“…For example, we have considered two 32-APSK constellation designs that are specified for the DVB-S2X standard [22]: one has three rings with 4, 12, and 16 points on each ring, and the other has four rings with 4, 8, 4, and 16 points on each ring. Our numerical investigation shows that the CD receiver is optimal (i.e., ρ * = 1) for the (4,12,16) design of 32-APSK, while the splitting receiver achieves a significant performance gain for the (4,8,4,16) design of 32-APSK and, interestingly, the gain is more profound at larger P or lower SER. Therefore, the performance analysis and characterization of the splitting receiver for practical modulation can only be done in a case-by-case basis.…”