OPTIMUM SYMBOL-BY-SYMBOL DETECTION OF UNCODED DIGITAL DATA OVER THE GAUSSIAN-CHANNEL WITH UNKNOWN CARRIER PHASE

A theory of optimum receiver design for symbol-by-symbol detection of an uncoded digital data sequence received over the Gaussian channel wi th unknown carrier phase is presented. Linear suppressed-carrier modul ation is assumed. The work here aims at laying a conceptual foundation for optimum symbol-by-symbol detection, and rectifies existing approa ches to the problem. The optimum receiver structure is obtained explic itly for an arbitrary carrier phase model, but its computational requi rements are too heavy in general for any practical implementation. In one important special case, namely, the case in which the carrier phas e can be treated as a constant over some K + 1 symbol intervals, the o ptimum receiver can be approximated by a readily implementable decisio n-feedback structure at high SNR. Simulated error performance results are presented for this latter receiver for PSK modulations with variou s carrier phase models. Since a decision-feedback receiver can encount er a ''runaway,'' a variation of this receiver is developed which uses feedforward of tentative decisions concerning future symbols. This mo dified receiver does not have any ''runaway'' problem, and has been sh own to yield good error performance via simulations.