Analysis of predetection diversity TCM-MPSK and postdetection diversity TCM-MDPSK systems on a Rayleigh fading channel

In this paper, the bit error rate (BER) performance of predetection diversity trellis coded multilevel phase shift keying (TCM-MPSK) and postdetection diversity trellis coded multilevel differential phase shift keying (TCM-MDPSK), transmitted over a Rayleigh fading channel is presented. Novel analytical upper bounds using the transfer function bounding technique are obtained and illustrated by several numerical examples. A new asymptotically tight upper bound for the maximal ratio combining (MRC) diversity schemes is also derived. In order to analyze practical TCM schemes (four or more states), only trellis codes holding uniform error property (UEP) and uniform distance property (UDP) are considered, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte-Carlo simulation results, which are more indicative of the exact system performance, are also given.>