Signal constellations for non-Gaussian communication problems

On the basis of a geometric theory of detection, the authors extend the notion of a signal constellation, a concept deeply rooted in Gaussian problems, to the non-Gaussian case. Significant differences between optimal designs for Gaussian and non-Gaussian situations are shown. In particular, square-wave signals are much more important in heavy-tailed, non-Gaussian noise situations than in Gaussian ones. Furthermore, design guidelines for non-Gaussian problems can vary with the number of signal set members and can depend on SNR. The extent to which suboptimal designs affect performance (using Gaussian-based designs in non-Gaussian situations, for example) can be predicted from calculations of the Kullback information, but only in the sense of determining how the logarithmic error probability rates differ.<>