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In this paper, we show how Alamouti's simple but useful transmit diversity scheme for two antennas can be combined with a standard outer error-correcting code to achieve a stronger concatenated space-time coding scheme. By introducing a matrix formalism that allows us to interpret the transmission channel as a rotation in an Euclidean space, it can be easily shown that this scheme with two transmit (TX) and Lr receive (RX) antennas is equivalent to a simple RX antenna setup with 2Lr RX antennas. Analytical formulas for pair error probabilities will be derived for the time and/or frequency flat fading and for the ideally interleaved Rayleigh fading channel as well as for the correlated fading channel. As a practical example, we study how the performance of a Walsh-Hadamard coded multicarrier code-division multiple-access system depends on the correlation bandwidth of the channel and the number of RX and TX antennas.