The directional RTS/CTS mechanism of mm-wave Wi-Fi hardly resolves the hidden terminal problem perfectly. This paper proposes cross-link RTS/CTS under multi-link operation (MLO) to address this problem and introduces a novel point process, named the generalized RTS/CTS hard-core process (G-HCP), to model the spatial transceiver relationships under the RTS/CTS mechanism, including the directional case and the omnidirectional case. Analytical expressions are derived for the intensity, the mean interference, an approximation of the success probability, and the expected number of hidden nodes for the directional RTS/CTS mechanism. Theoretical and numerical results demonstrate the performance difference between two RTS/CTS mechanisms. The cross-link RTS/CTS mechanism ensures higher link quality at the cost of reduced network throughput. In contrast, the directional RTS/CTS sacrifices the link quality for higher throughput. Our study reveals a fundamental trade-off between link reliability and network throughput, providing critical insights into the selection and optimization of RTS/CTS mechanisms in next-generation WLAN standards.

For a given set of transmitters such as cellular base stations or WiFi access points, is it possible to analytically characterize the set of locations that are “covered” in the sense that users at these locations experience a certain minimum quality of service? In this paper, we affirmatively answer this question, by providing explicit simple outer bounds and estimates for the coverage manifold. The key geometric elements of our analytical method are theQ cells, defined as the intersections of a small number of disks. The Q cell of a transmitter is an outer bound to the service region of the transmitter, and, in turn, the union of Q cells is an outer bound to the coverage manifold. In infinite networks, connections to the meta distribution of the signal-to-interference ratio allow for a scaling of the Q cells to obtain accurate estimates of the coverage manifold.

Communication reliability, as defined by 3GPP, is the probability of achieving a desired quality of service (QoS). Traditionally, this metric is evaluated by averaging the QoS success indicator over spatiotemporal random variables. Recently, the meta distribution (MD) has emerged as a two-level analysis tool that characterizes system-level reliability as a function of link-level reliability thresholds. However, existing MD studies have two limitations. First, they focus exclusively on spatial and temporal randomness corresponding to node distribution and fading channels, respectively, leaving stochastic behaviors in other domains largely unexplored. Second, they are restricted to first-order MDs with two randomness levels, restricting applicability to scenarios requiring higher-order MD characterization. To address these gaps, we propose a hierarchical framework for higher-order MD reliability in wireless networks, where each layer’s success probability is formulated and fed into the next layer, yielding overall MD reliability at the highest level. We apply this framework to wireless networks by capturing three levels of temporal dynamics representing fast, slow, and static random elements, and provide a comprehensive second-order MD reliability analysis for two application scenarios. The effectiveness of the proposed approach is demonstrated via these representative scenarios, supported by detailed analytical and numerical evaluations. Our results highlight the value of hierarchical MD representations across multiple domains and reveal the significant influence of inner-layer target reliabilities on overall performance.

We investigate simple packet fragmentation strategies to minimize the mean packet reception delay in a time-slotted wireless network where many static devices connect to their respective receivers, without prior knowledge of the effects of fading and interference on reception. When a packet of a given size is fragmented, and each slot is used to send one fragment, a smaller fragment size trades off an increase in the number of fragments for more robust reception of individual fragments (due to a lower per-slot transmission rate). Increasing fragment size has the opposite effect. We explicitly characterize this tradeoff in both noise-limited and interference-limited Poisson wireless networks, and derive bounds on the optimum number of fragments for a given packet size to minimize the mean packet delay. Beyond predicting the well-known threshold effect—i.e., packets smaller than the fragmentation threshold should not be fragmented to reduce mean packet delay—our model provides an analytical basis for deriving and applying such thresholds in practice. Interestingly, the fragmentation threshold depends on a parameter we term network conductance, which captures the average impact of the network’s geometry and fading. To the best of our knowledge, this is the first such analysis.

Communication reliability is typically assessed by averaging the QoS success indicator over spatial and temporal variables. The meta distribution (MD) has recently emerged as a powerful two-level analysis framework, providing insights into system-level (outer) reliability relative to link-level (inner) thresholds. While prior studies focus on first-order spatiotemporal MD reliability, applications beyond this structure remain unexplored. This work introduces a second-order MD reliability analysis framework and applies it to spatial-spectral-temporal MD analysis for frequency-hopping THz communication. Numerical results show how inner-layer target reliabilities in temporal/spectral domains affect overall spatial MD reliability. It is also shown that adopting a non-uniform frequency-hopping pattern enhances spatial MD reliability but reduces resiliency and increases jamming risk.

