Beyond the Poisson Point Process: Advanced Stochastic Geometry for Robust Modeling of Next-Generation ISAC Systems

Abstract

This study proposes and evaluates an Integrated Sensing and Communication (ISAC) framework that leverages a Multi-Hop Cluster-based Protocol (MHCP) for node deployment and Power Control (PC) for user clustering in a 1000m x 1000m urban vehicular simulation at 28 GHz mmWave. Employing stochastic geometry, ray-tracing channels, and MATLAB modeling, the framework supports 67 clusters (1268 users, density 0.0013/m²), 56 targets, and 92% sensing coverage, achieving 96.2% ranging accuracy (RMSE=0.8m) and 89% clustering precision while sustaining 2.1 Gbps communication rates. The findings from visualizations reveal heterogeneous topologies with central hotspots (42% UEs) and non-uniform target distributions (62% on horizontals, R²=0.91 LRP fit). Coverage metrics yield SINR means of 9.4 dB (comm) and 4.2 dB (sense), with 85–94% detection amid 3.2% multipath false positives. Pareto analyses expand joint utility 28% at λ=0.04, optimal r=0.6 (u=0.91); 3D surfaces peak at λ=0.02 (u=0.18, R²=0.94). Path loss sensitivity degrades P_sens 55% at α=4.5, mitigated 20% by MHCP. Advanced repulsion models curb PPP overestimation 25–40%, sustaining 0.82-0.84 P_comm (gaps -0.31 to -0.39, p=0.01). Optimizations tailor λ=0.001, r=0.5 for balanced ISAC (u=0.35), robust to high interference (9% drop), with ROI=1.8x. These affirm scalable dual-functionality with 5-18% overhead, aligning with 3GPP Rel-18 for 6G vehicular applications like traffic monitoring and AR offloading. Recommendations include RIS integration, ML-dynamic r, HAPS trials, and repulsion planning to enhance NLOS recovery (25%), adaptability (15%), and realism. This advances perceptive, efficient networks.