Recursive Probability Mass Function Method to Calculate Probability Distributions of Pulse-Shaped Signals

Abstract

This paper proposes an accurate and efficient method to calculate probability distributions of pulse-shaped complex signals. We show that the distribution over the in-phase and quadrature-phase (I/Q) complex plane is obtained by a recursive probability mass function of the accumulator for a pulse-shaping filter. In contrast to existing analytical methods, the proposed method provides complex-plane distributions in addition to instantaneous power distributions. Since digital signal processing generally deals with complex amplitude rather than power, the complex-plane distributions are more useful when considering digital signal processing. In addition, our approach is free from the derivation of signal-dependent functions. This fact results in its easy application to arbitrary constellations and pulse-shaping filters like Monte Carlo simulations. Since the proposed method works without numerical integrals and calculations of transcendental functions, the accuracy degradation caused by floating-point arithmetic is inherently reduced. Even though our method is faster than Monte Carlo simulations, the obtained distributions are more accurate. These features of the proposed method realize a novel framework for evaluating the characteristics of pulse-shaped signals, leading to new modulation, predistortion and peak-to-average power ratio (PAPR) reduction schemes.