We focus on stochastic geometry analysis of a low Earth orbit (LEO) narrowband terrestrial-satellite uplink with satellite base stations (SBSs) in a uniform constellation equipped with narrow Gaussian beams. The served and interfering omnidirectional user equipments (UEs) are distributed on the Earth’s surface according to a homogeneous Poisson point process (HPPP) with Nakagami faded signals. This study presents a detailed but comprehensive mathematical analysis of several key metrics: the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR), and the average throughput. Many results are presented in simple analytical and closed forms containing more insight than the expressions proposed in prior works. The results indicate an optimal UE density depending on the altitude, elevation angle, and the width of the antenna gain, maximizing the average throughput. However, this optimal density leads to a significant variance in the user experience regarding link quality (i.e., the users are not treated fairly).

For fifth-generation wireless networks to transition to sixth-generation wireless networks, the integration of coordinated multipoint (CoMP) and non-orthogonal multiple access (NOMA) techniques is expected to overcome new challenges and enhance performance compared to the CoMP or NOMA scheme. The joint-transmission CoMP (JT-CoMP) technique is a typical technical implementation of the CoMP scheme. In this study, we investigate a downlink network with a joint JT-CoMP-NOMA scheme. Based on the generalized Stienen model from stochastic geometry, we divide far and near NOMA user equipment (UE) and develop a theoretical framework to analyze the system performance. Expressions for the coverage probabilities and average achievable rates of two types of UEs (named CoMP and non-CoMP UEs) are derived. By comparing analytical results with Monte Carlo simulations, we show that the approximations in the analytical derivations are tight. The impact of certain network parameters, such as the power allocation coefficient, on the system performance is also studied. Notably, the developed transmission scheme is shown to outperform the NOMA-only and the JT-CoMP-only schemes.

To address the poor performance experienced by cell-corner users located equidistantly to the serving base station (BS) and the nearest interfering BSs, this paper proposes a flexible and general air-ground cooperation scheme based on unmanned aerial vehicles and dynamic BS coordination in the form of BS silencing (BSS) or joint transmission (JT). To show the role of unmanned aerial vehicle (UAV) in the cooperation, we define the UAV-to-BS power ratio (UBPR) as a critical parameter to measure whether introducing the UAV can improve the user’s performance. Using stochastic geometry tools, we derive the success probability of the user located at the corner of the Voronoi diagram, called the worst-case user, in Poisson cellular networks. To facilitate the comparison between different modes of cooperation, we further analyze the cooperation gain including the diversity and power gains through the asymptotic outage probability in the high-reliability regime. Furthermore, to reflect the impact of the cooperation scheme on the overall network performance, we analyze the normalized spectral efficiency, which, unlike those adopted in existing works, accounts for the costs of both resource occupancy and data exchange. Numerical results validate the accuracy of our analytical findings and demonstrate the effectiveness of the proposed scheme for cell-corner users.

This paper introduces a new stochastic geometry-based model to analyze the Request-to-Send/Clear-to-Send (RTS/CTS) handshake mechanism in wireless local area networks (WLANs). We develop an advanced hard-core point process model, termed the dual-zone hard-core process (DZHCP), which extends traditional hard-core models to capture the spatial interactions and exclusion effects introduced by the RTS/CTS mechanism. This model integrates key parameters accounting for the thinning effects imposed by RTS/CTS, enabling a refined characterization of active transmitters in the network. Analytical expressions are derived for the intensity of the DZHCP, the mean interference, and an approximation of the success probability, providing insight into how network performance depends on critical design parameters. Our results demonstrate that the Type II RTS/CTS mechanism significantly reduces mean interference by introducing additional protection regions, effectively mitigating the impact of nearby interferers. Compared to CSMA-based schemes, it achieves a lower mean interference level while maintaining a comparable or higher active node density.

To address the poor performance experienced by cell-edge users located equidistantly to the serving base station (BS) and the nearest interfering BS(s), this paper proposes an air-ground coordinated multipoint scheme assisted by unmanned aerial vehicles and the dynamic coordinated BSs selected from the sets of the serving and the equidistant interfering BSs. Using stochastic geometry tools, we derive success probabilities in a Poisson cellular network for the users located at corners of the Voronoi diagram called worst-case users served using non-coherent joint transmission. To reflect the impact of the coordinated transmission on the overall network performance, we also deduce the normalized spectral efficiency. Numerical results validate the accuracy of our analytical findings and show the superior performance of the proposed scheme for the worst-case users.

