We propose a semi-analytical amplitude phase shift keying (APSK) signaling framework for integrated sensing and communication (ISAC), focusing on i.i.d. uniform discrete input distributions for practicality and analytical tractability. First, we establish APSK design criteria in which communication performance is measured by the gap to capacity and linked to the minimum Euclidean distance, while sensing performance is characterized by the symbol-energy variance. Based on these criteria, we propose a family of APSK constellations whose key parameters follow explicit scaling laws. Then we prove that this design achieves a constant gap to capacity independent of the signal-to-noise ratio. Building upon this foundation, we further construct a parametric APSK family that bridges the communication-optimal and sensing-optimal designs, with the communication and sensing (C&S) tradeoff controlled by the number of rings and energy allocation among rings. Simulation results show that the proposed APSK achieves C&S performance very close to the Pareto boundary achieved with time-independent, circularly symmetric, and otherwise unconstrained continuous input distributions.

翻译：本文提出一种面向通感一体化（ISAC）的半解析振幅相移键控（APSK）信号框架，重点采用独立同分布均匀离散输入分布以保证实用性与解析可解性。首先，我们建立了APSK设计准则：通信性能以容量差距衡量，并关联至最小欧氏距离；而感知性能则以符号能量方差表征。基于这些准则，我们提出了一族关键参数遵循显式标度律的APSK星座。随后证明该设计能实现与信噪比无关的恒定容量差距。在此基础之上，我们进一步构建了一个参数化APSK星座族，用于桥接通信最优与感知最优设计，其通信与感知（C&S）权衡通过环数与环间能量分配控制。仿真结果表明，所提APSK方案能实现极接近帕累托边界的C&S性能，该边界由时间独立、圆对称且无其他约束的连续输入分布所决定。