On random sampling with nodes attraction: The case of Gauss-Poisson process

The deployment of sensing nodes is crucial for applications relying on the reconstruction of spatial fields. Theoretical analysis usually assumes that nodes are distributed according to a homogeneous Poisson point process (PPP), in which nodes positions are stochastically independent. However, realistic scenarios for crowd sourcing and Internet of Things call for clustered layouts of sensing nodes, for which homogeneous PPP is not appropriate. This paper analyzes sampling and reconstruction of finite-energy signals in Rd, with samples gathered in space according to a Gauss-Poisson point process (G-PPP), which has been recently proposed to model node spatial distribution with attraction (as in clustering). In particular, it is shown that attraction between nodes modeled by G-PPP reduces the reconstruction accuracy with respect the case of homogeneous PPP with the same intensity. This represents the opposite case of the repulsion effect, which was investigated in a previous work relying on Ginibre point process sampling.