On the Design of Super Constellations

In the evolving landscape of sixth-generation (6G) wireless networks that require ultra-high data rates, this study introduces the concept of super-constellation communications. We also introduce super amplitude phase shift keying (SAPSK), an innovative modulation technique designed to achieve these ultra-high data rate requirements. SAPSK is complemented by the generalized polar distance detector (GPD-D), which approximates the performance of Gaussian phase detector (GAP-D), which achieves equivalent performance to the maximum likelihood detector in channels with Gaussian phase noise (GPN). By utilizing the decision regions formulated by GPD-D, a tight closed-form approximation for the symbol error probability (SEP) of SAPSK constellations is derived, while a detection algorithm with $\mathcal {O}(1)$ time complexity is developed to ensure fast and efficient SAPSK symbol detection. Finally, the theoretical performance of SAPSK and the efficiency of the proposed $\mathcal {O}(1)$ algorithm are validated by numerical simulations, highlighting both its superiority in terms of SEP compared to various constellations and its practical advantages in terms of fast and accurate symbol detection.