Connectivity, Coverage and Placement in Wireless Sensor Networks

Wireless communication between sensors allows the formation of flexible sensor networks, which can be deployed rapidly over wide or inaccessible areas. However, the need to gather data from all sensors in the network imposes constraints on the distances between sensors. This survey describes the state of the art in techniques for determining the minimum density and optimal locations of relay nodes and ordinary sensors to ensure connectivity, subject to various degrees of uncertainty in the locations of the nodes

DISTRIBUTED FLOW OPTIMIZATION IN DENSE WIRELESS NETWORKS

Due to large number of variables, optimizing information flow in a dense wire- less network using discrete methods can be computationally prohibitive. Instead of treating the nodes as discrete entities, these networks can be modeled as continuum of nodes providing a medium for information transport. In this scenario multi-hop information routes transform into an information flow vector field that is defined over the geographical domain of the network. At each point of the network, the orientation of the vector field shows the direction of the flow of information, and its magnitude shows the density of information flow. Modeling the dense network in continuous domain enables us to study the large scale behavior of the network under existing routing policies; furthermore, it justifies incorporation of multivariate calculus techniques in order to find new routing policies that optimize a suitable cost function, which only depend on large scale properties of the network. Thus, finding an optimum routing method translates into finding an optimal information flow vector field that minimizes the cost function. In order to transform the optimal information flow vector field into a routing policy, connections between discrete space (small scale) and continuous space (large scale) variables should be made and the question that how the nodes should interact with each other in the microscopic scale in order that their large scale behavior become optimal should be answered. In the past works, a centralized method of calculating the optimal information flow over the entire geographical area that encompasses the network has been suggested; however, using a centralized method to optimize information flow in a dynamic network is undesirable. Furthermore, the value of information flow vector field is needed only at the locations of randomly scattered nodes in the network, thus calculation of the information flow vector field for the entire network region (as suggested in previous models) is an unnecessary overhead. This poses a gap between the continuous space and discrete space models of information flow in dense wireless networks. This gap is how to calculate and apply the optimum information flow derived in continuous domain to a network with finite number of nodes. As a first step to fill this gap, a specific quadratic cost function is considered. In previous works, it is proved that the the vector field that minimizes this cost function is irrotational, thus it is written as the gradient of a potential function. This potential function satisfies a Poisson Partial Differential Equation (PDE) which in conjunction with Neumann boundary condition has a unique solution up to a constant. In this thesis the PDE resulted by optimization in continuous domain is discretized at locations of the nodes. By assuming a random node distribution with uniform density, the symmetries present enable us to solve the PDE in a distributed fashion. This solution is based on Jacobi iterations and requires only neighboring nodes to share their local information with each other. The gradient of the resulting potential defines the routes that the traffic should be forwarded. Furthermore, based on a graph theory model, we generalize our distributed solution to a more general cost function, namely, the p-norm cost function. This model also enables us to enhance the convergence rate of the Jacobi iterations

A Survey of Anticipatory Mobile Networking: Context-Based Classification, Prediction Methodologies, and Optimization Techniques

A growing trend for information technology is to not just react to changes, but anticipate them as much as possible. This paradigm made modern solutions, such as recommendation systems, a ubiquitous presence in today's digital transactions. Anticipatory networking extends the idea to communication technologies by studying patterns and periodicity in human behavior and network dynamics to optimize network performance. This survey collects and analyzes recent papers leveraging context information to forecast the evolution of network conditions and, in turn, to improve network performance. In particular, we identify the main prediction and optimization tools adopted in this body of work and link them with objectives and constraints of the typical applications and scenarios. Finally, we consider open challenges and research directions to make anticipatory networking part of next generation networks

Characterization of the fundamental properties of wireless CSMA multi-hop networks

