On the Fundamentals of Stochastic Spatial Modeling and Analysis of Wireless Networks and its Impact to Channel Losses

With the rapid evolution of wireless networking, it becomes vital to ensure transmission reliability, enhanced connectivity, and efficient resource utilization. One possible pathway for gaining insight into these critical requirements would be to explore the spatial geometry of the network. However, tractably characterizing the actual position of nodes for large wireless networks (LWNs) is technically unfeasible. Thus, stochastical spatial modeling is commonly considered for emulating the random pattern of mobile users. As a result, the concept of random geometry is gaining attention in the field of cellular systems in order to analytically extract hidden features and properties useful for assessing the performance of networks. Meanwhile, the large-scale fading between interacting nodes is the most fundamental element in radio communications, responsible for weakening the propagation, and thus worsening the service quality. Given the importance of channel losses in general, and the inevitability of random networks in real-life situations, it was then natural to merge these two paradigms together in order to obtain an improved stochastical model for the large-scale fading. Therefore, in exact closed-form notation, we generically derived the large-scale fading distributions between a reference base-station and an arbitrary node for uni-cellular (UCN), multi-cellular (MCN), and Gaussian random network models. In fact, we for the first time provided explicit formulations that considered at once: the lattice profile, the users’ random geometry, the spatial intensity, the effect of the far-field phenomenon, the path-loss behavior, and the stochastic impact of channel scatters. Overall, the results can be useful for analyzing and designing LWNs through the evaluation of performance indicators. Moreover, we conceptualized a straightforward and flexible approach for random spatial inhomogeneity by proposing the area-specific deployment (ASD) principle, which takes into account the clustering tendency of users. In fact, the ASD method has the advantage of achieving a more realistic deployment based on limited planning inputs, while still preserving the stochastic character of users’ position. We then applied this inhomogeneous technique to different circumstances, and thus developed three spatial-level network simulator algorithms for: controlled/uncontrolled UCN, and MCN deployments