Random Shape Theory Research Articles

Performance Evaluation of Reconfigurable Intelligent Surfaces-Assisted Millimeter-Wave Network Using Stochastic Geometry-Based Model

Millimeter-wave (mm-wave) bands have received significant attention due to their large bandwidth and high frequency. However, mm-wave signals experience high attenuation primarily as a result of their high directivity and vulnerability to blockage, leading to non-line-of-sight (NLOS) conditions and signal outages. Buildings, structures, and natural obstacles can cause signal blockage, which increases connection challenges and creates coverage gaps. A reconfigurable intelligent surface (RIS) is a potential technique that can improve the coverage of mm-wave networks by intelligently reconfiguring the wireless propagation environment. RIS offers novel solutions to blockage issues by passively reflecting and rerouting mm-wave signals in desired directions. This paper presents a simulation-based evaluation of the signal-to-interference ratio coverage probability in RIS-assisted mm-wave networks based on stochastic geometry. We will use random shape theory to represent the blockages within the network. Furthermore, the impact of increasing the density of RIS and the number of reflective elements on network performance will be examined. The results show that RIS can enhance network coverage and decrease the effects of blockages, with considerable increases in coverage probability when compared to networks without RISs.

Performance of Indoor Small-Cell Networks Under Interior Wall Penetration Losses

The performance of indoor small-cell networks (SCNs) is affected by the indoor environment, such as walls, blockages, etc. In this paper, we investigate the effect of interior wall attenuation on the performance of an indoor SCN. Specifically, the spatial distribution of interior walls is modelled based on the random shape theory and the indoor base stations (BSs) are distributed following a homogeneous Poisson point process. The channel model includes the path loss, Rayleigh fading, and wall attenuation. We analytically derive the downlink coverage probability under the strongest received signal user association strategy, which is validated by Monte Carlo simulations for three typical interior wall layouts (i.e., random layout, binary orientation layout, and Manhattan grid). The analytical results show that for a given density of interior walls and signal strength attenuation per wall, there is an optimal BS density that maximises the coverage probability, and the optimal BS density increases as the wall attenuation increases.

Analysis of Blocking in mmWave Cellular Systems: Characterization of the LOS and NLOS Intervals in Urban Scenarios

In the millimeter waves (mmWave) bands considered for 5G and beyond, the use of very high frequencies results in the interruption of communication whenever there is no line of sight between the transmitter and the receiver. Blockages have been modeled in the literature so far using tools such as stochastic geometry and random shape theory. Using these tools, in this paper, we characterize the lengths of the segments in line-of-sight (LOS) and in non-line-of-sight (NLOS) statistically in an urban scenario where buildings (with random positions, lengths, and heights) are deployed in parallel directions configuring streets.

Performance Analysis of Millimeter-Wave UAV Swarm Networks under Blockage Effects.

Due to their high mobility, unmanned aerial vehicles (UAVs) can offer better connectivity by complement or replace with the existing terrestrial base stations (BSs) in the mobile cellular networks. In particular, introducing UAV and millimeter wave (mmWave) technologies can better support the future wireless networks with requirements of high data rate, low latency, and seamless connectivity. However, it is widely known that mmWave signals are susceptible to blockages because of their poor diffraction. In this context, we consider macro-diversity achieved by the multiple UAV BSs, which are randomly distributed in a spherical swarm. Using the widely used channel model incorporated with the distance-based random blockage effects, which is proposed based on stochastic geometry and random shape theory, we investigate the outage performance of the mmWave UAV swarm network. Further, based on our analysis, we show how to minimize the outage rate by adjusting various system parameters such as the size of the UAV swarm relative to the distance to the receiver.

