Outage probability of OSTBC: Optimal transmit strategy and suboptimality of odd number of transmit antennas

Orthogonal space-time block codes (OSTBC) are an efficient mean in order to exploit the diversity offered by the wireless multiple-input multiple-output (MIMO) channel. It was shown that the Alamouti scheme, an OSTBC for n _T = 2 transmit antennas, achieves the capacity of such MIMO channels with n_R = 1 receive antenna. However, by increasing the number of transmit antennas, the transmission rate of the OSTBC is monotonically decreasing. Recently, this rate reduction was characterized completely. Using a recent result on the properties of Gaussian quadratic forms, we show two key results: Assume the transmitter has not channel state information. We show that for given rate and SNR it is optimal to use a subset of all available antennas with equal power allocation. Further on, we show that an OSTBC for an odd number of transmit antennas is always outperformed by an OSTBC for either the next lower or the next higher even number of transmit antennas. Finally, the impact of spatial correlation with uninformed transmitter is characterized. We illustrate the theoretical results by numerical simulations. The theoretical and simulation results show the suboptimality of the OSTBC for an odd number of antennas with respect to the outage probability minimization.