On the Multivariate $\alpha$ – $\mu$ Distribution: New Exact Analytical Formulations

Correlation among channels is a physical phenomenon that affects the performance of a wireless communication system and that cannot be neglected in a myriad of realistic fading scenarios. Providing computable mathematical means to better characterize the corresponding statistics is certainly of interest to any design engineer. In this context, this paper further extends the statistical correlation investigations of the α-μ fading model, presenting a new, exact, and easily computable series-type formulation for the multivariate α-μ joint cumulative distribution function (JCDF). Along with this general result and capitalizing on practical assumptions, an alternative, simpler formulation for the α -μ multivariate joint density function and its corresponding distribution function are also provided. These formulations are still general and yet compact, assuming arbitrary fading parameters and correlations among the marginal variates. An important feature of the series-type distribution is that any truncation version of it is a valid distribution. As an application example, the truncated series-based outage probability of the selection combining scheme is computed and compared with that obtained by means of numerical methods and simulations. The results show that a small number of terms of the series are sufficient to provide excellent agreement between approximate and exact results.