Outage statistics for Beckmann fading channels in non-isotropic scattering environments

In this paper, the outage statistics are studied for non-isotropic Beckmann fading channel model. Non-isotropic scattering generally results in an asymmetrical Doppler power spectral density (PSD). In this context, an expression for the outage probability (OP) (or equivalently the cumulative distribution function (CDF)) of the fading envelope is first derived. Then, the probability density function (PDF) of the rate of change of the fading envelope is investigated. Thereafter, an expression for the average rate of outages (ARO) (or equivalently the level-crossing rate (LCR)) is provided. Finally, by making use of the analytical results of the ARO and OP, an expression for the average duration of outages (ADO) (or equivalently the average duration of fades (ADF)) is attained. The obtained results, which are given in the form of finite-range integrals that can efficiently be computed numerically, are verified to include a variety of already known expressions for models that are special cases of the Beckmann model. Numerical and simulation results are provided to verify the validity of the derivations and to analyze the effect of the fading parameters on the obtained metrics.