Abstract
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.
| Original language | English |
|---|---|
| Article number | 8396275 |
| Pages (from-to) | 8536-8548 |
| Number of pages | 13 |
| Journal | IEEE Transactions on Vehicular Technology |
| Volume | 67 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 2018 |
Funding
The statements made herein are solely the responsibility of the authors. We would like to acknowledge the support of the University of Surrey 5GIC (http://www.surrey.ac.uk/5gic) members for this work. Manuscript received May 6, 2017; revised October 19, 2017, January 10, 2018, February 22, 2018, and May 13, 2018; accepted June 20, 2018. Date of publication June 26, 2018; date of current version September 17, 2018. This research was supported in part by EPSRC Global Challenges Research Fund— the DARE project—EP/P028764/1. The review of this paper was coordinated by Prof. J.-M. Chung. (Corresponding author: Hafiz Attaul Mustafa.) H. A. Mustafa and R. Tafazolli are with the Institute for Communication Systems, University of Surrey, Guildford GU2 7XH, U.K. (e-mail:, [email protected]; [email protected]).
Keywords
- D2d communication
- Euler Characteristic
- Intracell interference
- Nearest-neighbor distribution function
- Permanental Cox process
- Random field
- Spatial correlation