Optimal Amplitude Design for MN-Ary Pulse Position Amplitude Modulation

The MN-ary pulse position amplitude modulation (PPAM) signal is constructed by combining M-ary pulse amplitude modulation and N-ary pulse position modulation. The PPAM scheme provides improved reciprocity in system performance and computational complexity. In this paper, we investigate the Euclidean distance in a set of MN-ary PPAM signals. And moreover, we derive the optimal amplitudes to maximize the minimum Euclidean distance for PPAM signals. Finally, simulation results are conducted to show the performance improvement from the proposed amplitude design.