Signal modelling in wireless fading channels using spherically invariant processes

We propose the application of spherically invariant random processes for joint modeling of the fluctuations of the signal envelope and phase in narrowband wireless fading channels. In this model, the phase has a uniform distribution (which is very common in fading channels), while the envelope can be distributed according to an arbitrary distribution law (which includes Rayleigh as a special case). The great utility of the spherically invariant random processes, as a large family of non-Gaussian random processes, lies on their many Gaussian-like properties, which make them very flexible for multivariate statistical analysis, optimal estimation, simulation, and other signal processing issues. Empirical justifications are also given, which strongly support the acceptability of the model