The homogeneous poisson point process (PPP) is widely used to model temporal, spatial or both topologies of base stations (BSs) and mobile terminals (MTs). However, negative spatial correlation in BSs, due to strategical deployments, and positive spatial correlations in MTs, due to homophilic relations, cannot be captured by homogeneous spatial PPP (SPPP). In this paper, we assume doubly stochastic poisson process, a generalization of homogeneous PPP, with intensity measure as another stochastic process. To this end, we assume Permanental Cox Process (PCP) to capture positive spatial correlation in MTs. We consider product density to derive closed-form approximation (CFA) of spatial summary statistics. We propose Euler Characteristic (EC) based novel approach to approximate intractable random intensity measure and subsequently derive nearest neighbor distribution function. We further propose the threshold and spatial extent of excursion set of chi-square random field as interference control parameters to select different cluster sizes for device-to-device (D2D) communication. The spatial extent of clusters is controlled by nearest neighbor distribution function which is incorporated into Laplace functional of SPPP to analyze the effect of D2D interfering clusters on average coverage probability of cellular user. The CFA and empirical results are in good agreement and its comparison with SPPP clearly shows spatial correlation between D2D nodes.

11 pages, 14 figures