Al-Semari, Saud A.Fuja, Tom E.Coherent trellis coded modulation (TCM) systems employing diversity combining are analyzed. Three different kinds of combining are considered: maximal ratio, equal gain, and selection combining. For each combining scheme, the cutoff rate parameter is derived assuming transmission over a fully- interleaved channel with flat, slow, Rayleigh fading; in addition, tight upper bounds on the pairwise error probabilities are derived. These upper bounds are expressed in product form to permit bounding of the BER via the transfer function approach. In each case it is assumed that the diversity branches are independent and that the channel state information (CSI) can be recovered perfectly.<P>Also included is an analysis of maximal ratio combining when the diversity branches are correlated; the cutoff rate and a tight upper bound on the pairwise error probability are derived. It is shown that, with double diversity, a branch correlation coefficient as high as 0.5 results in only slight performance degradation.en-USdetectiondigital communicationsdistributed information processingerror-detection codesinformation theoryrobust information processingwireless communicationfading channelsIntelligent Signal ProcessingCommunications SystemsTechnical Report