Asymptotic Behavior of Extended Alamouti Schemes for Large Number of Transmit and Receive Antennas

It is well known that quasi-orthogonal space time block codes (QSTBC) do not achieve full diversity with linear reception due to their loss of perfect orthogonality. In this paper, we show that the diversity order of such scheme with arbitrary n_T = 2^k transmit antennas converges to n_Tn_R, if the number of receive antennas n_R grows large even for simple ZF receiver techniques. More precisely, the full diversity order of n_Tn_R can be exploited asymptotically with such a simple linear equalization scheme. We show that moderate numbers of transmit and receive antennas achieve full diversity order by simple maximum ratio combining techniques in practice. This effect is demonstrated on the extended Alamouti code (also known as Jafarkhani Code), but the method can be applied to a more general class of QSTBCs.