Noisy Fading Channel Distributions Parameter Estimation and Reconstruction based on Truncation

In this paper, Rayleigh and Nakagami-m fading channels are considered that are positively correlated. The received signal statistics specifically mean and variance of sum of fading and noise variables in cases where fading distributions are considered ranging from zero to infinity compared to cases where the fading and noise distributions are truncated due to applying the energy criterion to each distribution are considered. Average number of required bits are derived by calculating Shannon entropy for each case investigated. The number of measurements required for distribution reconstruction based on CS reduced complexity method for each case are also computed. Furthermore, the Bit-Error-Rate (BER) curves for all respective cases are derived and directly compared. The results impose the effect of truncation on the quantification of variances as well as average number of bits as measures of uncertainty and number of measurements for reconstruction. The BER curves produced account for the Gaussian statistical assumption adopted. Applications to 5G communications are provided and future directions are highlighted.