Asymptotics and Error Rate Bounds for M-ary DPSK

The symbol error probability for -ary DPSK is shown to be bounded in terms of a recent asymptotic approximation by the inequalities ; where is the bit energy-to-noise spectral density ratio. Aside from the wide range of validity and the closeness of the lower and upper bounds, this result is striking in light of the often held view that such asymptotic approximations are primarily of value only in the limit ; thus, one of the goals of this note is to demonstrate that asymptotic methods can lead to extremely good error rate approximations in lieu of the more traditional and more widely used bounding techniques. The results are also noted to be applicable in other similar situations which commonly occur.