Fractional Low-order Cyclic Spectrum Analysis Of Digital Modulation Signals Under Alpha Stable Distribution Noise

The alpha stable distribution can well be described the non-Gaussian distribution with significant spike characteristics and thicker trailing characteristics in practical applications.Some of the digital modulation signals which are used in wireless communication systems usually show cyclic smoothness characteristics. However, the second-order cyclic statistic method for analyzing and processing these cyclostationary signals under the alpha stable distribution noise is significantly degraded. So the detection and estimation of the signal can not be achieved well. The fractional low-order cyclic statistic method is an effective tool for the detection of cyclostationary signals under the alpha stable distributed noise. The main contents of this paper include:1.The process of generating the alpha stable distribution sequence is deduced under the standard parameter system, and the details of the alpha stable distribution sequence and the probability density function are analyzed when the four parameters are changed.2.The cyclic spectral density function formulas of 2ASK, 2FSK and BPSK signal are presented. The spectrum and cyclic spectrum correlation characteristics of these three kinds of signal are analyzed, and also the Gaussian distribution noise under different signal-to-noise ratios are analyzed.3.Under the alpha stable distributed noise, combined with fractional low-order statistic and cyclic stationary theory,the fractional low-order cyclic autocorrelation function of 2ASK and 2FSK signal are deduced. The low-order cyclic spectrum and the corresponding cyclic frequency axis section of 2ASK, 2FSK and BPSK signal are analyzed under different mixed signal-to-noise ratios, characteristic exponents and fractional low order factors.The results show that the low-order cyclic spectrum structure of these three kinds of signal is the same as that of the traditional second-order cyclic spectrum, which peaks corresponding to the cyclic frequencies are the same, but the amplitude values of the peaks are different.Compared with the second-order cyclic spectrum, the fractional low-order cyclic spectrum can realize the detection of these three kinds of signal spectreum lines well under the alpha stable distribution noise, and the detection effect of different signals is different.