A wireless multi-hop network consists of a group of decentralized and self-organized wireless devices that collaborate to complete their tasks in a distributed way. Data packets are forwarded collaboratively hop-by-hop from source nodes to their respective destination nodes with other nodes acting as intermediate relays. Existing and future applications in wireless multi-hop networks will greatly benefit from better understanding of the fundamental properties of such networks. In this thesis we explore two fundamental properties of distributed wireless CSMA multi-hop networks, connectivity and capacity. A network is connected if and only if there is at least one (multi-hop) path between any pair of nodes. We investigate the critical transmission power for asymptotic connectivity in large wireless CSMA multi-hop networks under the SINR model. The critical transmission power is the minimum transmission power each node needs to transmit to guarantee that the resulting network is connected aas. Both upper bound and lower bound of the critical transmission power are obtained analytically. The two bounds are tight and differ by a constant factor only. Next we shift focus to the capacity property. First, we develop a distributed routing algorithm where each node makes routing decisions based on local information only. This is compatible with the distributed nature of large wireless CSMA multi-hop networks. Second, we show that by carefully choosing controllable parameters of the CSMA protocols, together with the routing algorithm, a distributed CSMA network can achieve the order-optimal throughput scaling law. Scaling laws are only up to order and most network design choices have a significant effect on the constants preceding the order while not affecting the scaling law. Therefore we further to analyze the pre-constant by giving an upper and a lower bound of throughput. The tightness of the bounds is validated using simulations

Characterization of the fundamental properties of wireless CSMA multi-hop networks

A wireless multi-hop network consists of a group of decentralized and self-organized wireless devices that collaborate to complete their tasks in a distributed way. Data packets are forwarded collaboratively hop-by-hop from source nodes to their respective destination nodes with other nodes acting as intermediate relays. Existing and future applications in wireless multi-hop networks will greatly benefit from better understanding of the fundamental properties of such networks. In this thesis we explore two fundamental properties of distributed wireless CSMA multi-hop networks, connectivity and capacity. A network is connected if and only if there is at least one (multi-hop) path between any pair of nodes. We investigate the critical transmission power for asymptotic connectivity in large wireless CSMA multi-hop networks under the SINR model. The critical transmission power is the minimum transmission power each node needs to transmit to guarantee that the resulting network is connected aas. Both upper bound and lower bound of the critical transmission power are obtained analytically. The two bounds are tight and differ by a constant factor only. Next we shift focus to the capacity property. First, we develop a distributed routing algorithm where each node makes routing decisions based on local information only. This is compatible with the distributed nature of large wireless CSMA multi-hop networks. Second, we show that by carefully choosing controllable parameters of the CSMA protocols, together with the routing algorithm, a distributed CSMA network can achieve the order-optimal throughput scaling law. Scaling laws are only up to order and most network design choices have a significant effect on the constants preceding the order while not affecting the scaling law. Therefore we further to analyze the pre-constant by giving an upper and a lower bound of throughput. The tightness of the bounds is validated using simulations

Performance Evaluation of Connectivity and Capacity of Dynamic Spectrum Access Networks

Recent measurements on radio spectrum usage have revealed the abundance of under- utilized bands of spectrum that belong to licensed users. This necessitated the paradigm shift from static to dynamic spectrum access (DSA) where secondary networks utilize unused spectrum holes in the licensed bands without causing interference to the licensed user. However, wide scale deployment of these networks have been hindered due to lack of knowledge of expected performance in realistic environments and lack of cost-effective solutions for implementing spectrum database systems. In this dissertation, we address some of the fundamental challenges on how to improve the performance of DSA networks in terms of connectivity and capacity. Apart from showing performance gains via simulation experiments, we designed, implemented, and deployed testbeds that achieve economics of scale. We start by introducing network connectivity models and show that the well-established disk model does not hold true for interference-limited networks. Thus, we characterize connectivity based on signal to interference and noise ratio (SINR) and show that not all the deployed secondary nodes necessarily contribute towards the network\u27s connectivity. We identify such nodes and show that even-though a node might be communication-visible it can still be connectivity-invisible. The invisibility of such nodes is modeled using the concept of Poisson thinning. The connectivity-visible nodes are combined with the coverage shrinkage to develop the concept of effective density which is used to characterize the con- nectivity. Further, we propose three techniques for connectivity maximization. We also show how traditional flooding techniques are not applicable under the SINR model and analyze the underlying causes for that. Moreover, we propose a modified version of probabilistic flooding that uses lower message overhead while accounting for the node outreach and in- terference. Next, we analyze the connectivity of multi-channel distributed networks and show how the invisibility that arises among the secondary nodes results in thinning which we characterize as channel abundance. We also capture the thinning that occurs due to the nodes\u27 interference. We study the effects of interference and channel abundance using Poisson thinning on the formation of a communication link between two nodes and also on the overall connectivity of the secondary network. As for the capacity, we derive the bounds on the maximum achievable capacity of a randomly deployed secondary network with finite number of nodes in the presence of primary users since finding the exact capacity involves solving an optimization problem that shows in-scalability both in time and search space dimensionality. We speed up the optimization by reducing the optimizer\u27s search space. Next, we characterize the QoS that secondary users can expect. We do so by using vector quantization to partition the QoS space into finite number of regions each of which is represented by one QoS index. We argue that any operating condition of the system can be mapped to one of the pre-computed QoS indices using a simple look-up in Olog (N) time thus avoiding any cumbersome computation for QoS evaluation. We implement the QoS space on an 8-bit microcontroller and show how the mathematically intensive operations can be computed in a shorter time. To demonstrate that there could be low cost solutions that scale, we present and implement an architecture that enables dynamic spectrum access for any type of network ranging from IoT to cellular. The three main components of this architecture are the RSSI sensing network, the DSA server, and the service engine. We use the concept of modular design in these components which allows transparency between them, scalability, and ease of maintenance and upgrade in a plug-n-play manner, without requiring any changes to the other components. Moreover, we provide a blueprint on how to use off-the-shelf commercially available software configurable RF chips to build low cost spectrum sensors. Using testbed experiments, we demonstrate the efficiency of the proposed architecture by comparing its performance to that of a legacy system. We show the benefits in terms of resilience to jamming, channel relinquishment on primary arrival, and best channel determination and allocation. We also show the performance gains in terms of frame error rater and spectral efficiency

