A Quadratic Polynomial Receiving Scheme for Sinusoidal Signals Enhanced by Stochastic Resonance Under Color Noise

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 1 × 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.