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OFDM is a convenient vehicle for high rate transmission. However, this requires an accurate estimation of the channel at the receiver side. This paper proposes an iterative/adaptive algorithm for semi-blind channel estimation. An initial channel estimate is obtained by relying on the artificial constraint of pilots. The algorithm subsequently switches to the blind mode powered by the natural constraints imposed by the sparsity of the channel and the redundant and finite alphabet nature of the data. It iterates between using the channel estimate to detect the data, and using the data estimate to further improve the channel estimate. The diagonal nature of the OFDM channel makes it possible to optimally detect the data with low complexity. The complexity of the algorithm is further reduced by performing channel estimation adaptively. The simulation results demonstrate the favorable behavior of the algorithm and the tradeoff that it provides between the number of pilots used and convergence speed.