Fractional lower order cyclic spectrum analysis of digital frequency shift keying signals under the alpha stable distribution noise

Aiming at the significant degradation of the statistical characteristics of the second and higher order cycle of the digital communication signal in the alpha stable distributed noise environment, the fractional lower-order cyclic spectrum formula of the frequency shift keying (FSK) signal is deduced with the fractional lower-order moments and the covariant theory. Then, the low-order cyclic spectrum characteristics of 2FSK signal under different mixed signal-to-noise ratios, fractional factors and characteristic exponents were analyzed in detail. The theory and simulation results show that the low-order and second-order cyclic spectrum structures of the 2FSK signal are the same, and the peak frequencies of the 2FSK signal are the same, but the amplitude of the spectrum is different that depending on the order factor of the cyclic spectrum. Fractional lower-order cyclic spectrum has stronger anti-interference and applicability to alpha stable distributed noise.