Abstract: This invention provides means 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. The signal processed is partially represented by a composite trellis diagram formed by combining multiple component trellis diagrams which are phase-displaced versions of a root trellis diagram. Desired variations in signal parameter values that result from modulating the signal effect transitions between states within the root trellis diagram.