System-level performance in massive ISAC networks

We propose a dynamic stochastic geometry framework to model and evaluate large-scale integrated sensing and communication (ISAC) networks. Base stations are distributed according to a homogeneous Poisson point process, while user equipments and sensing objects undergo localised random motion around their serving base station. Full spectrum reuse with a common waveform generates mutual interference that couples the two functionalities. Communication performance is characterised through downlink queues whose service rates are governed by the signal-to-interference-plus-noise ratio (SINR) via the Shannon capacity. Sensing performance is captured by a Kalman filter (KF) whose measurement noise covariance depends on the sensing SINR, yielding a non-classical state-dependent filtering problem. We define system-level performance metrics under the Palm distribution of the base station process and prove the consistency of their empirical estimators. We then prove that, for a typical base station, communication and sensing metrics are associated, so that operating regimes favourable to one functionality tend to benefit the other. The proof combines the monotonicity of the queue and filter recursions in the configuration of interferers with the Harris--FKG inequality for Poisson functionals. We also show that the excess association ratio of the two interference levels decays as the inverse of the network density. Simulations based on a ray-tracing channel model corroborate the analysis.