Abstract : The problem of simultaneously estimating phase and decoding data symbols from baseband data is posed. The phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally-likely symbols transmitted over a perfectly equalized channel. A dynamic programming algorithm (Viterbi algorithm) is derived for decoding a maximum a posteriori (MAP) phase-symbol sequence on a finite dimensional phase-symbol trellis. A new and interesting principle of optimality for simultaneously estimating phase and decoding phase-amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase-symbol sequences. Simulation results for binary, 8- ARY PM, and 16-QASK symbol sets transmitted over random walk and sinusoidal jitter channels are presented, and compared with results one may obtain with a decision-directed algorithm, or with the binary Viterbi algorithm introduced by Ungerboeck. When phase fluctuations are severe, and the symbol set is rich (as in 16-QASK), MAP phase-symbol sequence decoding on circles is superior to Underboeck's technique, which in turn is superior to decision-directed techniques.
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