On the Generation of Autocorrelated -, -, and - Fading Sequences

Despite their mathematical flexibility, great fit to empirical data, and increasing popularity, the \alpha - \mu , \eta - \mu , and \kappa - \mu fading models have to date no simulation framework as general as the models themselves. In this work, we overcome this drawback by proposing a unified simulation method for \alpha - \mu , \eta - \mu , and \kappa - \mu fading processes that accommodates full-range values of all the fading parameters. Not less important, the proposed method is simple, exactly matches the fading models' first-order statistics, and well approximates their second-order statistics. We derive the analytical expressions for the proposed method and optimize a crucial simulation parameter to improve the match for the second-order statistics. In passing, we obtain useful series representations and asymptotic expressions for essential first- and second-order statistics of the fading models investigated. Our results are fully validated via the Monte Carlo simulation.