The aim of' this investigation is to determine the combination of signal coding and modulation for satellite links, that, for a given degree of equipment complexity needed for the detection of the received signal, achieves the best tolerance to noise. Computer simulation tests and theoretical analyses are used to compare the various proposed signal designs The trellis coded M-ary phase-shift-keyed (MPSK) modulation method is introduced as the scheme for which different codes are to be devised. A class of known binary convolutional codes for 8 and 16 PSK signals is studied, and new correlative-level codes using modulo-M arthimetic are designed for MPSK signals. The soft-decision maximum likelihood Viterbi decoding algorithm is considered for the two proposed signal designs, and a more conventional near-maximum likelihood (reduced-state Viterbi) decoding scheme is also investigated for both types of coded signals. Two novel decoding schemes, derived from a more conventional near-maximum likelihood decoder, are proposed for coded 8PSK signals. In both decoders the amount of computation involved in decoding each data-symbol is adjusted to meet the prevailing noise level in transmission. Results of extensive computer simulation tests for both decoding schemes are presented. These results suggest that the new schemes come very close to achieving the maximum likelihood decoding of the coded signals without, however, requiring nearly as much storage and computation per decoded data symbol as does the Viterbi decoder. The carrier-phase synchronisation prob1em in a coherent trellis coded MPSK system is investigated. Eight new rotationally invariant rate-2/3 and rate-3/U convolutional codes for 8 and 16 PSK signals are designed. The new coded MPSK signals, when combined with a simple phase-error correction system proposed for the receiver, are able to tolerate the likely carrier-phase changes in the reference carriers of the coherent demodulation process and therefore avoid the prolonged error bursts that are otherwise caused in the decoded data symbols by such phase shifts. coding gains of the majority of the new codes The asymptotic here are either the same as, or come close to, those of the best known but not rotationally invariant convolutional codes of the same rates.