Emerging Communications for Wireless Sensor Networks

Wireless sensor networks are deployed in a rapidly increasing number of arenas, with uses ranging from healthcare monitoring to industrial and environmental safety, as well as new ubiquitous computing devices that are becoming ever more pervasive in our interconnected society. This book presents a range of exciting developments in software communication technologies including some novel applications, such as in high altitude systems, ground heat exchangers and body sensor networks. Authors from leading institutions on four continents present their latest findings in the spirit of exchanging information and stimulating discussion in the WSN community worldwide

NFV orchestration in edge and fog scenarios

Mención Internacional en el título de doctorLas infraestructuras de red actuales soportan una variedad diversa de servicios como video bajo demanda, video conferencias, redes sociales, sistemas de educación, o servicios de almacenamiento de fotografías. Gran parte de la población mundial ha comenzado a utilizar estos servicios, y los utilizan diariamente. Proveedores de Cloud y operadores de infraestructuras de red albergan el tráfico de red generado por estos servicios, y sus tareas de gestión no solo implican realizar el enrutamiento del tráfico, sino también el procesado del tráfico de servicios de red. Tradicionalmente, el procesado del tráfico ha sido realizado mediante aplicaciones/ programas desplegados en servidores que estaban dedicados en exclusiva a tareas concretas como la inspección de paquetes. Sin embargo, en los últimos anos los servicios de red se han virtualizado y esto ha dado lugar al paradigma de virtualización de funciones de red (Network Function Virtualization (NFV) siguiendo las siglas en ingles), en el que las funciones de red de un servicio se ejecutan en contenedores o máquinas virtuales desacopladas de la infraestructura hardware. Como resultado, el procesado de tráfico se ha ido haciendo más flexible gracias al laxo acople del software y hardware, y a la posibilidad de compartir funciones de red típicas, como firewalls, entre los distintos servicios de red. NFV facilita la automatización de operaciones de red, ya que tareas como el escalado, o la migración son típicamente llevadas a cabo mediante un conjunto de comandos previamente definidos por la tecnología de virtualización pertinente, bien mediante contenedores o máquinas virtuales. De todos modos, sigue siendo necesario decidir el en rutamiento y procesado del tráfico de cada servicio de red. En otras palabras, que servidores tienen que encargarse del procesado del tráfico, y que enlaces de la red tienen que utilizarse para que las peticiones de los usuarios lleguen a los servidores finales, es decir, el conocido como embedding problem. Bajo el paraguas del paradigma NFV, a este problema se le conoce en inglés como Virtual Network Embedding (VNE), y esta tesis utiliza el termino “NFV orchestration algorithm” para referirse a los algoritmos que resuelven este problema. El problema del VNE es NP-hard, lo cual significa que que es imposible encontrar una solución optima en un tiempo polinómico, independientemente del tamaño de la red. Como consecuencia, la comunidad investigadora y de telecomunicaciones utilizan heurísticos que encuentran soluciones de manera más rápida que productos para la resolución de problemas de optimización. Tradicionalmente, los “NFV orchestration algorithms” han intentado minimizar los costes de despliegue derivados de las soluciones asociadas. Por ejemplo, estos algoritmos intentan no consumir el ancho de banda de la red, y usar rutas cortas para no utilizar tantos recursos. Además, una tendencia reciente ha llevado a la comunidad investigadora a utilizar algoritmos que minimizan el consumo energético de los servicios desplegados, bien mediante la elección de dispositivos con un consumo energético más eficiente, o mediante el apagado de dispositivos de red en desuso. Típicamente, las restricciones de los problemas de VNE se han resumido en un conjunto de restricciones asociadas al uso de recursos y consumo energético, y las soluciones se diferenciaban por la función objetivo utilizada. Pero eso era antes de la 5a generación de redes móviles (5G) se considerase en el problema de VNE. Con la aparición del 5G, nuevos servicios de red y casos de uso entraron en escena. Los estándares hablaban de comunicaciones ultra rápidas y fiables (Ultra-Reliable and Low Latency Communications (URLLC) usando las siglas en inglés) con latencias por debajo de unos pocos milisegundos y fiabilidades del 99.999%, una banda ancha mejorada (enhanced Mobile Broadband (eMBB) usando las siglas en inglés) con notorios incrementos en el flujo de datos, e incluso la consideración de comunicaciones masivas entre maquinas (Massive Machine-Type Communications (mMTC) usando las siglas en inglés) entre dispositivos IoT. Es más, paradigmas como edge y fog computing se incorporaron a la tecnología 5G, e introducían la idea de tener dispositivos de computo más cercanos al usuario final. Como resultado, el problema del VNE tenía que incorporar los nuevos requisitos como restricciones a tener en cuenta, y toda solución debía satisfacer bajas latencias, alta fiabilidad, y mayores tasas de transmisión. Esta tesis estudia el problema des VNE, y propone algunos heurísticos que lidian con las restricciones asociadas a servicios 5G en escenarios edge y fog, es decir, las soluciones propuestas se encargan de asignar funciones virtuales de red a servidores, y deciden el enrutamiento del trafico en las infraestructuras 5G con dispositivos edge y fog. Para evaluar