High-order statistical analysis for linearly modulated signals

Statistical properties of digital modulation signals play an important role in their signal dynamic range analysis as well as modulation classification. However, its distribution cannot be expressed in a closed form in general. This paper addresses high-order moments and cumulants of linearly modulated signals, assuming that the modulated symbols are statistically independent. We demonstrate that in the case of an ideal pulse-shaping filter with rectangular spectrum, simple closed-form expressions of the moments can be found for up to the eighth order. The derived expressions may be helpful in gaining insight on the statistical properties of band-limited digital signal waveforms.