The problems of sequence decision, sample timing, and carrier phase recovery in a class of linear modulation data transmission systems are treated from the viewpoint of multiparameter estimation theory. The structure of the maximum-likelihood estimator is first obtained, and a decision-directed receiver is then derived. These receivers are different from the conventional one in that the carrier phase is extracted from the signal components themselves in an adaptive fashion. The structure of this adaptive demodulator and detector is then extended to the case in which the channel characteristic is unknown, and the algorithm for adjusting the carrier phase and sample instant is discussed in combination with that of adaptive equalization. Copyright © 1971 by The Institute of Electrical and Electronics Engineers, Inc.