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Kam and Sinha (1995) have proposed a Viterbi-type algorithm for efficient estimation of both coded and uncoded MPSK sequences received over the AWGN channel with unknown carrier phase. The aim is to achieve the BEP performance of coherent detection. The metric for choosing the survivors employed by Kam et al. is non-adaptive in that the observation window length for forming the metric is fixed, and is chosen a priori based on knowledge of the fluctuation rate of the carrier phase. The work here seeks to render the algorithm adaptive by developing a decision metric that can be adjusted to achieve coherent node error event probability without prior knowledge of the carrier phase characteristics. The metric is based on the use of a first-order adaptive filter for carrier reference tracking. The input gain of the filter is adapted on-line based on the received signal samples. The resulting receiver structure can be interpreted as a per survivor processing receiver. Both analytical and simulation results are presented to show that the receiver performs well in the presence of both static and time-varying carrier phase processes.