On the distribution of instantaneous power in single carrier: Effective numerical approach

This paper investigates the statistical distribution of instantaneous power (IP) in pulse-shaped single-carrier (SC) modulation. Such knowledge is required due to the nonlinearity of the power amplifier (PA). Exact analytical derivation of the distribution is an open problem. The existing works rely on Monte-Carlo simulations or on an approximated numerical analysis. In this paper we propose a straightforward method, based on numerical integration, to evaluate the complementary cumulative distribution function (CCDF) of IP by using characteristic function approach. Error analysis of the proposed numerical approach is given. It is shown that by investing relatively small computation power in the proposed numerical solution we can derive the CCDF of IP with high and controlled accuracy.