High-Order Moments and Gaussianity of Single-Carrier and OFDM Signals

This paper analyzes the high-order moments of linearly modulated single-carrier as well as orthogonal frequency-division multiplexing (OFDM) signals assuming that the modulated symbols that form resulting continuous signal waveform are statistically independent. For a single-carrier case with the ideal low-pass filter used for pulse shaping, closed-form expressions of the moments with up to the eighth-order are derived. The proposed approach is then extended to Gaussianity assessment of OFDM signals; we show how the moments of OFDM signals can approach to those of Gaussian distribution as the number of subcarriers increases for a given modulation constraint on each subcarrier. Also reported is the peculiar nonstationary behavior of the fourth-order moments in the case of BPSK modulated OFDM signals.