Performance optimization of open-loop MIMO systems with orthogonal space-time block codes

In order to obtain full spatial diversity available in a multiple-input multiple-output (MIMO) system, orthogonal space-time block codes (OSTBC) are employed due to their low decoding complexity. However, the drawback of OSTBC is that the code rate decreases with increasing number of transmit antennas. Using a recent result on the properties of Gaussian quadratic forms, we show that an OSTBC for an odd number of transmit antennas is always outperformed in terms of different performance measures, namely, the outage probability, the outage mean-squared error (MSE), and the raw bit-error rate (BER), by an OSTBC for an even number of transmit antennas, which has a strong impact on the design and application of OSTBC.