On Mutual Information of Stacked OSTBC

It is well known, that the Alamouti scheme is the only space-time code from orthogonal design achieving the capacity of multiple-input multiple-output (MIMO) wireless communication systems with n(T) = 2 transmit antennas and n(R) = 1 receive antenna. In this work, we propose the n-times stacked Alamouti scheme for n(T) = 2n transmit antennas and show that this scheme achieves the capacity in the case of n(R) = 1 receive antenna. For the more general case of more than one receive antenna, we show that if the number of transmit antennas is higher than the number of receive antennas we achieve a high portion of the capacity with this scheme. Further, we show that the MIMO capacity is at most twice the rate achieved with the proposed scheme for all SNR. We derive lower and upper bounds for the rate achieved with this scheme and compare it with upper and lower bounds for the capacity. Finally, we illustrate the theoretical results by numerical simulations.