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It is well known that the Alamouti scheme is the only space-time code from orthogonal designs achieving the capacity of a multiple-input multiple-output (MIMO) wireless communication system with nT=2 transmit antennas and nR=1 receive antenna. In this paper, we propose the n-times stacked Alamouti scheme for nT=2n transmit antennas and show that this scheme achieves the capacity in the case of nR=1 receive antenna. This result may regarded as an extension of the Alamouti case. 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 signal-to-noise ratio (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. In addition to the capacity analysis based on the assumption of a coherent channel, we analyze the error rate performance of the stacked orthogonal space-time block code (OSTBC) with the optimal maximum-likelihood (ML) detector and with the suboptimal lattice-reduction (LR)-aided zero-forcing detector. We compare the error rate performance of the stacked OSTBC with spatial multiplexing (SM) and full-diversity achieving schemes. Finally, we illustrate the theoretical results by numerical simulations.