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On the capacity of quasi orthogonal space-time block codes for MIMO systems

It is well known that the Alamouti scheme with two transmit antennas and one receive antennas is the only capacity-achieving complex orthogonal space-time block code (OSTBC). The rate of complex OSTBC for systems with more than two transmit antennas is always less than 1. Recently, a quasi orthogonal space-time block code (QSTBC) with four transmit antennas and one receive antenna was proposed, which has the ability to approach the capacity, although at the price of sacrificing part of the diversity gain. In this paper, we analyze the capacity of QSTBC with four transmit antennas and arbitrary number of receive antennas. We show that the portion of the capacity that the QSTBC can achieve decreases with the number of receive antennas, and the (4,1) configuration is the only capacity-approaching case. In the high signal-to-noise ratio regime, we calculate the limit portion of capacity of QSTBC, and find that it is fixed to 1/4 when the number of receive antennas is no less than four. Numerical simulations verify our conclusions.