The current analysis of wireless networks with transceivers confined to streets is primarily based on Poissonian models, such as Poisson line processes and Poisson line Cox processes. We demonstrate important scenarios where a model with a finite and deterministic number of streets, termed the binomial line process (BLP), is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process (BLCP) and apply them to analyze the performance of a network whose access points are deployed along the streets of a city. Such a deployment scenario will be typical for 5G and future wireless networks. In order to obtain a fine-grained insight into the network performance, we derive the meta distribution of the signal-to-interference and noise ratio. Accordingly, we investigate the mean local delay in transmissions and the density of successful transmission. These metrics, respectively, characterize the latency and coverage performance of the network and are key performance indicators of next-generation wireless systems.

In the analysis of wireless networks, the standard signal-to-interference (SIR) distribution does not capture the performance at the individual link level. The meta distribution (MD) of the SIR resolves this problem by separating different sources of randomness, such as fading and point process(es). While it allows for a much sharper performance characterization, it can in most cases only be calculated based on the moments of the underlying conditional distribution, i.e., by solving a Hausdorff moment problem. Several methods to reconstruct MDs from the moments have been proposed but a rigorous analysis, comparison of their performance, and practical implementations are missing. In addition, a standard is needed for a consistent and objective comparison. This paper addresses the above-mentioned important shortcomings, introduces a tweaking mapping for adjusting approximations, presents terminology to categorize the quality of approximations, proposes the use of the Fourier-Legendre method, which has not previously been applied to MDs, and provides the achievable lower and upper bounds on the MD given the firstnmoments. Further, to facilitate the use of MDs, we give comprehensive guidance on the selection of the best method to determine MDs, and we offer ready-to-use implementations of the proposed algorithms. This study fills an important gap in the literature by rigorously analyzing the MDs, comparing the performance of different methods, and offering user-friendly implementations for recovering MDs from moments.

While meta distribution (MD) reconstruction methods based on moments play an important role in analyzing wireless network performance, a critical gap exists in comprehending the impact and consequences of inaccurate moments on MD reconstructions. The reliability and robustness of these techniques remain unexplored. In this paper, we address this gap by analyzing the sensitivity of commonly used MD reconstruction methods to perturbations to moments and provide valuable guidelines for the application of these methods. Furthermore, we quantify the impact of inaccurate moments on MD reconstructions, examining the validity of perturbed moment sequences and demonstrating the critical importance of moment accuracy. Our investigation demonstrates the necessity for precise moment computation. Succinctly put, moment quality is preferred over moment quantity.

The stochastic geometry analysis of vehicular networks and on-street deployment of base stations is largely based on Cox processes driven by Poissonian models. In this paper, we investigate scenarios where a model with a finite and deterministic number of streets, termed the binomial line process (BLP), is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process (BLCP). We derive the line length density and the intersection density for the BLP and demonstrate how it models the inhomogeneity of the streets in a city. Finally, leveraging the derived framework, we analyze the performance of a network whose access points are deployed along the streets of a city. Our study captures the variation in the service performance of the users across different locations of a city and thus it leads to key network planning and dimensioning rules for the operators.

We investigate the performance of a random access network consisting of source-destination dipoles. The source nodes transmit information packets to their destinations over a shared spectrum. All the transmitters in this network adhere to an age threshold slotted ALOHA (TSA) protocol: every source node remains silent until the age of information (AoI) reaches a threshold, after which the source accesses the radio channel with a certain probability. We derive a tight approximation for the signal-to-interference-plus-noise ratio (SINR) meta distribution and verify its accuracy through simulations. We also obtain analytical expressions for the average AoI. Our analysis reveals that when the network is densely deployed, employing TSA significantly decreases the average AoI. The update rate and age threshold must be jointly optimized to fully exploit the potential of the TSA protocol.

