Abdel Nasser S.A.A. Hassan¹, Ahmed M. Gad^1,, Wafaa M. Ibrahim¹

Radio channel signals are heavily used tool in telecommunications. A suitable probability distribution is needed to model signals. Many probability distributions have been introduced for this purpose. The α-μ probability distribution is a general channel signal fading model that encompasses many applied important distributions as a special case. This distribution is also known as generalized gamma, Stacy distribution. This distribution is used to describe the fading mobile radio signal under a general diffuse scattering. The main advantage of this probability distribution is that it is flexible and mathematically tractable. Also, many other distributions can be considered as a special case of α-μ probability distribution. In this article we discuss the model parameters' estimation. Two new maximum likelihood (ML) and Psi-inverse (PI) estimators for the α-μ channel signal fading distribution have been proposed. Simulation study is finally conducted to evaluate the performance of the proposed estimators. Simulation results show that the proposed methods perform well comparable to the existing estimators. This behavior is valid for limited sample size; n<1000 or large sample size; n≥1000.

fading radio signals, α-μ distribution, Stacy distribution, gamma distribution, Erlang distribution, chi-squared, Nakagami distribution, size-biased distributions, ML estimators