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In this paper, a computationally efficient, non-data-aided maximum a posteriori (MAP) channel estimation algorithm is proposed for orthogonal frequency division multiplexing (OFDM) systems with transmitter diversity using space-time block coding. The Alamouti's transmit diversity scheme with two transmit antennas is employed here and generalized for OFDM systems. The algorithm requires a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve orthogonal expansion and estimates the complex channel parameters of each subcarrier iteratively using the Expectation Maximization (EM) method, which converges to the true MAP estimation of the unknown channel. An analytical expression is derived for the Modified Cramer-Rao lower bound of the proposed MAP channel estimator. The performance is presented in terms of the mean-square error for a system employing QPS signaling.