一种随机共振增强正弦信号的二次多项式接收方法  

A quadratic polynomial receiving scheme for sine signals enhanced by stochastic resonance

作　　者：刘广凯 全厚德 康艳梅[2] 孙慧贤 崔佩璋 韩月明 Liu Guang-Kai;Quan Hou-De;Kang Yan-Mei;Sun Hui-Xian;Cui Pei-Zhang;Han Yue-Ming(Department of Electronics and Optical Engineering,Army Engineering University,Shijiazhuang 050003,China;School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an 710049,China;The Troop of 66389,Shijiazhang 050000,China)

机构地区：[1]陆军工程大学石家庄校区电子与光学工程系,石家庄050003 [2]西安交通大学数学与统计学院,西安710049 [3]中国人民解放军66389部队,石家庄050000

出　　处：《物理学报》2019年第21期26-36,共11页Acta Physica Sinica

基　　金：河北省自然科学基金(批准号:F2017506006)资助的课题~~

摘　　要：针对雷达、通信系统的正弦中频信号在低信噪比中难以接收的问题,提出一种经随机共振增强正弦信号的接收方法.通过分析正弦信号的随机共振机理,引入判决时刻,将非自治的福克-普朗克方程(Fokker-Planck Equation,FPE)转化为自治方程求解,得到FPE的含时间参量的周期定态解;在得到随机共振输出粒子的概率密度基础上,通过分析能量接收、匹配滤波接收特点,提出基于二次多项式的接收结构,通过使偏移系数最大化,确定二次多项式系数,初步确定了检验统计量;为进一步减小误码率,结合“N次采样取平均”思想,根据中心极限定理,将问题转换为高斯分布下的假设检验问题,最终提出了随机共振增强正弦信号的二次多项式接收方法和处理流程.仿真验证了理论的正确性,并得到:在最佳匹配随机共振参数的限制下,当N=500时,二次多项式接收结构在信噪比大于–17 dB时误码率低于2.2×10^–2.Aiming at the reception of the intermediate frequency signal of sine wave of radio and communicationsystem at extremely low signal-to-noise ratio(SNR),a quadratic polynomial receiving scheme for sine signalsenhanced by stochastic resonance(SR)is proposed.Through analyzing the mechanism of sine signals enhancedby SR and introducing the decision time,the analytic periodic stable solution with time parameters of theFokker-Planck Equation(FPE)is obtained through converting the non-autonomous FPE into an autonomousequation.Based on the probability density function of the particle of SR output,a quadratic polynomialreceiving scheme is proposed by analyzing the feature of energy detector and matching filter receiver.Bymaximizng the deflection coefficient,the binomial coefficients and the test statistic are obtained.For furtherreducing the bit error,by combining the thought of“the average of N samples”,a quadratic polynomialreceiving scheme for sine signals enhanced by SR is proposed through the hypothesis under Gaussiandistribution approximation of the law of large N.And the conclusion is obtained as follows.When N is 500 andthe SNR is greater than 17 dB,the bit error rate is less than 2.2×10^-2,under the constraint of theparameters of the optimally matched SR.

关 键 词：随机共振 正弦信号接收 二次多项式接收 福克-普朗克方程 偏移系数 

分 类 号：TN911.2[电子电信—通信与信息系统]