Hesham ElSawy

Stochastic Geometry for Modeling, Analysis, and Design of Multi-Tier and Cognitive Cellular Wireless Networks: A Survey

For more than three decades, stochastic geometry has been used to model large-scale ad hoc wireless networks, and it has succeeded to develop tractable models to characterize and better understand the performance of these networks. Recently, stochastic geometry models have been shown to provide tractable yet accurate performance bounds for multi-tier and cognitive cellular wireless networks. Given the need for interference characterization in multi-tier cellular networks, stochastic geometry models provide high potential to simplify their modeling and provide insights into their design. Hence, a new research area dealing with the modeling and analysis of multi-tier and cognitive cellular wireless networks is increasingly attracting the attention of the research community. In this article, we present a comprehensive survey on the literature related to stochastic geometry models for single-tier as well as multi-tier and cognitive cellular wireless networks. A taxonomy based on the target network model, the point process used, and the performance evaluation technique is also presented. To conclude, we discuss the open research challenges and future research directions.

Analytical Modeling of Mode Selection and Power Control for Underlay D2D Communication in Cellular Networks

Device-to-device (D2D) communication enables the user equipments (UEs) located in close proximity to bypass the cellular base stations (BSs) and directly connect to each other, and thereby, offload traffic from the cellular infrastructure. D2D communication can improve spatial frequency reuse and energy efficiency in cellular networks. This paper presents a comprehensive and tractable analytical framework for D2D-enabled uplink cellular networks with a flexible mode selection scheme along with truncated channel inversion power control. The developed framework is used to analyze and understand how the underlaying D2D communication affects the cellular network performance. Through comprehensive numerical analysis, we investigate the expected performance gains and provide guidelines for selecting the network parameters.

On Stochastic Geometry Modeling of Cellular Uplink Transmission With Truncated Channel Inversion Power Control

Using stochastic geometry, we develop a tractable uplink modeling paradigm for outage probability and spectral efficiency in both single and multi-tier cellular wireless networks. The analysis accounts for per user equipment (UE) power control as well as the maximum power limitations for UEs. More specifically, for interference mitigation and robust uplink communication, each UE is required to control its transmit power such that the average received signal power at its serving base station (BS) is equal to a certain threshold ρ_o. Due to the limited transmit power, the UEs employ a truncated channel inversion power control policy with a cutoff threshold of ρ_o. We show that there exists a transfer point in the uplink system performance that depends on the following tuple: BS intensity λ, maximum transmit power of UEs P_u}, and ρ_o. That is, when P_u is a tight operational constraint with respect to (w.r.t.) λ and ρ_o, the uplink outage probability and spectral efficiency highly depend on the values of λ and ρ_o. In this case, there exists an optimal cutoff threshold ρ_o*, which depends on the system parameters, that minimizes the outage probability. On the other hand, when P_u is not a binding operational constraint w.r.t. λ and ρ_o, the uplink outage probability and spectral efficiency become independent of λ and ρ_o. We obtain approximate yet accurate simple expressions for outage probability and spectral efficiency, which reduce to closed forms in some special cases.

Two-Tier HetNets with Cognitive Femtocells: Downlink Performance Modeling and Analysis in a Multichannel Environment

In a two-tier heterogeneous network (HetNet) where femto access points (FAPs) with lower transmission power coexist with macro base stations (BSs) with higher transmission power, the FAPs may suffer significant performance degradation due to inter-tier interference. Introducing cognition into the FAPs through the spectrum sensing (or carrier sensing) capability helps them avoiding severe interference from the macro BSs and enhance their performance. In this paper, we use stochastic geometry to model and analyze performance of HetNets composed of macro BSs and cognitive FAPs in a multichannel environment. The proposed model explicitly accounts for the spatial distribution of the macro BSs, FAPs, and users in a Rayleigh fading environment. We quantify the performance gain in outage probability obtained by introducing cognition into the femto-tier, provide design guidelines, and show the existence of an optimal spectrum sensing threshold for the cognitive FAPs, which depends on the HetNet parameters. We also show that looking into the overall performance of the HetNets is quite misleading in the scenarios where the majority of users are served by the macro BSs. Therefore, the performance of femto-tier needs to be explicitly accounted for and optimized.

Modeling and Analysis of Cellular Networks Using Stochastic Geometry: A Tutorial

This paper presents a tutorial on stochastic geometry (SG)-based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. This paper starts by modeling and analyzing the baseband interference in a baseline single-tier downlink cellular network with single antenna base stations and universal frequency reuse. Then, it characterizes signal-to-interference-plus-noise-ratio and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and transmission rate analysis is presented. Although the main focus of this paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. This paper then extends the unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. To this end, this paper highlights the state-of-the-art research and points out future research directions.

