Construction of Higher-Level 3-D Signal Constellations and Their Accurate Symbol Error Probabilities in AWGN

A simple and straightforward method of constructing higher-level three-dimensional (3-D) signal constellations for a reliable digital communication system is proposed in this paper. The new method expands basic 8-ary constellation into 3-D signal space systematically so that it produces lattice configurations. We also derive accurate closed-form symbol error probability (SEP) of cross-lattice constellations in additive white Gaussian noise (AWGN). It is verified that the theoretical SEPs are almost the same as simulation results. Minimum Euclidean distance (MED) of the higher-level 3-D constellations is increased at least 49% in comparison with quadrature amplitude modulation (QAM). When the number of symbols is 256, the 3-D constellation has around 105% longer MED than the 2-D QAM. Due to increase in MED, the 3-D constellations have much improved error performance compared to the QAM configurations. It is, therefore, considered that the higher-level 3-D constellations are appropriate for high-quality digital communications.