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Channel estimation for a space-time block coded transmission system is considered. By assuming that the channel frequency response is quasi-static, we develop channel estimation based on the use of a space-time block coded (STBC) training block. The optimality criterion for training sequence design is derived and the design tradeoffs associated with the choice of training length are discussed. A novel equalization and detection algorithm for the Alamouti scheme is developed, which is derived from the max-log maximum a posteriori (MAP) algorithm for conventional single-antenna systems. Zero-forcing (ZF) and minimum mean square error (MMSE) equalization are derived for the suboptimal detection algorithm. Numerical results are provided to demonstrate the performance of the proposed channel estimation and equalization algorithm for space-time block coded transmission systems.