On the Performance of the Multiple Active Antenna Spatial Modulation with 3-Dimensional Constellation

In spatial modulation (SM), a single signal symbol is transmitted from a given physical antenna, where both the signal symbol and the antenna index carry information. SM with multiple active antennas (MA-SM) transmits several signal symbols from a combination of antennas at each channel use, thereby increasing the spectral efficiency. MA-SM is proposed in combination with a new 3-dimensional constellation, where signal symbols transmitted from a given antenna combination are rotated before transmission. In this paper, we derived an upper-bound on the error probability of the MA-SM as a function of the rotation angles. The search for the optimal rotation angles is modeled as a multi-objective optimization problem. We concluded based on both analytical and simulation results that the 3-dimensional constellation with the optimal angles achieved negligible improvement. Therefore, we do not recommend using the 3-dimensional constellation with the MA-SM system.