Tight Upper Bounds on the Probability of Error of Quaternary Simplex Signals

We present new upper bounds on the error probability of quaternary simplex signals in additive white Gaussian noise. The proposed upper bounds are simple to compute than the exact probability of error and are tighter than the existing bounds for any value of the signal-to-noise ratio. Some new lower bounds are also presented. As a side result, the proposed bounds can be easily extended to quaternary orthogonal signals, such as coherently detected frequency-shift keying and pulse-position modulation.