On the probability density functions of outage and inter-outage durations of the capacity of Rayleigh fading channels

Approximations for the probability density functions (PDFs) of the capacity outage and inter-outage durations over Rayleigh fading channels are studied. Exact closed form expressions for the Rice probability functions of the level-crossing intervals of the capacity process are derived, assuming a symmetrical Doppler power spectral density (PSD). These probability functions, which are obtained by applying the classical level-crossing theory, are known to describe the PDFs of outage and inter-outage durations only over their initial behavior. Additionally, the derived quantities are used to calculate approximate solutions for the considered PDFs based on the assumption of statistical independence between the level-crossing intervals. Numerical examples, considering Rayleigh mobile-tomobile fading channels, are presented together with simulation results to illustrate the analysis and examine the validity of the derived expressions. Particularly, it is shown that the theoretical results obtained provide accurate approximations for the PDFs of outage and inter-outage durations at low and high outage levels, respectively.