Correlation between symmetric capacity and parameters of two dimensional signal constellations

Signal constellation has an important influence on the capacity of communication system. Two dimensional signal constellation is of most prevalent in modern communication systems. Traditionally it is considered that the performance of some signal constellation is mainly decided by the minimum of the Euclidean distance between signal pairs in two-dimensional plane [2] [3]. However several numerical characters of the Euclidean distances in a signal constellation correlate with the performance. We find that minimum of the Euclidean distance shows uncertain dependence on capacity, meanwhile variance and mean of the Euclidean distance between signal pairs maintain strong dependence on capacity. In this paper, the correlation between capacity and some parameters of two dimensional signal constellations is analyzed. As the parameters for describing the signal constellation, variance, mean, minimum and maximum of Euclidean distance between signal point pairs are considered. The conclusion is presented through the analysis of the computing results.