Performance Bounds of Non-Uniform Signaling over AWGN Channels

| In this work, we present two bounds (one lower bound and one upper bound) on the probability of a union of a nite number of events. The bounds { which are expressed in terms of only the individual event probabilities and the pairwise event probabilities { are applied to examine the symbol error (P s ) and bit error (P b ) probabilities of an uncoded communication system used in conjunction with M-ary PSK/QAM modulations and maximum a posteriori (MAP) decoding over AWGN channels. It is shown that both bounds provide a good, and often excellent, estimate of the error probabilities over the entire range of the signal-to-noise ratio E b =N 0 . The upper bound on P s and the lower bound on P b are particularly impressive as they agree with the simulation results even during very severe channel conditions.