Design of APSK Constellations Approaching the Communication-Sensing Pareto Boundary for ISAC
This work provides a practical discrete-input design for ISAC systems, bridging communication and sensing tradeoffs with near-optimal performance.
The paper proposes a semi-analytical APSK signaling framework for ISAC that achieves a constant gap to capacity and C&S performance close to the Pareto boundary of continuous inputs, with explicit scaling laws for constellation parameters.
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.