中文摘要：

快速、准确、有效的频谱检测算法是实现认知无线电的必要条件，文中主要研究了超低信噪比（小于-20 dB）环境下的频谱感知问题。首先，基于混沌动力学理论并结合频谱感知技术的特点，建立了具有强非线性特征的Duffing振子频谱感知模型。通过引入无量纲系数，实现了不同频率周期激振力作用下振子间的等效转换。然后，针对频谱检测的实际要求，提出了阵列式Duffing振子频谱感知方案。最后采用数值方法，重点分析了所述系统的检测性能。结果表明：在超低信噪比环境下，文中方法与传统的检测方法相比实现原理简单，且检测性能更好，更符合频谱感知技术的实际应用场合。

英文摘要：

As a rapid,correct and efficient spectrum detection algorithm is necessary for cognitive radio,this paper mainly focuses on the spectrum sensing under ultra-low signal-to-noise ratio （SNR,less than -20 dB）.In the in-vestigation,first,a Duffing oscillator spectrum sensing model with strong nonlinearity is established based on the theory of chaotic dynamics and the characteristics of spectrum sensing.Next,by introducing a dimensionless coeffi-cient as the transformation parameter of the system,the equivalence relationship between oscillators with different driving forces is derived.Then,a spectrum sensing approach based on the array Duffing oscillator is proposed to detect signals in a frequency band.Finally,the detection performance of the established model is numerically ana-lyzed.The results indicate that,as compared with the conventional spectrum detection methods,the proposed ap-proach is simpler to implement and is of higher detection performance.It is thus more applicable in practice.