Evaluation of the exact union bound for trellis-coded modulations over fading channels

An analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over Rayleigh, Rician, or shadowed Rician-fading channels. To this end, an integral expression is derived for the pairwise error event probability (PEP). Existing bounds can be obtained as special cases of this expression. It turns out that a Gauss-Chebyshev quadrature rule offers excellent accuracy for this integral. By extension, the exact union bound (i.e., the weighted sum of an exact PEPs of a code) can readily be evaluated. This method has the same complexity as the union-Chernoff bound, and a few examples are given to show its application.