Air platforms, such as unmanned aerial vehicles, airships, and balloons are expected to complement traditional ground networks to provide flexible coverage solutions. However, most existing models for air-ground integrated networks (AGINs) neglect the spatial dependence caused by the complementary deployment of the aerial and ground nodes. Accordingly, in this paper, we propose two AGIN models with horizontal dependence that differ in the vertical dimension, namely uniformly independent altitudes and location-dependent altitudes. The air platforms serve as aerial base stations, distributed as a marked Poisson hole process, and provide flexible beam coverage through varying altitudes. Under this setup, we propose a region-based user association scheme and derive the association probabilities as well as the serving distance distributions of an arbitrarily located user. Considering Nakagami fading and air-to-ground propagation properties, we characterize the signal-to-interference ratio and area spectral efficiency for each model. Using the proposed analytical framework, we demonstrate the importance of deploying the air platforms more sensibly to provide targeted services and flexible beam coverage in reducing the load of base stations and improving the user coverage and network capacity performance.

Abstract With the growing popularity of the Internet-of-Vehicles (IoV), it is of pressing necessity to understand transportation traffic patterns and their impact on wireless network designs and operations. Vehicular mobility patterns and traffic models are the keys to assisting a wide range of analyses and simulations in these applications. This study surveys the status quo of vehicular mobility models, with a focus on recent advances in the last decade. To provide a comprehensive and systematic review, the study first puts forth a requirement-model-application framework in the IoV or general communication and transportation networks. Existing vehicular mobility models are categorized into vehicular distribution, vehicular traffic, and driving behavior models. Such categorization has a particular emphasis on the random patterns of vehicles in space, traffic flow models aligned to road maps, and individuals’ driving behaviors (e.g., lane-changing and car-following). The different categories of the models are applied to various application scenarios, including underlying network connectivity analysis, off-line network optimization, online network functionality, and real-time autonomous driving. Finally, several important research opportunities arise and deserve continuing research efforts, such as holistic designs of deep learning platforms which take the model parameters of vehicular mobility as input features, qualification of vehicular mobility models in terms of representativeness and completeness, and new hybrid models incorporating different categories of vehicular mobility models to improve the representativeness and completeness.

In millimeter-wave (mm-wave) cellular networks, directional antenna arrays are typically adopted to mitigate the severe propagation loss. However, the interference caused by such highly directional beams may, in turn, result in a significant number of transmission failures, especially for dense networks. To tackle this problem, we propose two inter-cell interference coordination (ICIC) schemes in mm-wave bands: one is merely based on the path loss incorporating the blockage effect (PL-ICIC); the other considers both path loss and directivity gain (PG-ICIC). To fully investigate both schemes, we first derive an exact expression for the success probability (reliability) of the typical (served) user. We further provide an asymptotic analysis for the success probability and propose an effective approximation based on the asymptotic signal-to-interference ratio (SIR) gain relative to no ICIC. Secondly, to incorporate the cost of ICIC schemes, we derive the approximate normalized throughput taking into account that some users cannot be served due to limited resources. Numerical results show that the two proposed schemes provide significant reliability improvements in the low-SIR regime, and the higher the number of antennas, the wider the SIR range for which there is an improvement. In addition, compared with PL-ICIC, PG-ICIC balances the available resources among all users well.

The spatial correlation of the energy harvested from RF transmitters, named energy correlation, plays a key role in the performance evaluation of wirelessly powered networks. This paper introduces an analytical framework with foundations in stochastic geometry to characterize the energy correlation based on the energy correlation coefficient (ECC). For a model where RF power sources are distributed according to a Poisson point process and employ beamforming techniques to transfer energy directionally, we focus on two cases: i) each power source points the beam in a random direction; ii) each power source points the beam to an RF-powered node located in its Voronoi cell. We first analyze the ECC of the two cases, and then give the asymptotic results with respect to the antenna array size. It turns out that in both cases the harvested energy at two locations exhibit positive correlation, and when the antenna array size tends to infinity, the correlation in the first case vanishes while the one in the second case is still positive. Numerical results give useful insights into the effect of several system parameters on the energy correlation from directed wireless energy transfer.

