A new complex Duffing oscillator used in complex signal detection  

作　　者：DENG XlaoYing LIU HaiBo LONG Teng 

机构地区：[1]School of in formation and Electronics,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Chinese Science Bulletin》2012年第17期2185-2191,共7页

基　　金：supported by the National Natural Science Foundation of China (40804022,61032009 and 61001198)

摘　　要：In view of the fact that complex signals are often used in the digital processing of certain systems such as digital communication and radar systems,a new complex Duffing equation is proposed.In addition,the dynamical behaviors are analyzed.By calculating the maximal Lyapunov exponent and power spectrum,we prove that the proposed complex differential equation has a chaotic solution or a large-scale periodic one depending on different parameters.Based on the proposed equation,we present a complex chaotic oscillator detection system of the Duffing type.Such a dynamic system is sensitive to the initial conditions and highly immune to complex white Gaussian noise,so it can be used to detect a weak complex signal against a background of strong noise.Results of the Monte-Carlo simulation show that the proposed detection system can effectively detect complex single frequency signals and linear frequency modulation signals with a guaranteed low false alarm rate.In view of the fact that complex signals are often used in the digital processing of certain systems such as digital communication and radar systems, a new complex Duffing equation is proposed. In addition, the dynamical behaviors are analyzed. By calculat- ing the maximal Lyapunov exponent and power spectrum, we prove that the proposed complex differential equation has a chaotic solution or a large-scale periodic one depending on different parameters. Based on the proposed equation, we present a complex chaotic oscillator detection system of the Duffing type. Such a dynamic system is sensitive to the initial conditions and highly immune to complex white Gaussian noise, so it can be used to detect a weak complex signal against a background of strong noise. Results of the Monte-Carlo simulation show that the proposed detection system can effectively detect complex single frequency signals and linear frequency modulation signals with a guaranteed low false alarm rate.

关 键 词：信号检测 DUFFING方程 振荡器 LYAPUNOV 复域 雷达系统 线性调频信号 检测系统 

分 类 号：TN911.23[电子电信—通信与信息系统] O175.1[电子电信—信息与通信工程]