Weak Signal Detection Based On Chaotic Oscillator And Its FPGA Implementation

Weak signal detection（WSD） is a newly arisen scientific technology in recent years, it hasovercomed the shortcoming of high signal to noise ratio (SNR) threshold based on the traditionaltechnology. As a typical model of the nonlinear dynamical systems, chaos has been receivedconsiderable attention by many researchers when it was introduced to the field of WSD. For theproperty of being sensitive to weak signal and immune to noise, chaos has a great potential inWSD. This article is based on this property, and Duffing chaotic oscillator is chose to detect theweak signal.The definition and characteristic are introduced in this paper, and the Lyapunov exponentbased on the phase space reconstruction using the method of Wolf is proposed. The experimentalresults had certified its accuracy. Lyapunov exponent and observation method arecomprehensively used to decide the threshold of the chaotic system in order to improve theaccuracy. Being supported by those theories, The model of Duffing chaotic oscillator is used todetect the amplitude and frequency of the sinusoidal signal which is buried in Gaussian whitenoise and color noise. The results which are under the influence of the sampling frequency on thebasis of theory that the output variance of the system will reach a maximum when the referencefrequency equals to the signal frequency are analyzed. Experiments have indicated that theaccuracy rate of the results will be improved and the signal to noise ratio (SNR) threshold will bereduced by increasing the sampling frequency to a certain degree. Besides, we have a furtherresearch on detecting the frequency of a signal with an initial phase based on the theorymentioned above, simulation experimental results have verified the output variance still has adrastic change when the reference frequency is equal to the signal frequency, and the conclusionis successfully applied to detecting the frequency of amplitude modulated signal produced bysignal generator. Finally, the hardware model of Duffing oscillator is built by using systemgenerator, and the property is applied to FPGA implementation.