The probability density of intersymbol interference for trellis-coded modulation

Knowledge of the probability density function (pdf) of intersymbol interference (ISI) can be used in the computation of system error probabilities and to help identify the cause of the errors. Exact computation of the probability density is only practicable in a few special cases. Several algorithms exist for computing approximate pdfs of ISI but these only work with certain signal constellations and transmitted symbols that are mutually independent or coded by partial response. This paper considers an algorithm for the computation of ISI pdfs for trellis-coded modulation with general 1D and 2D constellations. The results suggest that symbol dependencies introduced into the transmitted signal by symmetric trellis-codes have negligible effect on the pdf of the ISI. Although the ideas presented are general in nature, examples are given for ISI pdfs on a line-of-sight radio channel