Energy correlation critically affects the performance of a wirelessly powered network due to its key effect on the spatial distribution of concurrent RF-powered transmitters. This paper introduces a powerful analytical framework with foundations in stochastic geometry to characterize the energy correlation in a general wirelessly powered network. Unlike the commonly used pair correlation function (pcf)-based method, it is based on theenergy correlation coefficient(ECC) and yields the energy correlation distance that gives a sufficiently small ECC. Specifically, we focus on the spatial correlation of the energy harvested from a Poisson field of RF power sources with directional beams under two cases: i) each power source points the beam in a random direction; ii) each power source points the beam to an RF-powered node located in its Voronoi cell. The results demonstrate that the energized RF-powered nodes in both cases exhibit positive correlation that is weaker than in the omni-directional case due to the introduction of energy beamforming. As an application, we provide an ECC-based method using the energy correlation distance to approximate the success probability and area spectral efficiency in the communication phase. It turns out that the ECC-based approximation matches the exact result well, and, more importantly, it can deal with the energy correlation in more general and complicated scenarios (where the pcf analysis is infeasible) due to its superior tractability.

In coverage-oriented networks, base stations (BSs) are deployed in a way such that users at the cell boundaries achieve sufficient signal strength. The shape and size of cells vary from BS to BS, since the large-scale signal propagation conditions differ in different geographical regions. This work proposes and studies a joint spatial-propagation (JSP) model, which considers the correlation between cell radii and the large-scale signal propagation (captured by shadowing). We first introduce the notion of the directional radius of Voronoi cells, which has applications in cellular networks and beyond. The directional radius of a cell is defined as the distance from the nucleus to the cell boundary at an angle relative to the direction of a uniformly random location in the cell. We study the distribution of the radii in two types of cells in the Poisson Voronoi tessellations: the zero-cell, which contains the origin, and the typical cell. The results are applied to analyze the JSP model. We show that, even though the Poisson point process (PPP) is often considered as a pessimistic spatial model for BS locations, the JSP model with the PPP achieves coverage performance close to the most optimistic one-the standard triangular lattice model. Further, we show that the network performance depends critically on the variance of the large-scale path loss along the cell boundary.

We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of ℝ2. The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street. Models in this Coxian framework can characterize streets of different lengths and orientations forming intersections or T-junctions. The lengths of the streets can be infinite or finite and mutually independent or dependent. We analyze the reliability of communication for different models, where reliability is the probability that a vehicle at an intersection, a T-junction, or a general location can receive a message successfully from a transmitter at a certain distance. Further, we introduce a notion of equivalence between vehicular models, which means that a representative model can be used as a proxy for other models in terms of reliability. Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants.

A comprehensive vehicular network analysis requires modeling the street system and vehicle locations. Even when Poisson point processes (PPPs) are used to model the vehicle locations on each street, the analysis is barely tractable. That holds for even a simple average-based performance metric—the success probability, which is a special case of the fine-grained metric, the meta distribution (MD) of the signal-to-interference ratio (SIR). To address this issue, we propose the transdimensional approach as an alternative. Here, the union of 1D PPPs on the streets is simplified to the transdimensional PPP (TPPP), a superposition of 1D and 2D PPPs. The TPPP includes the 1D PPPs on the streets passing through the receiving vehicle and models the remaining vehicles as a 2D PPP ignoring their street geometry. Through the SIR MD analysis, we show that the TPPP provides good approximations to the more cumbrous models with streets characterized by Poisson line/stick processes; and we prove that the accuracy of the TPPP further improves under shadowing. Lastly, we use the MD results to control network congestion by adjusting the transmit rate while maintaining a target fraction of reliable links. A key insight is that the success probability is an inadequate measure of congestion as it does not capture the reliabilities of the individual links.

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored for analytical tractability. Accounting for the energy correlation, this paper introduces and promotes the Poisson disk process (PDP) as a model for the active RF-powered nodes that succeed in harvesting energy. To show that the model leads to tractable results in several cases of interest, we derive the density and second moment density of the PDP and find the key property that the PDP can be fully characterized by its first- and second-order statistics. Tight bounds for its probability generating functional (PGFL) are also provided. To show that the model is relevant for wirelessly powered networks that exhibit positive energy correlation, we fit the PDP to a given energized point process incorporating practical energy harvesting factors and derive the information transmission success probability. It turns out that the resulting PDP can closely model the distribution of actual energized RFpowered nodes in terms of the success probability and other statistics while preserving analytical tractability.

