An asymptotic approximate solution to the distribution of the capacity outage intervals in OSTBC-MIMO Rayleigh fading channels

This paper deals with the study of asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity (also referred to as the mutual information) in orthogonal space-time block code (OSTBC) transceiver systems over multiple-input multiple-output (MIMO) Rayleigh fading channels. The Rayleigh fading subchannels are assumed to be frequency-nonselective and mutually uncorrelated, whereas the associated Doppler power spectral density is supposed to be symmetric about the origin. In addition, the channel state information (CSI) is considered to be available only at the receiver side. Taking these assumptions into account, and drawing upon known statistical properties for the asymptotic behavior of chi-square processes at low levels, we provide a closed-form approximate solution for the PDF of the outage intervals of the underlying capacity processes. Furthermore, an analytical expression is also provided for the kth-order moments of the outage intervals. These statistical quantities will as well be shown to be useful for studying the statistics of the capacity outage durations of single-input multiple-output (SIMO) and multiple-input single-output (MISO) systems. The validity of the obtained approximate asymptotic solutions has been confirmed by means of computer simulations.