Complex Nakagami Channel Simulator with Accurate Phase and Auto-Correlation Properties

Accurate and systematic channel simulation technique is critical for performance verification of digital transceiver design over wireless channels. Despite the abundant results on Nakagami-m channel simulation techniques available in the literature, the accurate simulation of Nakagami-m fading channels satisfying the prescribed temporal autocorrelation property is still an open problem. Furthermore, the generation of Nakagami sequences satisfying proper phase distribution has not been studied yet. In this paper, we provide a systematic procedure on the reconstruction techniques of Nakagami-m fading autocorrelation property. We propose several new cumulative distribution function (CDF) mapping methods to realize arbitrary pre-specifled Nakagami auto-correlation function and with good numerical stability. In our method, we map the real and imaginary parts of complex Rayleigh fading samples disjointly to form complex Nakagami samples, which solves the phase ambiguity problem. Furthermore, we study the mapping between Rayleigh and Nakagami auto-correlation functions, and design an approach to calculate the original Rayleigh auto-correlation function to realize a specified Nakagami correlation function. Simulation results verify that our approach can accurately reconstruct arbitrary pre-specified auto-correlation property for the Nakagami channel generation, and also satisfy the proper phase property which follows a non-uniform distribution.