On the Statistical Properties of Capacity Outage Intervals in OSTBC-MIMO Rayleigh Fading Channels

Abstract

This paper deals mainly with the study of the asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity of orthogonal space-time block code (OSTBC) multiple-input multiple-output (MIMO) systems over Rayleigh channels. Drawing upon known statistical properties for the asymptotic behavior of chi-squared processes at low levels, we provide approximate solutions for the PDF, the cumulative distribution function (CDF), and the $k$ th-order moments of the outage intervals of the underlying capacity processes. Then, as an application of the derived PDF, the performance assessment of capacity simulators is reported. Following this, we introduce the newly defined average-to-trough capacity ratio (ATCR) metric, and investigate its PDF and CDF. The validity of the derived results is confirmed by specializing them to already known ones, although they have been obtained by using a rather different approach. The accuracy and applicability of the asymptotic analysis to practical values of capacity thresholds have been examined by means of computer simulations. The theoretical results presented contribute to the statistical characterization of outage events, the study of which has mainly been limited to the analysis of the probability, the occurrence rate, and the average duration of outages.