【作者】 刘勇；

【导师】 徐博侯；

【作者基本信息】 浙江大学 ， 固体力学， 2004， 硕士

【摘要】 随机共振是非线性系统、随机力(噪声)和输入信号三者之间产生的一种奇特的协同现象。与传统的噪声总是有害的观点相反，随机共振现象反映了随机力的积极作用，它是自然科学中一种普遍存在的非线性现象，涉及到几乎每个学科。在过去的二十多年里，随机共振现象受到广泛的关注，本文主要的研究对象是众多随机共振理论中的一支——参数调节随机共振(PSR)理论，及其在多进制基带数字信号传输中的应用。 传统的随机共振研究一般都从调节噪声强度出发，但在参数调节随机共振理论提出之后，我们发现参数调节随机共振就是寻找传统的噪声调谐共振峰值所对应系统的一种理论和方法，而且参数调节随机共振具有适应范围广和调节方便的优点。在白噪声假设下，本文以系统随机微分方程和其概率密度满足的FPK方程为基础，详细研究了非线性双稳态信号处理系统输出的数字特征，引入了系统响应速度，并从参数调节的角度重新解释了随机共振现象产生的机理。 本文研究了参数可调双稳态随机共振系统作为一个非线性接收装置的基带数字通信系统，基带信号主要考虑脉冲幅值调制(PAM)信号的传输。对于二进制PAM信号输入的情况，在过去的几年中已有颇多研究结果。考虑到多进制数字信号与二进制数字信号相比具有信息传输效率更高的优点，本文对输入信号为四进制PAM信号的情况进行了详细的研究。在加性高斯白噪声信道中，通过理论分析与仿真实验，本文研究了这个非线性数字通信系统的性能，给出了误码率和信道容量公式，提出了系统参数调节的方法。结果表明，在宽带噪声干扰下，通过随机共振接收器来传输四进制PAM信号是可以得到满足要求的误码率的。同时，通过对数字仿真实验结果的深入分析，本文提出了能够更加精确对系统性能进行理论分析的方法。 本文对于参数随机共振在多进制基带数字信号传输中的应用作了一些基本的理论和仿真实验工作，在未来的研究中，我们认为参数可调的自适应随机共振理论，色噪声条件下的随机共振，以及完善系统性能的衡量标准将是很有意义的方向。更多还原

【Abstract】 Stochastic resonance (SR) is a synergistic phenomenon happened among nonlinear dynamic system, stochastic force (noise) and input signals. On the contrary of the conventional conception that noise is always plays a destructive role, SR shows the constructive effect caused by stochastic force. What is more, as a ubiquitous nonlinear phenomenon, SR lies in almost every subject of natural science. In the past 20 years, SR has been paid broad attention on. The main subject of this article is theory of Parameter-induced Stochastic Resonance (PSR) and its application in multi-ary baseband digital signal transmission.Normally, the classic researches about SR are carried on from the perspective of noise tuning. However, it has been proved that SR via tuning noise could be made equivalent to tune system parameters. Additionally, PSR can be realized easier and under a worse environment than SR via adding noise can. In the case of white noise, based on the system stochastic differential equation and Fokker-Planck (FPK) equation we make detailed research on the output characters of nonlinear bistable system. From the perspective of parameter tuning, the mechanism of SR is also re-explained by the conception of system response speed.The application of PSR system in baseband digital signal, mainly the pulse amplitude modulated (PAM) signal, is studied in this article. There has been lots of research in the case of using binary PAM signal as input. Considering the higher efficiency of information transmission, however, we study the case of using quaternary PAM signal as input here. Over an additive white Gaussian noise (AWGN) channel, the communication system’s performance is studied via theoretical analyze and simulation experiment. The method for calculating system bit error rate (BER), channel capacity, and how to tune system parameters are also introduced. Finally, it is proved that under broadband noise the PSR system could transmit quaternary baseband PAM signal effectively.It should be noticed that in this article only limited theoretical analyze and simulation experiments about application of PSR in baseband digital signal transmission have been done. In order to consummate this subject, further work needs to be done in the fields of adaptive PSR, SR under colored noise and more accurate standards for judgment of communication system’s performance.更多还原