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This paper presents a reduced-complexity maximum-likelihood sequence estimation receiver, based on the Viterbi algorithm (VA), suitable for rapidly fading mobile communication channels. The channel impulse response is expanded onto a set of basis sequences and time-invariant (TI) expansion parameters. The proposed receiver continuously estimates the TI expansion parameters directly within the metric calculation of the VA. At every time instant of the VA, the accumulated metrics of the survivor paths are compared, and the survivors whose metrics are lower than the average value of the accumulated survivor metrics are retained. The other survivors are discarded from the trellis. Then the sequences associated with the minimum survivor of the retained survivors are used to update the estimate of the TI expansion parameters. The convergence properties of the estimation algorithm are investigated, and the steady-state value of the mean square error of estimation is derived. The performance of the proposed receiver is evaluated in terms of the symbol-error probability and compared with other receivers. The effects of time offset and frequency offset on the performance of the receiver are studied.