Design of multidimensional signal constellations

An algorithmic technique intended for signal constellation design for an N-dimensional Euclidean signal space is presented. Such signals are used for reliable and efficient digital communications on an additive white Gaussian noise channel. The minimum Euclidean distance between signals and the constellation-constrained capacity are used as performance measures. The basic idea is to spread out the signal vectors using an iterative method modelling the behaviour of equally charged particles in free space. Initially, the vectors are randomly distributed. The vectors reach equilibrium after a few iterations. Numerical calculations for N=2, 3, 4 and 5 dimensions and M=N+1, N+2, ...,20 signals show that the generated codes are nearly as good as previously known codes, and in some cases even better.