The detection performance of the dual-sequence-frequency-hopping signal via stochastic resonance processing under color noise

Can the Dual-Sequence-Frequency-Hopping (DSFH) as a military emergency communication mode work under strong color noise? And is there any detection improvement of the DSFH signal via stochastic resonance (SR) processing under color noise? To deal with this problem, we analyze the physical feature of the DSFH signal. Firstly, the signal models of transmission, reception and the intermediate frequency (IF) are constructed. And the scale transaction is used to adjust the IF signal to fit the SR. Secondly, the non-markovian Langevin Equation (LE) is transformed into a markovian one by expand the 1-D LE to a 2-D one. Thirdly, the non-autonomous Fokker-Plank Equation (FPE) is transformed into an autonomous one by assuming that the SR transition of magnetic particles is instantaneous and introducing the decision time. Therefore, the analytical periodic steady solution of the probability density function (PDF) with the parameter of the correlation time of the color noise is obtained. Finally, the detection probability, false alarm probability and Receiver Operating Characteristics (ROC) curve are obtained, under the criterion of the maximum a posterior probability (MAP). Theoretical and simulation results show as below: 1) whether the DSFH can work under strong color noise is decided by the correlation time of the color noise; 2) when the power intensity of the color noise is constant, the smaller the correlation time with the bigger local SNR, the greater PDF difference of the SR output under two hypothesis, leading to better detection performance.