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The mean first passage time (MFPT) represents the dynamic characteristic of stochastic resonance (SR). The study focuses on how can the Dual-Sequence-Frequency-Hopping (DSFH) signal influence the MFPT and any difficulty in solving the MFPT problem considering the DSFH signal. In this current study, the SR system driven by DSFH signal and Gaussian white noise is described with the parameters of the signal amplitude, the frequency of Intermediate Frequency (IF) of the receptive DSFH signal, the SR system parameter, scale transformation coefficient, the noise intensity, and the sampling multiple, firstly. Secondly, under the assumption that MFPT is small aqueous about the domain of 0, the nonautonomous differential equation with MFPT is transformed to a nonhomogeneous differential equation with one unknown variable coefficient of second order. Finally, the numerical solution of MFPT can be obtained by the method of Runge–Kutta. Theoretical and simulation results are shown as below: (1) the effect of the signal amplitude, the IF frequency, the noise intensity, the SR system parameter, and the scale transformation coefficient, for decrease the MFPT, are positive; however, the effect of the sampling multiple is negative; (2) the MFPT cannot follow the dynamic period of the SR controlled by the IF frequency, when SNR is low; (3) when SNR = −12 dB, the sampling multiple is 200, the IF frequency is 2100, and the duty cycle reaches 25% (available for DSFH signal detection with peek or valley decision Liu et al. (2019)), so we need to decrease the IF frequency or increase the SNR for further availability.

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 Fokker–Planck 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 −20 dB, which provides a theoretical basis for the application of SR in the DSFH communication system.

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.

The Dual-Sequence-Frequency-Hopping (DSFH) communication system based on software defined radio (SDR) system belongs to the field of information and communication security of software engineering. At very low signal-to-noise ratio (SNR), which is lower than -10dB, the DSFH fails to synchronize. Synchronization acquisition method via a combined multi-signal detection (SAMCMD) is proposed. The feature of a short sequence of frequency hopping (FH) frequency point is utilized to express the information of the time of date (TOD), and the time accumulation of several FH signals is used to extend the detection time. This method can not only be appropriate for DSFH but also greatly improve the synchronization performance at low SNR. Explain the principle and structure of the SAMCMD. And obtain the performance of this method of the SDR synchronization acquisition. The conclusions are as below: 1) the longer detection time is, the better the anti-jamming performance of SAMCMD is; 2) SAMCMD can gain about 22.5dB-24dB when the SNR is -20dB and the acquisition probability requirement is 96.31% due to the extension of the detection time, compared with the traditional FH synchronization acquisition method.