  In this paper, we propose a new upper bound on the error probability
performance of maximum-likelihood (ML) detection. The proposed approach
provides a much tighter upper bound when compared to the traditionally used
union bound, especially when the number of pairwise error probabilities (PEPs)
is large. In fact, the proposed approach tightens the union bound by first
assuming that a detection error always occurs in a deep fading event where the
channel gain is lower than a certain threshold. A minimisation is then taken
with respect to the gain threshold in order to make the upper bound as tight as
possible. We also prove that the objective function has a single minimiser
under several general assumptions so that the minimiser can be easily found
using optimisation algorithms. The expression of the new upper bound under
correlated Rayleigh fading channels is derived and several analytical and
numerical examples are provided to show the performance of the proposed bound.
