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In this paper, we consider channel estimation with the use of dedicated pilot signal in multiple-input multiple-output orthogonal frequency division multiplexing wireless systems. The dedicated pilot signal is transmitted through a channel virtually transformed by means of beam weighting. We consider the use of a minimum mean squared error (MMSE)-type estimator that fully exploits the statistics of beam-weighted channel. Without the statistics of the beam-weighted channel, conventional channel estimators cannot noticeably enhance the estimation performance even with the use of dedicated pilot signal. Obtaining the statistics of the beam-weighted channel from that of the common pilot channel, we design an affine MMSE channel estimator in consideration of biased beam weighting for the transmission of dedicated pilot signal. Simulation results show that the proposed scheme noticeably outperforms conventional estimation schemes in poor operation condition.