Spatiotemporal Tracking in Cooperative ISAC Networks: A Stochastic Geometry Framework

Abstract

We adopt a stochastic-geometry framework to study continuous target tracking in integrated sensing and communication (ISAC) networks, with base-station locations modelled as a Poisson point process. The single-BS analysis shows that the antenna energy-conservation identity forces the mean inter-BS coupling gain to unity, making densification an antenna-irreducible liability for monostatic sensing, while a first-passage-time analysis reveals a target-distance-dependent beamwidth trap. These findings rule out single-BS tracking under densification, motivating a multi-BS cooperative treatment. The static-cluster cooperative mean tracking lifetime is then shown to exhibit a sharp percolation phase transition, with the resulting sensing-capacity ceiling saturating above a critical macro density. Yet the static-cluster idealisation itself misrepresents modern network deployments, where the cooperating cluster is dynamically re-selected as the target drifts; we therefore lift this assumption with a dynamic clustering model that maps the $K$-nearest-neighbour handover onto a 2D Brownian motion with stochastic resetting, and obtain a Bessel-function closed form for the dynamic mean tracking lifetime that dissolves the phase transition under any positive handover rate. With a per-link reliability floor, the dynamic clustering framework preserves classical linear density scaling throughout the realistic 6G regime and delivers an order-of-magnitude capacity lift at small-cell densities. Monte-Carlo simulations corroborate all theoretical predictions.