Matched Filter Bound for Trellis-Coded Transmission over Frequency-Selective Fading Channels with Diversity

Transmission of trellis-coded digital information over time-variant frequency-selective multipath radio channels leads to receiver design considerations and bit error characteristics fundamentally different from those of links using static channels. Making use of diversity is of prime importance in a fading environment. Explicit antenna diversity, implicit time diversity from interleaved trellis-coded modulation, and implicit multipath diversity via energy detection/equalization are three methods of transmission quality enhancement that can be jointly employed without loss of power and bandwidth. The matched filter bound (MFB) is a lower bound on the average bit error rate under ideal conditions, i.e. perfect channel estimation, interleaving, and equalization. In this paper, a new method of evaluating the MFB based on an eigenvalue approach is presented and the analysis extended to include transmission of trellis-coded linearly modulated signals over selective diversity channels having arbitrary fading multipath profiles. MFB results are generated for a number of illuminating examples (trellis codes with effective code lengths up to 5, selective two-ray and GSM Rayleigh as well as flat Rician channels) that demonstrate the potential benefits of implicit time and multipath diversity. Some simulation results are presented giving rise to concluding remarks on the tightness of the bound.