Abstract: This invention provides a method and apparatus for processing a received digitally-modulated carrier signal to coherently demodulate or, for some applications, coherently demodulate and decode said signal when the signal's phase has an undesired component and/or to generate successive estimated values of said undesired phase of the received signal. Signal processing operations are performed in accord with a composite trellis diagram formed from one or more component trellis diagrams that are phase-displaced versions of a root trellis diagram and, when applicable, phase migration transitions. Desired variations in signal parameter values that result from modulating the signal effect transitions between states in the root trellis diagram.