Aiming at the reception of the intermediate frequency signal of sine wave of radio and communication system at extremely low signal-to-noise ratio (SNR), a quadratic polynomial receiving scheme for sine signals enhanced by stochastic resonance (SR) is proposed. Through analyzing the mechanism of sine signals enhanced by SR and introducing the decision time, the analytic periodic stable solution with time parameters of the Fokker-Planck Equation (FPE) is obtained through converting the non-autonomous FPE into an autonomous equation. Based on the probability density function of the particle of SR output, a quadratic polynomial receiving scheme is proposed by analyzing the feature of energy detector and matching filter receiver. By maximizng the deflection coefficient, the binomial coefficients and the test statistic are obtained. For further reducing the bit error, by combining the thought of " the average of <i>N</i> samples”, a quadratic polynomial receiving scheme for sine signals enhanced by SR is proposed through the hypothesis under Gaussian distribution approximation of the law of large <i>N</i>. And the conclusion is obtained as follows. When <i>N</i> is 500 and the SNR is greater than –17 dB, the bit error rate is less than 2.2 × 10<sup>–2</sup>, under the constraint of the parameters of the optimally matched SR.
To address the problem that it is difficult to detect an intermediate frequency (IF) signal at the receiving end of a communication system under extremely low signal-to-noise ratio (SNR) conditions, we propose a stochastic resonance (SR)-enhanced sine-signal detection method based on the sign function. By analyzing the SR mechanism of the sine signal and combining it with the characteristics of a dual-sequence frequency-hopping (DSFH) receiver, a periodic stationary solution of the Fokker–Planck equation (FPE) with a time parameter is obtained. The extreme point of the sine signal is selected as the decision time, and the force law of the electromagnetic particles is analyzed. A receiving structure based on the sign function is proposed to maximize the output difference of the system, and the value condition of the sign function is determined. In order to further improve the detection performance, in combination with the central-limit theorem, the sampling points are averaged N times, and the signal-detection problem is transformed into a hypothesis-testing problem under a Gaussian distribution. The theoretical analysis and simulation experiment results confirm that when N is 100 and the SNR is greater than 20 dB, the bit-error ratio (BER) is less than 1.5 × 10−2 under conditions in which the signal conforms to the optimal SR parameters.
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