Constellation choosing based on multi-dimensional sphere packing technique

• A novel constellation points selection method based on threshold theory.
• The method can increase minimum Euclidean distance, and decrease the BER.
• We also compared random and distant points selection methods to threshold points selection method.

In this paper we address the sphere packing lattice points selection problem being used as constellation points in high-dimensional modulation. We propose a new type of points selection method based on threshold theory. Theoretically, this method improves the transmission performance of high-dimensional signal modulation systems. We find that the BER of a 4D modulation signal using the threshold value points selection method reduces. We also compared random and distant points selection methods in a BER of 10−3 and obtained a reduced SNR of about 2 db. At a 10−3 BER, a 8D modulation signal with points selected using the threshold selection methods obtained a reduced SNR of about 3 db. At a 10−3 BER, a 16D modulation signal with points selected using the threshold selection methods obtained a reduced SNR of about 3.5 db.