A Modified Hard Core Point Process for Analysis of Random CSMA Wireless Networks in General Fading Environments

For spectrum sharing and avoidance of mutual interference, carrier-sense multiple access (CSMA) protocols are very popular in distributed wireless networks. CSMA protocols aim to maximize the spatial frequency reuse while limiting the mutual interference and outage. The hard core point process (HCPP) is a very popular tool for modeling and analysis of random CSMA networks. However, the traditional HCPP suffers from the node intensity (and hence the interference) underestimation flaw. Therefore, we propose a modified hard core point process to mitigate this flaw. The proposed modified HCPP is generalized for any fading environment. To this end, we derive a closed-form expression for the intensity of simultaneously active transmitters in a random wireless CSMA network. Then, we derive a closed-form expression for approximating the outage probability experienced by a generic receiver in the network, and subsequently, use it to obtain the transmission capacity of the network. Finally, we show the existence of an optimal carrier-sensing threshold for the CSMA protocol that maximizes the transmission capacity of the network. Simulation results validate the analysis and also provide interesting insights into the design of practical CSMA networks.

Characterizing random CSMA wireless networks: A stochastic geometry approach

We charachterize the random CSMA wireless networks by statistically quantifing the intensity of simultaneously active nodes and the aggregate interference experienced by a generic node in the network. First, starting from a Poisson point process to model the spatial distribution of the network nodes, we propose a modified hard core point process (MHCPP) to model the spatial distribution of the simultaneously active users in a random CSMA network. Our motivation to propose the MHCPP is to mitigate the node intensity underestimation problem of the traditional hard core point process (HCPP). Then, we use the shot noise theory to statistically quantify the interference experienced by a generic node in the network. Closed-form expressions for the intensity of the simultaneously active nodes and the Laplace transform of the probability density function (and hence the moment generating function and the characteristic function), mean, and variance of the approximate aggregate interference are obtained. The accuracy of our model is validated by simulations.

Traffic offloading techniques in two-tier femtocell networks

Due to the scarcity of the wireless spectrum along with the ever increasing number of cellular wireless users and the associated drastic increase in the data traffic demand, femtocells are envisioned to provide fast, flexible, cost-efficient, and customer driven solutions to offload users from the congested macro access network and enhance the overall system performance. To control offloading and to achieve the required balance of users and traffic served by each network tier, we quantify offloading and discuss different techniques that can be used to offload users from the macro access network to the femto access network, namely, offloading via power control, offloading via femtocell deployment and offloading via biasing. In this paper, we quantify offloading when users connect to the network entity that provides the strongest instantaneous signal power in a Nakagami-m fading environment. To this end, we discuss the merits and drawbacks of each of the offloading techniques.

In-Band

In-band full-duplex (FD) communications have been optimistically promoted to improve the spectrum utilization and efficiency. However, the penetration of FD communications to the cellular networks domain is challenging due to the imposed uplink/downlink interference. This paper presents a tractable framework, based on stochastic geometry, to study FD communications in cellular networks. Particularly, we assess the FD communications effect on the network performance and quantify the associated gains. This paper proves the vulnerability of the uplink to the downlink interference and shows that FD rate gains harvested in the downlink (up to 97%) come at the expense of a significant degradation in the uplink rate (up to 94%). Therefore, we propose a novel fine-grained duplexing scheme, denoted as the α-duplex scheme, which allows a partial overlap between the uplink and the downlink frequency bands. We derive the required conditions to harvest rate gains from the α-duplex scheme and show its superiority to both the FD and half-duplex (HD) schemes. In particular, we show that the α-duplex scheme provides a simultaneous improvement of 28% for the downlink rate and 56% for the uplink rate. Finally, we show that the amount of the overlap can be optimized based on the network design objective.

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Carrier-sense multiple access (CSMA) protocols coordinate the spectrum access to maximize the spatial frequency reuse and minimize the mutual interference in distributed wireless networks. Since the CSMA protocol correlates the positions of the simultaneously active transmitters, the analytically tractable Poisson point process (PPP) cannot be used to model the spatial distribution of the simultaneously active transmitters. Instead, the hard core point process (HCPP) is widely used to model the spatial distribution of the simultaneously active transmitters. However, the HCPP can be directly applied to CSMA random networks under deterministic channel gains only. In this paper, we integrate the fading and spatial distribution statistics in the analysis of the HCPP, and thus provide a unified framework to capture the intensity of simultaneously active transmitters in a random CSMA wireless network under general fading environments.