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We consider the problem of simultaneous ML estimation of data and carrier phase from a linear suppressed-carrier modulated signal received in the presence of additive white Gaussian noise. The ML detector of the data sequence is derived, and its error probability performance is analyzed. The result shows that the performance loss due to the unknown carrier phase can be reduced by increasing the sequence length. A suboptimum decision-aided subsequence-by-subsequence detector whose complexity does not increase exponentially with sequence length is proposed, and its performance is analyzed.