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.

In this paper, a receiving scheme for intermediate frequency (IF) signals enhanced by stochastic resonance (SR) is proposed. The proposed scheme mitigates the reception failure of these signals, which can occur in radio and communication systems under extremely low signal-to-noise ratio (SNR). The SR mechanism for enhancing sinusoidal signals is analyzed. An analytic solution with time parameters of the Fokker-Planck Equation (FPE) is obtained by introducing the decision time from the non-autonomous FPE into an autonomous one. A quadratic polynomial receiving structure for sinusoidal signals enhanced by SR is proposed by comparing the characteristics of energy detection and matched filter detection. And the polynomial coefficients of the quadratic system are obtained by maximizing the deflection. Based on the idea of “the average of N samples” and the assumption of Gaussian distribution approximation under the law of large numbers, a quadratic polynomial receiving scheme for sinusoidal signals enhanced by SR is proposed. The conclusions are as below: 1) when the noise intensity is constant, the smaller the correlation time, the bigger the local SNR around the IF frequency due to the better performance of the low-pass filter; 2) The error bit ratio of the quadratic polynomial receiver is less than 2 × 10-2 when N =20 and the SNR is above -14 dB, which can be applied to the military emergency communication under extremely low SNR. Experiment verifies the theory.

Aimed at the antijamming needs of the space tracking, telemetry command (TTC) receiver under a low signal-to-noise ratio, the anti-interference advantage of the dual-sequence frequency hopping (DSFH) communication system is applied. The channel amplitude fading influence of the receiver operating characteristics (ROC) of the TTC receiver based on the DSFH is studied. Firstly, based on the typical channel model of the Rayleigh fading without direct path transmission, the conditional Fokker-Planck equation (FPE) is obtained by analyzing the statistical independence of the Rayleigh fading signal and SR output particle moments. Secondly, the probability density function (PDF) of the DSFH signal via channel Rayleigh fading enhanced by stochastic resonance (SR) is obtained by introducing the decision time. Thirdly, the detection probability, false alarm probability, ROC, and system bit error rate (BER) of the DSFH signals enhanced by SR under the Rayleigh fading conditions are obtained, under the minimum BER criterion. Finally, the conclusions are reached: one is that the DSFH signals via channel Rayleigh fading can still be detected by the SR system under low SNR, and the other one is that the SNR can reach the -13dB by the reception of DSFH signal enhanced by SR, when the Rayleigh fading parameter is 0.2042.

In Dual Sequence Frequency Hopping (DSFH) communication mode, aiming at improving the detection performance to weak signal under low signal-to-noise ratio (SNR) conditions, stochastic resonance (SR) detection method is proposed. First, the α-stable distribution is used as the impulsive noise model and the influence of α value on the properties of α-stable noise is analyzed. Second, the transmitting and receiving signal model of DSFH communication system is introduced. The SR method is used to detect DSFH signal. In order to analyze the output signal, the fractional FokkerPlanck equation (FFPE) is established, and a new simplified solution method based on sampling decision time is proposed to solve the time-varying fractional differential equation. Base on the theoretical solution of FFPE, a binary hypothesis test statistic is constructed to quantify the signal detection probability and false alarm probability, and the detection performance is analyzed. Finally, simulation experiments verify the theoretical conclusions. The minimum effective SNR for SR detection is obtained, and it is about 20dB, which provides a theoretical basis for the application of SR in the DSFH communication system.