Analysis of Blocking in mmWave Cellular Systems: Application to Relay Positioning

Within the framework of 5G, blockage effects occurring in the mmWave band are critical. Previous works describe the effects of blockages in isolated and multiple links for simple blocking objects, modeled with mathematical tools such as stochastic geometry and random shape theory. Our study uses these tools to characterize a scenario with N links, including the possible correlation among them in terms of blocking for several models of blocking objects. We include numerical evaluations highlighting that assuming independence among the links' blocking elements is a too-brief simplification and does not accurately describe the real scenario. This paper also applies the formulation developed for the case of N links to optimize the relay positioning in mmWave cells for coverage enhancement, that is, to minimize the communication failure probability. We also show that both link budget and blockages affect the optimum positioning of the relays as they are both essential for successful transmission.

Relay selection scheme for device‐ to‐device based 3D millimetre‐wave cellular networks

Millimetre-wave (mmWave) communication is a key technology for future cellular networks. However, mmWave signals may be limited in coverage since they are susceptible to blockages. In order to mitigate blockages effect and enhance the coverage probability, device-to-device relaying can be used to improve the direct link reliability. In this study, the authors propose a new communication scheme to enhance the successful transmission probability. This scheme is based on a selected user equipment relay that can assist the transmission from the base station (BS) to the target user. The selected relay is an available user that provides the minimum distance among the retained maximum distances (the distance between this relay and the served user, and that between the same relay and the serving BS). Based on the stochastic geometry and random shape theory, they derive the expressions of the probability density function, and the successful transmission probability within the proposed scheme under the Nakagami-m fading assumption. Using numerical results, the derived expressions are evaluated, and the advantages of the proposed scheme are investigated. The results confirm the analytical derived expression. In addition, the performance of their proposed scheme in terms of coverage probability outperform the existing schemes.

Connectivity and Blockage Effects in Millimeter-Wave Air-To-Everything Networks

Millimeter-wave (mmWave) offers high data rate and bandwidth for air-to-everything (A2X) communications including air-to-air, air-to-ground, and air-to-tower. MmWave communication in the A2X network is sensitive to buildings blockage effects. In this paper, we propose an analytical framework to define and characterise the connectivity for an aerial access point (AAP) by jointly using stochastic geometry and random shape theory. The buildings are modelled as a Boolean line-segment process with fixed height. The blocking area for an arbitrary building is derived and minimized by optimizing the altitude of AAP. A lower bound on the connectivity probability is derived as a function of the altitude of AAP and different parameters of users and buildings including their densities, sizes, and heights. Our study yields guidelines on practical mmWave A2X networks deployment.

Enclosed mmWave Wearable Networks: Feasibility and Performance

This paper investigates the feasibility of mmWave frequencies for personal networks of wireless wearable devices in enclosed settings (e.g., commuter trains, subways, airplanes, airports, or offices). At these frequencies, specular reflections off surfaces are expected to contribute intended signal power and, simultaneously, to aggravate the interference at the receivers. Meanwhile, blockages by obstacles and people---including the individuals wearing the devices---are expected to shield receivers from interference. With the aid of stochastic geometry and random shape theory, we assess the interplay of surface reflections and blockages for dense deployments of wearable networks equipped with directional antenna arrays in relevant indoor settings.

Analyzing Wireless Indoor Communications by Blockage Models

The performance of wireless cellular networks in indoor scenarios is in large parts characterized by the blockage objects such as walls. These objects can be included in the system model in several ways. We present in this paper different wall generation methods, ranging from approaches from random shape theory (in 1-D and 2-D) to semideterministic and heuristic approaches. To attain comparable results, we ensure that the average wall volume for each method is constant. This results in the same average attenuation for distinct paths, which is shown analytically as well as by simulations. We apply a regular transmitter grid, show the influence of the relative orientation between walls and transmitter–receiver path and also elaborate on the influence of interferers in different tiers around the desired transmitter. Based on the average attenuation, we introduce the necessary approximations to yield tractable expressions for average performance in terms of Signal-to-Interference Ratio (SIR). These approximations are necessary to reflect the fluctuations among the instantaneous SIR values for the individual realizations of the blockage scenario and also due to the spatial correlation of blockages influencing several transmitter-signals simultaneously. Our results show a good accordance among the analytical and simulation results. Furthermore, we find the random wall generation method in two dimensions as the worst case scenario and the regular wall generation method as the best case scenario under the constraint of constant average wall volume.