Moving networks (MNs) with moving base stations (BSs) provide ubiquitous and constant services to cellular devices/user equipment (UEs) in 5-th generation systems. Moving BSs are mounted on top of vehicles. To describe the randomness of the BSs, a tractable stochastic geometry model for MNs is proposed. A definition of the conditional success probability and meta distribution (MD) of the signal-to-interference ratio (SIR) for MNs is proposed. The MD is used to assess the benefits of MNs. In single-tier MNs with high mobility, we determine the moments of the conditional success probability given the point process for the calculation of the MD and the mean local delay. The results show that the mean local delay is finite and the variance is reduced to 0. A closed-form approximation of the variance is proposed for general mobility levels. Using the approximated variance, we propose a beta approximation of the MD. The single-tier model is then extended to a two-tier heterogeneous MN model. Tractable expressions of the mean success probability and the variance for both the overall network and the typical UE in each tier are obtained. They reveal that moving BSs can reduce the variance among UEs while keeping the mean success probability constant.

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored. While this leads to remarkably simple results for key performance metrics, it is typically not realistic and accurate. Considering the accuracy, tractability, and practicability tradeoffs, this paper introduces and promotes the Poisson disk process (PDP) as a model for the energized nodes that succeed in harvesting energy. To show that the model leads to analytically tractable results in several cases of interest, we derive its first and second moment densities, which fully characterize the PDP. Besides, we also provide tight bounds for its probability generating functional as well as its contact and nearest-neighbor distance distributions. Then, to show that the model is relevant for wirelessly powered networks-which all have positive energy correlation-we provide two approaches to fit the PDP to a given energized point process incorporating practical energy harvesting factors. Further, we derive the success probability in the information transmission phase, where the distribution of the active transmitters is modeled by a PDP. It turns out that the resulting PDP can closely model the distribution of actual energized nodes in terms of the success probability and other statistics while preserving analytical tractability.

The signal-to-interference-ratio (SIR) meta distribution (MD) characterizes the link performance in interference-limited wireless networks: it evaluates the fraction of links that achieve an SIR threshold θ with a reliability above x. In this work, we show that in Poisson networks, for any independent fading and power-law path loss with exponent α, the SIR MD can be expressed as the product of θ-2/αand a function of x when (θ, x) is in the so-called “separable region”. We show by simulation that the separable form serves as a good approximation of the SIR MD in Ginibre and triangular lattice networks when θ is chosen large enough. Given the quest for ultra-reliable transmission, we study the asymptotics of the SIR MD as x → 1 for general cellular networks with Rayleigh fading. Finally, we apply our results to characterize the distribution of the link rate, where each link transmits with a rate satisfying a given reliability x, and the asymptotic distribution of the local delay, defined as the number of transmissions needed for a message to be received successfully.

The meta distribution (MD) of the signal-to-interference ratio (SIR) provides more fine-grained information about the link performance than the standard success probability. This paper focuses on a fundamental extension of the SIR MD-the joint MD of the SIR at different locations, and studies its applications to physical layer security and cooperative reception. The concept of the joint MD of the SIR is formally introduced for two or more users (locations), as well as the joint conditional success probability and the n -th order product MD, which is a simpler version of the joint MD. The joint MD is first applied to physical layer security. The network reliability of the secrecy transmission based on the MD is studied, taking into account the signal and interference correlations between the legitimate user and the eavesdropper. Next the joint MD is applied to cooperative reception, where we consider the scenario that the base station sends a message to a group of users, and the goal is that at least one user successfully receives the message. The moments of the conditional probability of the event that the transmission succeeds at at least one of the two users are derived. The results demonstrate the practical relevance of the joint MD.

This paper studies the spatial correlation of the energy harvested from a Poisson field of millimeter-wave (mm-wave) RF power sources which employ beamforming techniques to transfer energy directionally. In particular, each node harvests and stores energy from its nearest RF transmitter and uses it to power the information transmission. Under this setup, we show how the actual point process of nodes that successfully harvest energy looks visually and provide an accurate characterization of its density and pair correlation function theoretically. Surprisingly, it turns out that the process of the energized nodes exhibits repulsive correlations for small distances which wears off as the distance increases. Therefore, we further approximate the energized point process with a fitted β-Ginibre point process, which is shown to provide a good approximation of the success probability in the information transmission. A useful insight is that there are energy correlations caused by the directional energy transfer, which should be reflected accurately in modeling the active mm-wave RF-powered nodes.