el rendimiento de las soluciones propuestas, esta tesis estudia en primer lugar la generación de grafos que representan redes 5G. Los mecanismos propuestos para la generación de grafos sirven para representar distintos escenarios 5G. En particular, escenarios de federación en los que varios dominios comparten recursos entre ellos. Los grafos generados también representan servidores en el edge, así como dispositivos fog con una batería limitada. Además, estos grafos tienen en cuenta los requisitos de estándares, y la demanda que se espera en las redes 5G. La generación de grafos propuesta sirve para representar escenarios federación en los que varios dominios comparten recursos entre ellos, y redes 5G con servidores edge, así como dispositivos fog estáticos o móviles con una batería limitada. Los grafos generados para infraestructuras 5G tienen en cuenta los requisitos de estándares, y la demanda de red que se espera en las redes 5G. Además, los grafos son diferentes en función de la densidad de población, y el área de estudio, es decir, si es una zona industrial, una autopista, o una zona urbana. Tras detallar la generación de grafos que representan redes 5G, esta tesis propone algoritmos de orquestación NFV para resolver con el problema del VNE. Primero, se centra en escenarios federados en los que los servicios de red se tienen que asignar no solo a la infraestructura de un dominio, sino a los recursos compartidos en la federación de dominios. Dos problemas diferentes han sido estudiados, uno es el problema del VNE propiamente dicho sobre una infraestructura federada, y el otro es la delegación de servicios de red. Es decir, si un servicio de red se debe desplegar localmente en un dominio, o en los recursos compartidos por la federación de dominios; a sabiendas de que el último caso supone el pago de cuotas por parte del dominio local a cambio del despliegue del servicio de red. En segundo lugar, esta tesis propone OKpi, un algoritmo de orquestación NFV para conseguir la calidad de servicio de las distintas slices de las redes 5G. Conceptualmente, el slicing consiste en partir la red de modo que cada servicio de red sea tratado de modo diferente dependiendo del trozo al que pertenezca. Por ejemplo, una slice de eHealth reservara los recursos de red necesarios para conseguir bajas latencias en servicios como operaciones quirúrgicas realizadas de manera remota. Cada trozo (slice) está destinado a unos servicios específicos con unos requisitos muy concretos, como alta fiabilidad, restricciones de localización, o latencias de un milisegundo. OKpi es un algoritmo de orquestación NFV que consigue satisfacer los requisitos de servicios de red en los distintos trozos, o slices de la red. Tras presentar OKpi, la tesis resuelve el problema del VNE en redes 5G con dispositivos fog estáticos y móviles. El algoritmo de orquestación NFV presentado tiene en cuenta las limitaciones de recursos de computo de los dispositivos fog, además de los problemas de falta de cobertura derivados de la movilidad de los dispositivos. Para concluir, esta tesis estudia el escalado de servicios vehiculares Vehicle-to-Network (V2N), que requieren de bajas latencias para servicios como la prevención de choques, avisos de posibles riesgos, y conducción remota. Para estos servicios, los atascos y congestiones en la carretera pueden causar el incumplimiento de los requisitos de latencia. Por tanto, es necesario anticiparse a esas circunstancias usando técnicas de series temporales que permiten saber el tráfico inminente en los siguientes minutos u horas, para así poder escalar el servicio V2N adecuadamente.Current network infrastructures handle a diverse range of network services such as video on demand services, video-conferences, social networks, educational systems, or photo storage services. These services have been embraced by a significant amount of the world population, and are used on a daily basis. Cloud providers and Network operators’ infrastructures accommodate the traffic rates that the aforementioned services generate, and their management tasks do not only involve the traffic steering, but also the processing of the network services’ traffic. Traditionally, the traffic processing has been assessed via applications/programs deployed on servers that were exclusively dedicated to a specific task as packet inspection. However, in recent years network services have stated to be virtualized and this has led to the Network Function Virtualization (Network Function Virtualization (NFV)) paradigm, in which the network functions of a service run on containers or virtual machines that are decoupled from the hardware infrastructure. As a result, the traffic processing has become more flexible because of the loose coupling between software and hardware, and the possibility of sharing common network functions, as firewalls, across multiple network services. NFV eases the automation of network operations, since scaling and migrations tasks are typically performed by a set of commands predefined by the virtualization technology, either containers or virtual machines. However, it is still necessary to decide the traffic steering and processing of every network service. In other words, which servers will hold the traffic processing, and which are the network links to be traversed so the users’ requests reach the final servers, i.e., the network embedding problem. Under the umbrella of NFV, this problem is known as Virtual Network Embedding (VNE), and this thesis refers as “NFV orchestration algorithms” to those algorithms solving such a problem. The VNE problem is a NP-hard, meaning that it is impossible to find