried out to verify the reliability and accuracy of derived results, and we further proved that the SNR gains can be greater than one after SR processing. Besides, we also considered the cases of non-Gaussian noise, in which the output SNR is too difficult to be calculated from the related FPEs directly. Thus, we made some assumptions on the noise, so that we could calculate the output SNR numerically. The results indicate that larger SNR gain can be derived via tuning system parameters in non-Gaussian cases than that in the Gaussian noise. Meanwhile, the receivers based on the bistable system are used to detect the periodic signals in Gaussian and non-Gaussian noise, so that we could investigate the effects of SR and the SNR gain on signal detection.Later, as a new trial of application of parameter-induced stochastic resonance in signal processing, the problem of target detection in sea reverberation is considered. The structure of the receiver based on the bistable system is designed after studying the simplified model of the problem; the reverberation is generated according to point scattering model; with the help of numerical simulation, the performance of our designed receiver is evaluated versus the conventional receiver, and some preliminary results are obtained.Through some simplifications and modifications in discretizing the bistable system in continuous time, we designed a kind of bistable system in discrete time, and analyzed its output properties when driven by a periodic signal and white noise, giving the results similar to those of the bistable system in continuous time. The receiver structure based on discrete-time bistable system is designed for the constant binary signal detection, and it is compared with the matched filter in some cases of non-Gaussian noise.Finally, the receiver based on discrete-time bistable processing is applied to the problem of target detection mentioned above. The directional source and environmental noise are further considered, and the effects of the effective length of transmitted signal on the receiver performance are investigated. Likewise, the comparisons with conventional linear receivers show some results that may be valuable in some degree.