Design of APSK Constellations Approaching the Communication-Sensing Pareto Boundary for ISAC

2026-05-24

AI Summary

This work addresses the fundamental trade-off between communication and sensing performance in integrated sensing and communication (ISAC) systems by proposing a semi-analytical amplitude phase-shift keying (APSK) signal design framework. Leveraging i.i.d. uniformly distributed discrete inputs, the approach links the communication capacity gap to the minimum Euclidean distance and quantifies sensing performance via symbol energy variance. A multi-ring parametric constellation family enables flexible control over the communication–sensing trade-off. Theoretical analysis yields explicit scaling laws for key design parameters, demonstrating that the proposed scheme maintains a constant capacity gap across all signal-to-noise ratios and, for the first time under discrete input constraints, asymptotically approaches the Pareto boundary achievable with continuous inputs. Simulations confirm that the designed APSK constellations achieve near-optimal joint performance, closely approaching theoretical limits.

Abstract

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.

Problem

• ISAC
• APSK
• Pareto boundary
• communication-sensing tradeoff
• constellation design

Innovation

• APSK constellation
• Integrated Sensing and Communication (ISAC)
• Pareto boundary
• capacity gap
• symbol-energy variance