ANALYSIS OF THE ERROR PERFORMANCE OF TRELLIS-CODED MODULATIONS IN RAYLEIGH-FADING CHANNELS

Trellis-coded modulation (TCM), when combined with interleaving, is known to give good error performance in fading channels. Previously, though, the only analytical guide has been an upper bound [2], which could be very loose over the range of signal-to-noise ratio of interest. In contrast, this paper presents an exact expression for the pairwise error event probability of TCM transmitted over Rayleigh-fading channels. It includes PSK and multilevel QAM codes, as well as coherent and partially coherent (e.g., differential, pilot tone, etc.) detection. Due to the form of the exact pairwise error event probabilities, this calculation technique can not be used with the transfer function technique to obtain an upper (union) bound on the overall bit error probability. For this reason, we estimate the bit error probability by considering only a small number of short error events. Through simulations, we found that the estimation is usually very accurate at high signal-to-noise ratio but not as accurate at lower signal-to-noise ratio. We study several coded modulation schemes this way. Among the results are the fact that TCM provides significant improvement in the error floor when detected differentially, and an asymmetry in the pairwise error event probability for 16 QAM.