Gamma-Distributed Geometric Constellation for ISAC: Design and Analysis

2026-04-24

AI Summary

This work addresses the challenge of designing constellations for integrated sensing and communication (ISAC) systems that simultaneously optimize both sensing and communication performance. To this end, the authors propose a two-dimensional geometric constellation design framework based on Gamma-distributed amplitudes and uniformly distributed phases. The constellation is optimized jointly with respect to detection probability and mutual information using a particle swarm optimization algorithm, marking the first application of the Gamma distribution in ISAC constellation design. Theoretical analyses derive joint bounds on symbol error rate and the Cramér–Rao bound. The proposed method operates without requiring training data, outperforms existing neural network–based approaches in both sensing detection performance and communication mutual information, and achieves these gains with significantly fewer parameters while maintaining compatibility with existing communication architectures.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A novel Gamma-distributed geometric constellation design framework for integrated sensing and communication (ISAC) is proposed in this paper. In this framework, constellation points are modeled as samples drawn from a parameterized two-dimensional distribution, with a Gamma distribution for the amplitude and a uniform distribution for the phase. End-task performance metrics, namely, the probability of detection for sensing and mutual information for communication, are used as objective functions of the optimization problem, and the problem is solved via particle swarm optimization. We further derive analytical performance bounds for the proposed design, including the union bound on the symbol error rate for communication and the Cramer--Rao bound for sensing parameter estimation. The proposed method is compared with constellations obtained via end-to-end neural network design, demonstrating competitive performance while requiring significantly fewer parameters and no training data. Moreover, the proposed geometric constellation is more compatible with conventional system architectures than probabilistic or neural network-based designs.

Problem

• ISAC
• constellation design
• integrated sensing and communication
• Gamma distribution
• geometric constellation

Innovation

• Gamma-distributed constellation
• integrated sensing and communication (ISAC)
• geometric constellation design
• particle swarm optimization
• Cramér–Rao bound