Inhomogeneous Double Thinning—Modeling and Analysis of Cellular Networks by Using Inhomogeneous Poisson Point Processes

In this paper, we introduce a new methodology for modeling and analyzing downlink cellular networks, where the base stations (BSs) constitute a motion-invariant point process (PP) that exhibits some degree of interactions among the points, i.e., spatial repulsion or spatial clustering. The proposed approach is based on the theory of inhomogeneous Poisson PPs (I-PPPs) and is referred to as inhomogeneous double thinning (IDT) approach. In a PP, the distribution of the distance from a randomly distributed (typical) user to its nearest BS depends on the degree of spatial repulsion or clustering exhibited by the PP. In addition, the average number of interfering BSs that lies within a given distance from the typical user is a function of the repulsion and clustering characteristics of the PP. The proposed approach consists of approximating the original motion-invariant PP with an equivalent PP that is made of the superposition of two conditionally independent I-PPPs. The inhomogeneities of both PPs are created from the point of view of the typical user (“user-centric”): the first one is based on the distribution of the user’s distance to its nearest BS and the second one is based on the distance-dependent average number of interfering BSs around the user. The inhomogeneities are mathematically modeled through two distance-dependent thinning functions and a tractable expression of the coverage probability is obtained. Sufficient conditions on the parameters of the thinning functions that guarantee better or worse coverage compared with the baseline homogeneous PPP model are identified. The accuracy of the IDT approach is substantiated with the aid of empirical data for the spatial distribution of the BSs

Approximations of functionals of some modulated-Poisson Voronoi tessellations with applications to modeling of communication networks

We consider the Voronoi tessellation of Euclidian plane that is generated by an inhomogeneous Poisson point process whose intensity takes different constant values on sets of some finite partition of the plane. We show that mean functionals of a cell with the nucleus located in a given set of the partition can be approximated by the mean functionals of the typical cell of the homogeneous Poisson Voronoi tessellation with intensity appropriate to this partitioning set. We give bounds for the approximation errors, which depend on the distance of the nucleus to the boundary of the element of the partition it belongs to. In the case of a stationary random partition, we show that mean functionals of the typical cell of the respective double-stochastic Poisson-Voronoi tessellation admit an approximate decomposition formula. The true value is approximated by a mixture of respective mean functionals for homogeneous models, while the explicit upper bound for the remaining term, which depends on the covariance functions of the random partitioning elements, can be computed numerically for a large class of practical examples. This paper complements the previous studies, where the distribution of the typical cell is approximated. One of the motivations for the study in question is modeling of modern communication networks, where application of the Poisson Voronoi tessellation has already proven to give some interesting results and where the assumption of the homogeneity is often non-adequate

Fine-grained performance analysis of massive MTC networks with scheduling and data aggregation

Abstract. The Internet of Things (IoT) represents a substantial shift within wireless communication and constitutes a relevant topic of social, economic, and overall technical impact. It refers to resource-constrained devices communicating without or with low human intervention. However, communication among machines imposes several challenges compared to traditional human type communication (HTC). Moreover, as the number of devices increases exponentially, different network management techniques and technologies are needed. Data aggregation is an efficient approach to handle the congestion introduced by a massive number of machine type devices (MTDs). The aggregators not only collect data but also implement scheduling mechanisms to cope with scarce network resources. This thesis provides an overview of the most common IoT applications and the network technologies to support them. We describe the most important challenges in machine type communication (MTC). We use a stochastic geometry (SG) tool known as the meta distribution (MD) of the signal-to-interference ratio (SIR), which is the distribution of the conditional SIR distribution given the wireless nodes’ locations, to provide a fine-grained description of the per-link reliability. Specifically, we analyze the performance of two scheduling methods for data aggregation of MTC: random resource scheduling (RRS) and channel-aware resource scheduling (CRS). The results show the fraction of users in the network that achieves a target reliability, which is an important aspect to consider when designing wireless systems with stringent service requirements. Finally, the impact on the fraction of MTDs that communicate with a target reliability when increasing the aggregators density is investigated

Modeling of Locally Scaled Spatial Point Processes, and Applications in Image Analysis

Spatial point processes provide a statistical framework for modeling random arrangements of objects, which is of relevance in a variety of scientific disciplines, including ecology, spatial epidemiology and material science. Describing systematic spatial variations within this framework and developing methods for estimating parameters from empirical data constitute an active area of research. Image analysis, in particular, provides a range of scenarios to which point process models are applicable. Typical examples are images of trees in remote sensing, cells in biology, or composite structures in material science. Due to its real-world orientation and versatility, the class of the recently developed locally scaled point processes appears particularly suitable for the modeling of spatial object patterns. An unknown normalizing constant in the likelihood, however, makes inference complicated and requires elaborate techniques. This work presents an efficient Bayesian inference concept for locally scaled point processes. The suggested optimization procedure is applied to images of cross-sections through the stems of maize plants, where the goal is to accurately describe and classify different genotypes based on the spatial arrangement of their vascular bundles. A further spatial point process framework is specifically provided for the estimation of shape from texture. Texture learning and the estimation of surface orientation are two important tasks in pattern analysis and computer vision. Given the image of a scene in three-dimensional space, a frequent goal is to derive global geometrical knowledge, e.g. information on camera positioning and angle, from the local textural characteristics in the image. The statistical framework proposed comprises locally scaled point process strategies as well as the draft of a Bayesian marked point process model for inferring shape from texture

Optimal Mode Selection for Full-Duplex Enabled D2D Cognitive Networks

© 2019 IEEE. Full-Duplex (FD) and Device-to-Device (D2D) communications have been recognized as one of the successful solutions of spectrum scarcity in 5G networks. Significant advancements in self-interference-to-power-ratio (SIPR) reduction have paved the way for FD use to double the data rates and reduce the latency. This advantage can now be exploited to optimize dynamic spectrum sharing among different radio access technologies in cognitive networks. However, protecting the primary user communication has been a challenging problem in such coexistence. In this paper, we provide an abstract level analysis of protecting primary users reception based on secondary users FD enabled communication. We also propose optimal mode selection (Half-duplex, Full-duplex, or silent) for secondary D2D users depending on its impact on primary users. Our analysis presents the significant advantage of D2D mode selection in terms of efficient spectrum utilization while protecting the primary user transmission, thus, leading the way for FD enabled D2D setup. Depending on the location and transmit power of D2D users, the induced aggregate interference should not violate the interference threshold of primary users. For this, we characterize the interference from D2D links and derive the probability for successful D2D users for half-duplex and full-duplex modes. The analyses are further supported by theoretical and extensive simulation results

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