Outage Analysis of Multihop Wireless Backhaul Using Millimeter Wave under Blockage Effects

We consider multihop millimeter-wave (mm-Wave) wireless backhaul communications, by which small cell base station (SBS) clusters can connect to a macrocell base station (MBS). Assuming the mm-Wave wireless backhaul links suffer from outage caused by obstacles that block the line-of-sight (LoS) paths, we derive the statistics of a perhop distance based on the blockage model using stochastic geometry and random shape theory and analyze the multihop outage probability using the statistics of a perhop distance. We also provide an optimal number of hops to minimize the end-to-end outage performance between the MBS and the destination SBS cluster when the end-to-end distance is given.

Outage Analysis of Millimeter-Wave Wireless Backhaul in the Presence of Blockage

In this letter, we consider the fifth-generation (5G) wireless backhaul network with small cells and millimeter-wave (mm-Wave) communication. We assume mm-Wave wireless backhaul is used for a physically separated 5G macro base station (MBS) to communicate with small-cell base stations (SBSs) that have wired connections to each other. Thus, a user in the coverage of the SBSs can receive its desired signal when at least one of the SBSs is connected to the 5G MBS. However, a blockage problem of line-of-sight paths can induce an outage event in mm-Wave communication. Using stochastic geometry and random shape theory, we analyze the outage probability of the mm-Wave wireless backhaul in the presence of blockage and investigate impacts of various system parameters.

A survey on modeling interference and blockage in urban heterogeneous cellular networks

In this paper, we provide a survey on abstraction models for evaluating aggregate interference statistics in urban heterogeneous cellular networks. The two principal interference shaping factors are the path loss attenuation and the interference geometry. For both factors, our survey systematically summarizes state-of-the-art models and outlines their strengths and weaknesses. In the context of path loss attenuation, we give an overview on the basic propagation mechanisms and the various approaches for their abstraction. We specifically elaborate on random shape theory and its application for representing blockages in indoor and outdoor scenarios. In terms of interference geometry, we present techniques from stochastic geometry as well as deterministic approaches, outlining their evolution and limitations. Throughout the paper, challenges under discussion are scenarios with both indoor and outdoor environments, distance-dependent shadowing due to blockages, and correlations among node and blockage locations as well as the distinction between cell center and cell edge. Our goal is to raise awareness on not only the validity and tractability but also the limitations of state-of-the-art techniques. The presented models were chosen with regard to their adaptability for a broad range of scenarios. They are therefore expected to be adopted for describing the fifth generation of mobile networks (5G).

Analysis of Blockage Effects on Urban Cellular Networks

Large-scale blockages such as buildings affect the performance of urban cellular networks, especially at higher frequencies. Unfortunately, such blockage effects are either neglected or characterized by oversimplified models in the analysis of cellular networks. Leveraging concepts from random shape theory, this paper proposes a mathematical framework to model random blockages and analyze their impact on cellular network performance. Random buildings are modeled as a process of rectangles with random sizes and orientations whose centers form a Poisson point process on the plane. The distribution of the number of blockages in a link is proven to be a Poisson random variable with parameter dependent on the length of the link. Our analysis shows that the probability that a link is not intersected by any blockages decays exponentially with the link length. A path loss model that incorporates the blockage effects is also proposed, which matches experimental trends observed in prior work. The model is applied to analyze the performance of cellular networks in urban areas with the presence of buildings, in terms of connectivity, coverage probability, and average rate. Our results show that the base station density should scale superlinearly with the blockage density to maintain the network connectivity. Our analyses also show that while buildings may block the desired signal, they may still have a positive impact on the SIR coverage probability and achievable rate since they can block significantly more interference.