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A general approach that allows the extension of an CRB-achieving unbiased frequency estimator developed for the AWGN channel to be used for the multipath fading channel by using a periodic transmit sequence is given. The optimality of its performance is guaranteed in a multipath fading channel under certain conditions. The proposed method has low complexity but a reduced frequency operating range. The exploitation of the multipath diversity for fading channel is also investigated. It is illustrated through a correlation based frequency estimator how the general approach can be used, leading to a known estimator being used in a novel way.