Trellis-coded modulation on time-dispersive channels.

In this thesis we examine the performance of trellis-coded modulation (TCM) on time-dispersive channels. More specifically, we are interested in the performance improvements that TCM can offer in the presence of the residual intersymbol interference (ISI) that remains after non-ideal equalization on digital microwave radio (DMR) channels. The results are, however, applicable to other time-dispersive channels. The performance of TCM on additive white Gaussian noise (AWGN) channels is well understood, and tight analytical bounds exist on the probability of the Viterbi decoder making a decision error. When a channel is also time-dispersive, the performance of TCM systems has, in the past, been studied mainly by simulation, due to the difficulty of formulating tractable analytical bounds on the error probability. In the work reported here, both simulation and analytical techniques are used. The results of the simulation study show that TCM can improve the performance of a system with residual ISI. Although significant coding gains are achieved, the improvements in link outage are small, but useful. Simulation, however, is limited to symbol error probabilities greater than about 10-5 , and is not a particularly useful tool for estimating error probabilities over the range required for designing codes. There is a need for tight analytical bounds on error probability for TCM on time-dispersive channels so that the issues of designing good codes on such channels can be studied. Analytical upper bounds on error probability that rely on knowing the probability density function (pdf) of the ISI are derived. These bounds are closed-form expressions, but numerical techniques must be used to evaluate them. The emphasis in this work has been to obtain upper bounds that are tight for a wide range of time-dispersive channel conditions. A lower bound is also presented; this bound is tight for low levels of ISI, but loose for severe ISI. The pdf of the ISI must be computed to evaluate the analytical upper bounds. However, exact computation of the pdf is only tractable in a few special cases. Algorithms are presented for computing approximations to the ISI pdf for uncoded and trellis-coded systems with general one- and two-dimensional signal constellations. Procedures for forming worst and best case ISI pdf's that can be used to compute upper and lower bounds on symbol error probability are also developed. Examples show that the dependence between symbols, introduced into the transmitted signal by Ungerboeck codes, has negligible effect on the pdf of the ISI. In summary, the performance of TCM in a residual ISI environment has been studied using computer simulation. To overcome the limitations of simulation, analytical bounds on error probability have been developed. The numerical evaluation of these analytical bounds relies on algorithms to compute approximate ISI pdf's. The tightness of the bounds has been verified by computer simulation where possible