optimal solutions in polynomial time, no matter the network size. As a consequence, the research and telecommunications community rely on heuristics that find solutions quicker than a commodity optimization solver. Traditionally, NFV orchestration algorithms have tried to minimize the deployment costs derived from their solutions. For example, they try to not exhaust the network bandwidth, and use short paths to use less network resources. Additionally, a recent tendency led the research community towards algorithms that minimize the energy consumption of the deployed services, either by selecting more energy efficient devices or by turning off those network devices that remained unused. VNE problem constraints were typically summarized in a set of resources/energy constraints, and the solutions differed on which objectives functions were aimed for. But that was before 5th generation of mobile networks (5G) were considered in the VNE problem. With the appearance of 5G, new network services and use cases started to emerge. The standards talked about Ultra Reliable Low Latency Communication (Ultra-Reliable and Low Latency Communications (URLLC)) with latencies below few milliseconds and 99.999% reliability, an enhanced mobile broadband (enhanced Mobile Broadband (eMBB)) with significant data rate increases, and even the consideration of massive machine-type communications (Massive Machine-Type Communications (mMTC)) among Internet of Things (IoT) devices. Moreover, paradigms such as edge and fog computing blended with the 5G technology to introduce the idea of having computing devices closer to the end users. As a result, the VNE problem had to incorporate the new requirements as constraints to be taken into account, and every solution should either satisfy low latencies, high reliability, or larger data rates. This thesis studies the VNE problem, and proposes some heuristics tackling the constraints related to 5G services in Edge and fog scenarios, that is, the proposed solutions assess the assignment of Virtual Network Functions to resources, and the traffic steering across 5G infrastructures that have Edge and Fog devices. To evaluate the performance of the proposed solutions, the thesis studies first the generation of graphs that represent 5G networks. The proposed mechanisms to generate graphs serve to represent diverse 5G scenarios. In particular federation scenarios in which several domains share resources among themselves. The generated graphs also represent edge servers, so as fog devices with limited battery capacity. Additionally, these graphs take into account the standard requirements, and the expected demand for 5G networks. Moreover, the graphs differ depending on the density of population, and the area of study, i.e., whether it is an industrial area, a highway, or an urban area. After detailing the generation of graphs representing the 5G networks, this thesis proposes several NFV orchestration algorithms to tackle the VNE problem. First, it focuses on federation scenarios in which network services should be assigned not only to a single domain infrastructure, but also to the shared resources of the federation of domains. Two different problems are studied, one being the VNE itself over a federated infrastructure, and the other the delegation of network services. That is, whether a network service should be deployed in a local domain, or in the pool of resources of the federation domain; knowing that the latter charges the local domain for hosting the network service. Second, the thesis proposes OKpi, a NFV orchestration algorithm to meet 5G network slices quality of service. Conceptually, network slicing consists in splitting the network so network services are treated differently based on the slice they belong to. For example, an eHealth network slice will allocate the network resources necessary to meet low latencies for network services such as remote surgery. Each network slice is devoted to specific services with very concrete requirements, as high reliability, location constraints, or 1ms latencies. OKpi is a NFV orchestration algorithm that meets the network service requirements among different slices. It is based on a multi-constrained shortest path heuristic, and its solutions satisfy latency, reliability, and location constraints. After presenting OKpi, the thesis tackles the VNE problem in 5G networks with static/moving fog devices. The presented NFV orchestration algorithm takes into account the limited computing resources of fog devices, as well as the out-of-coverage problems derived from the devices’ mobility. To conclude, this thesis studies the scaling of Vehicle-to-Network (V2N) services, which require low latencies for network services as collision avoidance, hazard warning, and remote driving. For these services, the presence of traffic jams, or high vehicular traffic congestion lead to the violation of latency requirements. Hence, it is necessary to anticipate to such circumstances by using time-series techniques that allow to derive the incoming vehicular traffic flow in the next minutes or hours, so as to scale the V2N service accordingly.The 5G Exchange (5GEx) project (2015-2018) was an EU-funded project (H2020-ICT-2014-2 grant agreement 671636). The 5G-TRANSFORMER project (2017-2019) is an EU-funded project (H2020-ICT-2016-2 grant agreement 761536). The 5G-CORAL project (2017-2019) is an EU-Taiwan project (H2020-ICT-2016-2 grant agreement 761586).Programa de Doctorado en Ingeniería Telemática por la Universidad Carlos III de MadridPresidente: Ioannis Stavrakakis.- Secretario: Pablo Serrano Yáñez-Mingot.- Vocal: Paul Horatiu Patra

