Exact calculation of the union bound on performance of trellis-coded modulation in fading channels

This paper presents a method for the exact calculation of the union bound on the error performance of trellis-coded modulation (TCM) in fading channels. Previous analyses have approximated the error expression to allow the use of the transfer function, or restricted their attention to the most common error events, or both. In contrast, we combine the transfer function, which counts all error events, with exact calculation of event probabilities, and produce an exact expression for the union bound. Although computationally intensive, the technique produces the tightest bound yet published. In addition, it is very general and is applicable to coherent, differential, and pilot-based detection, and to phase-shift keying (PSK)- and quadrature amplitude modulation (QAM)-types of constellations.