Fourth-Order Moment Analysis of Filtered Single-Carrier and OFDM Signals

This paper discusses a statistical property of single- carrier and OFDM signals pulse-shaped by the square- root raised-cosine (RRC) filter. In general, strictly band- limited signals exhibit high peak power, and the baseband signal with large signal dynamic range severely suffers from nonlinearity of power amplifiers. Therefore, in practical systems operated with a pulse-shaping filter, its roll-off factor (or excess bandwidth) should be carefully chosen considering the trade-off between the bandwidth and dynamic range of resulting signals. In this work, we investigate this trade-off relationship for the RRC-filtered single-carrier signals composed of statistically independent input symbols through the analysis of their fourth-order moments. The expression for the complementary cumulative distribution function (CCDF) of the instantaneous power in the case of RRC-filtered Gaussian signals is also developed, which serves as an accurate reference for the RRC-filtered OFDM signals with a large number of subcarriers. Based on these observations, we show that the RRC filtered OFDM signals tend to exhibit larger dynamic range than the conventional OFDM signaling filtered by a periodic sinc function.