  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.
