Generalized 3-D Constellation Design for Spatial Modulation

Spatial modulation (SM) conveys information bits by utilizing both the antenna index and complex symbols to form a 3-D constellation. Similar to 2-D modulation, the structure of 3-D constellation could greatly affect the transmission reliability. In this paper, a generalized 3-D constellation design is proposed to optimize the constellation diagram used for each antenna, i.e., to optimize the complex symbols and their total number for each antenna and finally to enhance the transmission reliability. The optimal design method with exhaustive search algorithm may cause prohibitive computational complexity, especially when the cardinality of 3-D constellation is large. To overcome this issue, a recursive design algorithm is proposed with a computational complexity increasing polynomially with the cardinality of 3-D constellation. Extensions of the proposed methods to the SM constellation design for massive multiple-input multiple-output transmission, generalized spatial modulation (GSM) constellation design, and the SM constellation design with transmit antenna correlation are also discussed. Simulations are done to validate those theoretical analysis, and results show that the proposed 3-D constellation design is a generalized design scheme and can be adopted in any SM/GSM systems without constraints on the number of transceiver antennas. It is also shown that the proposed approach offers better symbol-error-rate performance than other solutions.