Abstract: Aiming at the problem that common nonlinear Stochastic Resonance (SR) system is subject to the restriction of small parameter and is failure to detect the high frequency weak signal, a new detection method of parameter-tuning SR for weak signal with high frequency was proposed. Firstly, the relationship between the damping coefficient and the signal frequency was derived in a bistable system, and by using Kramers rate for analysis, the influence of changing damping coefficient on the SR of the system was verified. Then, the influence of SR phenomenon produced by system shape parameters was deduced, the SR of high frequency weak signal was realized through adjusting the damping coefficient and the system shape parameters, and the effect of output spectrum characteristics of the system and different sampling frequency was discussed, the stability of the algorithm was verified by the results. Finally, using the received actual signals with noise as experimental research data, the experimental results show that ultrahigh frequency weak signal under strong noise background can be extracted effectively and steadily using the strategy even when the signal frequency reaches MHz and GHz. The proposed method extends the application field of SR principle of weak signal detection.

Key words: Stochastic Resonance (SR), attractor curve, weak signal detection, parameter-tuning, Kramers rate

摘要： 针对经典随机共振（SR）理论只适用于小参数，在提取高频微弱信号失效而无法使用的问题，提出一种调参随机共振检测高频率微弱信号的方法。首先，推导出双稳系统中阻尼系数与信号频率的关系，并以Kramers逃逸速率为分析手段，讨论阻尼系数变化对系统发生随机共振的影响；然后，分析了系统形状参数对系统产生随机共振现象的影响，通过联合调整阻尼系数和系统参数实现了大频率微弱信号的检测，并讨论了不同采样频率与调参系统输出频谱特性的影响，验证了该方法在低采样率下仍具有较强的稳定性；最后，以通用软件无线电设备（USRP）接收的无线电带噪信号作为系统的输入进行仿真。实验结果表明，利用该调参随机共振策略能够稳定有效地检测出强噪声背景下的超高频微弱信号，信号频率可达到MHz、GHz，拓展了随机共振原理的微弱信号检测的应用领域。

关键词: 随机共振, 吸引子曲线, 微弱信号检测, 参数调节, Kramers逃逸速率