Exact Closed-Form Expressions for the Distribution, the Level-Crossing Rate, and the Average Duration of Fades of the Capacity of OSTBC-MIMO Channels

This paper deals with some important statistical properties of the channel capacity of multiple-input-multiple-output (MIMO) systems with orthogonal space-time block code (OSTBC) transmission. We assume that all the subchannels are uncorrelated. For OSTBC-MIMO systems, exact closed-form expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity. Furthermore, it will be shown that these exact closed-form expressions can be used to characterize the channel capacity of single-input-multiple-output (SIMO) and multiple-input-single-output (MISO) systems. In addition, a Gaussian approximation to the exact LCR of the capacity of OSTBC-MIMO systems is derived. The correctness of the derived closed-form expressions and the approximation is confirmed by simulations.