Signal constellations in the hyperbolic plane are provided as an alternative to traditional signal constellations in the Euclidean plane, since channels may actually exist for which the latter signal constellations are not as suitable as the former. A hyperbolic gaussian probability density function, based solely on geometrical considerations, is derived to determine the performance of the hyperbolic signal constellations. Benefits result from an approach conceived in terms of reduced signal-to-noise ratio, needed to achieve a prescribed error rate and equivalent optimum receiver complexity. (c) 2005 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.34316982