CHANNEL MODELING FOR FIFTH GENERATION CELLULAR NETWORKS AND WIRELESS SENSOR NETWORKS

In view of exponential growth in data traffic demand, the wireless communications industry has aimed to increase the capacity of existing networks by 1000 times over the next 20 years. A combination of extreme cell densification, more bandwidth, and higher spectral efficiency is needed to support the data traffic requirements for fifth generation (5G) cellular communications. In this research, the potential improvements achieved by using three major 5G enabling technologies (i.e., small cells, millimeter-wave spectrum, and massive MIMO) in rural and urban environments are investigated. This work develops SPM and KA-based ray models to investigate the impact of geometrical parameters on terrain-based multiuser MIMO channel characteristic. Moreover, a new directional 3D channel model is developed for urban millimeter-wave (mmW) small cells. Path-loss, spatial correlation, coverage distance, and coherence length are studied in urban areas. Exploiting physical optics (PO) and geometric optics (GO) solutions, closed form expressions are derived for spatial correlation. Achievable spatial diversity is evaluated using horizontal and vertical linear arrays as well as planar 2D arrays. In another study, a versatile near-ground field prediction model is proposed to facilitate accurate wireless sensor network (WSN) simulations. Monte Carlo simulations are used to investigate the effects of antenna height, frequency of operation, polarization, and terrain dielectric and roughness properties on WSNs performance