Spatial and Social Paradigms for Interference and Coverage Analysis in Underlay D2D Network

The homogeneous Poisson point process (PPP) is widely used to model spatial distribution of base stations and mobile terminals. The same process can be used to model underlay device-to-device (D2D) network, however, neglecting homophilic relation for D2D pairing presents underestimated system insights. In this paper, we model both spatial and social distributions of interfering D2D nodes as proximity based independently marked homogeneous Poisson point process. The proximity considers physical distance between D2D nodes whereas social relationship is modeled as Zipf based marks. We apply these two paradigms to analyze the effect of interference on coverage probability of distance-proportional power-controlled cellular user. Effectively, we apply two type of functional mappings (physical distance, social marks) to Laplace functional of PPP. The resulting coverage probability has no closed-form expression, however for a subset of social marks, the mark summation converges to digamma and polygamma functions. This subset constitutes the upper and lower bounds on coverage probability. We present numerical evaluation of these bounds on coverage probability by varying number of different parameters. The results show that by imparting simple power control on cellular user, ultra-dense underlay D2D network can be realized without compromising the coverage probability of cellular user.Comment: 10 pages, 10 figure

Intracell interference characterization and cluster interference for D2D communication

The homogeneous spatial Poisson point process (SPPP) is widely used for spatial modeling of mobile terminals (MTs). This process is characterized by a homogeneous distribution, complete spatial independence, and constant intensity measure. However, it is intuitive to understand that the locations of MTs are neither homogeneous, due to inhomogeneous terrain, nor independent, due to homophilic relations. Moreover, the intensity is not constant due to mobility. Therefore, assuming an SPPP for spatial modeling is too simplistic, especially for modeling realistic emerging device-centric frameworks such as device-to-device (D2D) communication. In this paper, assuming inhomogeneity, positive spatial correlation, and random intensity measure, we propose a doubly stochastic Poisson process, a generalization of the homogeneous SPPP, to model D2D communication. To this end, we assume a permanental Cox process (PCP) and propose a novel Euler-Characteristic-based approach to approximate the nearest-neighbor distribution function. We also propose a threshold and spatial distances from an excursion set of a chi-square random field as interference control parameters for different cluster sizes. The spatial distance of the clusters is incorporated into a Laplace functional of a PCP to analyze the average coverage probability of a cellular user. A closed-form approximation of the spatial summary statistics is in good agreement with empirical results, and its comparison with an SPPP authenticates the correlation modeling of D2D nodes