Abstract: There are described apparatus and methods for producing time-varying of trellis-coded modulations, specifically, time-varying trellis-coded phase-shift-keying, to facilitate carrier phase recovery when the signal has been exposed to extraneous phase variations and noise.Typically, eight-phase-shift-keying (8-PSK), with rate 2/3 convolutional coding, is followed on a repetitive basis by one or two formats of four-phase-shift-keying (4-PSK), which formats are chosen to ease phase synchronization and to conserve the use of bandwidth and not to worsen the bit error probability while reducing the probability of synchronization loss and the length of error bursts or "random walks".The variation of the modulation formats could be:(1) 8-PSK (rate 2/3) followed by 4-PSK,(2) 8-PSK (rate 2/3) followed by 4-PSK (preferred format) and then 4-PSK (secondary format) or,(3) any of many other periodic formats of 8-PSK and 4-PSK sections.