Tight lower bounds on the symbol error rate of uncoded nonuniform signalling over AWGN channel

New Bonferroni-type lower bounds on the word error probability of uncoded systems are developed. The new family of bounds is based on a recent Bonferroni inequality proposed by Cohen and Merhav. These novel tight bounds are developed for optimal maximum a posteriori (MAP) coherent detectors with nonuniform signalling over additive white Gaussian noise channel. The results are compared to the state-of-the-art KAT lower bounds and it is shown that the superiority of one bound to another is dependent on the signal constellation, the amount of nonuniformity of the Bernoulli source to be communicated, and the SNR range of interest. For instance, for smaller deviations from the uniform case, which are in fact more plausible, and at low SNRs, the new bounds are tighter than KAT lower bounds for all the constellations studied