Four-Dimension Cross Constellations with Gray Mapping

Recently a four-dimension (4D) cross constellation has been proposed, where a 4D-vector is drawn from two $(3\times 4^m)$-ary QAM constellations, in an effort to reduce the peak-to-average-power ratio (PAPR). We construct a bits-to-signal mapping and prove that it is a Gray mapping. Simulation results show that the proposed modulation scheme is effective in reducing the PAPR while providing better error performance than existing 4D modulation schemes.