A Simple Numerical Method for Non-Gaussian Signal Ensembles in Nonlinear Power Amplifiers

Beam tracking in vehicular communication systems is inherently challenging due to high mobility and the use of narrow millimeter-wave (mmWave) beams. These challenges are further exacerbated by power amplifier (PA) nonlinearities, which introduce distortion-induced beam pattern deviations, array-gain loss, and non-Gaussian signal distortions. Motivated by the need for analytical tools capable of characterizing such effects, this paper extends Rice characteristic-function (ch. f.) method for the stochastic analysis of signals and noise in memoryless nonlinear systems. The proposed approach represents the nonlinearity using a Fourier series rather than a Fourier transform, transforming the evaluation of output correlation functions from computationally intensive double or triple improper integrals into tractable summations. The resulting framework preserves the generality of the original method, supporting one or more sinusoidal signals and noise processes that are not restricted to Gaussian distributions. A new fundamental ch. f.-based formulation is derived in terms of Fourier-series coefficients and a discrete parameterization of the generalized characteristic function. Numerical results are presented for a nonlinear GaN HEMT transconductance characteristic driven by a sinusoidal signal and Gaussian noise, demonstrating the applicability of the proposed method. The framework provides a computationally efficient tool for analyzing nonlinear RF front-end impairments and their impact on future wireless and vehicular communication systems.