Exact and Approximate Distributions of Instantaneous Power for Pulse-Shaped Single-Carrier Signals

We develop two approaches to calculating statistical distributions of instantaneous power of pulse-shaped single-carrier signals. Our first approach is to derive a formula that can calculate exact distributions of pulse-shaped signals with arbitrary constellations. The exact approach is versatile but turns out to be computationally demanding except for some cases where the constellation has circular symmetry. Our second approach is thus based on approximation, which is valid only for M-ary phase shift keying (MPSK) or phase-shifted MPSK constellations, but requires substantially less computation. The validity of the proposed approaches is confirmed by numerical analysis.