A tighter upper bound on the error probability of signals in white Gaussian noise

Abstract

A new upper bound is presented to the probability of error in detecting one out of M equiprobable signals in additive white Gaussian noise. This bound employs the same number of erfc function evaluations as the well-known Union Bound, but it is tighter. For high cardinality constellations, the Union Bound is useless for low signal-to-noise ratios being above 1, while the proposed new bound maintains its significance. This bound can also be extended to the Bit Error Probability computation associated to the same decision problem, and again it is tighter than the Union Bound.