Asymptotically optimum (in the sense of minimum per-symbol error rate) receiver structures for data communication over the white Gaussian channel with unknown time delay and carrier phase jitter are developed. The receiver structures apply to the following suppressed-carrier modulation systems: double sideband (DSB), quadrature amplitude modulation (QAM) with an arbitrary constellation, vestigial sideband (VSB) and single sideband. The resulting minimum error probability receivers are asymptotically equivalent to maximum-likelihood digital sequence-estimating receivers. The optimum structures implicitly derive joint maximum-likelihood estimates of the unknown parameters and of the sequence of data symbols. It is shown that the parameter estimates can be obtained from two data-directed stochastic approximation algorithms. Unlike traditional theoretical treatments of this communication situation, which have separated the highly important carrier phase and timing recovery problem from the detection problem, a unified theory is presented from which the complete ideal receiver structure can be deduced.

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Journal IEEE Transactions on Information Theory
Falconer, D.D, & Salz, J. (Jack). (1977). Optimal Reception of Digital Data over the Gaussian Channel with Unknown Delay and Phase Jitter. IEEE Transactions on Information Theory, 23(1), 117–126. doi:10.1109/TIT.1977.1055663