Trellis coded modulation on time-selective fading channels

A general analysis of trellis coded modulation (TCM) on time-selective fading channels with correlated signal samples is presented. Gaussian quadratic forms are used to evaluate the pairwise sequence error probability. The effect of interleaving is studied and it is shown that moderate interleaving with respect to the doppler frequency of the channel suffices to achieve good performance. The analysis is then extended to treat non-ideal estimation of the complex channel gain in the coherent case using a general linear channel estimator. It is shown that differential phase shift keying (DPSK) and differential trellis coded modulation (DTCM) on correlated fading channels call be treated analytically and that the error probability of DTCM, like of coherent TCM, depends only on the Euclidean distance of the error sequences. Results show that DTCM suffers a degradation of up to 3 dB with respect to coherent TCM on slow fading channels but performs better on fast fading channels. Error floor curves are presented for DTCM for different interleaving depths. The event error probability P_e and the bit error probability P_b of TCM, approximated by truncated averaged union bounds, are calculated for the codes used. A comparison of the approximations of P_b with simulation results show that the union bound is relatively loose for fading channels