Multi-dimensional Constellation refers to a set of points in a multi-dimensional space that represents the symbols used in a communication system. Each point in the constellation corresponds to a specific symbol, and the arrangement of these points in the multi-dimensional space affects the efficiency and robustness of the communication system. In digital communications, the choice of a multi-dimensional constellation has implications for factors such as data rate, error performance, and bandwidth efficiency.


Constellation Design with Geometric and Probabilistic Shaping

A systematic study, including theory, simulation and experiments, is carried out to review the generalized pairwise optimization algorithm for designing optimized constellation. In order to verify its effectiveness, the algorithm is applied in three testing cases: 2-dimensional 8 quadrature amplitude modulation (QAM), 4-dimensional set-partitioning QAM, and probabilistic-shaped (PS) 32QAM. The results suggest that geometric shaping can work together with PS to further bridge the gap toward the Shannon limit.