A new, simple, and exact union bound for reference-based predetection and postdetection diversity TCM-MPSK systems in Rayleigh fading

Trellis-coded modulation (TCM), when combined with interleaving of sufficient depth, is known to provide some form of time diversity that allows for the achievement of good error performance in fading environments. Also, space diversity reception, in which several signals received at different antennas are combined, is a well-known method that can be used to combat the effects of fading in wireless systems. In this paper, we consider the analysis of the error performance of reference-based predetection and postdetection diversity systems when used in conjunction with trellis-coded modulation techniques. Based on the combination of the transfer function upper bounding technique with the exact calculation of pairwise error event probabilities, we present a new and simple method for exact calculation of the union bound on the average bit error rate (BER) performance of these systems in correlated Rayleigh fading channels. This method has the same complexity as the union-Chernoff bound, and some examples are given to illustrate its application. Monte-Carlo simulation results, which are more indicative of the exact system performance, are also shown