The α - λ-μ and -α-η-μ small-Scale General Fading Distributions: A Unified Approach

In this paper, a general small-scale fading model for wireless communications, that explores the nonlinearity and at the same time the inhomogeneous nature of the propagation medium, is presented, studied in terms of its first-order statistics of the envelope, and validated by means of field measurements and the Monte Carlo simulation. It is indeed a novel distribution with many advantages such as its generality, its physical interpretation that is directly associated with the propagation channel, and its mathematical tractability due to its simple and closed-form expression. By fitting to measurement data, it has been shown that the proposed distribution outperforms the widely known fading distributions. Namely, the α - λ - μ model, which can be in fact called α - η - μ format 2 model, can also be obtained from the α - η - μ format 1 model by a rotation of the axes. Both formats are combined, in order to result to a unified model in a closed form that may describe the propagation environment in a variety of different fading conditions. Its physical background is hidden behind the names of its parameters. The unified model includes the already known general distributions α - μ′, η - μ, λ - μ (η - μ format 2), and their inclusive ones as special cases.