Statistical Analysis of the Channel Capacity Outage Intervals in Massive MIMO Systems with OSTBC over Rayleigh Fading Channels

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the outage intervals only over its initial part. By applying the asymptotic behavior of level crossings of Gaussian processes, an alternative expression, valid only for low capacity thresholds, is obtained, which, in turn, is applied to determine an approximate solution for the kth-order moments of the outage intervals. Also presented is the PDF of the so- called instantaneous capacity loss with respect to the average capacity. Simulation results have been shown to be in good agreement with the theoretical approximations, thereby confirming their validity. Although, the focus of the study is on massive MIMO systems, it has been observed that the approximations are accurate even for a moderate number of antennas such as the case of 4×4 MIMO-OSTBC systems.