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In this paper, a new semi-blind channel estimation method for orthogonal frequency division multiplexing (OFDM) is presented. A deterministic frequency domain objective function for an OFDM frame is defined, which contains a sum of squared error for the pilot signals and a sum of weighted squared generalized magnitude error for data signals. It is found that the sum of squared absolute magnitude error for data signals, as a special case of the generalized term, provides an excellent block mean square error. An efficient iterative algorithm for obtaining an optimal solution is derived, that takes several iterations to converge to the steady state solution. The new algorithm is shown to provide a better performance gain than other pilot-based channel estimation methods and semi-blind methods.