Performance Analysis of M-PSK Signal Constellations in Riemannian Varieties

In this paper we consider the performance analysis of a digital communication system under the hypothesis that the signal constellations are on Riemannian manifolds. As a consequence of this new approach, it was necessary to extend the concepts related to signal constellations, symbol error probability and average energy of the signal constellation to the theory of differentiable manifolds. The important result coming out of this formalism is that the sectional curvature of the variety is a relevant parameter in the design and in the performance analysis of signal constellations.