Poisson line processes (PLPs) describe a street system as a random collection of lines. Poisson point processes (PPPs) model vehicle locations on each line or street as random points. The characterization of vehicular networks as their combination, i.e., the PLP-PPP model, is relevant and widely used in the literature. However, the analytical expression for even a simple performance metric such as the probability of successful message reception in the PLP-PPP is quite complex and provides little insights into the network behavior. Here, we propose a transdimensional Poisson model-superposition of the 1D and 2D PPPs- as an alternative. It considers the vehicles on the same line as the receiving vehicle as a 1D PPP and the vehicles on the other streets as random points on the 2D plane neglecting their street geometry. We show that the success probability in the proposed transdimensional model is tractable and provides a tight approximation to that of the PLP- PPP. Also, it is asymptotically exact on both the upper and lower tails of the success probability.

The stochastic geometry-based downlink analysis of a cellular network modeled as a Poisson point process (PPP) has traditionally focused on the typical user placed at the origin, which does not lie in the typical cell. In order to characterize the performance of the typical cell, one needs to explicitly consider the point process of users scheduled in a given resource block (RB), which is dependent on the base station (BS) point process. Therefore, we model the locations of the scheduled users using the so-called Type I user process, which places one user uniformly at random in each cell. However, this dependency in the locations of the BSs and users complicates the characterization of the point process of interferers as seen by the typical user of the Type I process. In order to overcome this challenge, we present a general approach to determine the pair correlation function (pcf) of stationary point processes with respect to a reference point. This approach is used to approximate the pcf the point process of interferers with respect to the typical user of the Type I process. With the pcf in hand, we provide the tightest known approximation of the point process of interfering BSs as seen by the typical user of Type I process, which is used to derive remarkably tight expressions for the moments of the downlink signal-to-interference- ratio (SIR) meta distribution for the typical cell.

In millimeter-wave (mm-wave) cellular networks, high-gain beamforming, realized with directional antenna arrays, is typically adopted to mitigate the severe propagation loss. However, the interference caused by such highly directional beams may, in turn, result in a significant number of transmission failures, especially for dense networks. To tackle this problem, we propose two inter-cell interference coordination (ICIC) schemes in mm-wave bands: one is merely based on the path loss incorporating the blockage effect (PL-ICIC); the other considers both path loss and directivity gain (PG-ICIC). To fully investigate the performance of both schemes, we first derive the exact expression for the success probability (reliability) of the typical user that is served. Secondly, to reflect the cost of interference coordination, we further derive the overall success probability taking into account that some users cannot be served due to limited resources. Numerical results show that both the proposed two schemes provide significant reliability improvements in the low signal-to-interference ratio (SIR) regime, in particular, the higher the number of antennas, the wider the range of SIR threshold for which there is an improvement. In addition, compared with PL-ICIC, PG-ICIC balances the available resources among all users well.

This paper investigates the spatial correlation of the energy harvested from a Poisson field of RF power sources. Specifically, we focus on two energy harvesting models-one dependent on distance alone and the other with more practical factors taken into account-with the aim of showing how the actual point process of nodes that successfully harvest energy looks visually and characterize the pair correlation functions for such point process under the two models theoretically. It turns out that for both models the resulting process of the energized nodes exhibits positive correlations. Therefore, we further approximate the point process formed by active RF-powered nodes with a fitted Poisson cluster process, which is shown to provide a good approximation of the success probability in the information transmission. An important conclusion is that though the Poisson point process has been widely used to model the spatial configuration of energized nodes, it is inadequate for modeling the locations of the active RF-powered nodes due to the positive correlation.

Unlike earlier works on rateless codes that mostly considered finite networks or ignored the traffic dynamics, this paper focuses on the end-to-end delay performance of rateless codes in large-scale wireless ad hoc networks with traffic dynamics. Specifically, the end-to-end delay is divided into two parts, namely the packet waiting time before transmission and the transmission time, whose statistical distributions are given by exact results as well as simple yet accurate approximations. This way, the statistics of the end-to-end delay are fully investigated. The proposed analytical framework and the end-to-end performance metric help obtain more insights on the role of scheduling, queueing, and coding scheme in practical networks. The approximations are verified to be effective and reliable through simulations. Overall, the results show the significant benefits of rateless codes relative to the fixed-rate codes in terms of the end-to-end delay performance.

As a key enabling technology for truly sustainable operation of devices, wireless energy and information transfer (WEIT) has attracted significant attention in wireless communication networks. Previous works on WEIT network analysis mostly concentrated on the energy outage probability or the expectation of the transferred energy at the typical wirelessly powered device using stochastic geometry. These calculations are relatively straightforward, but they only provide limited information on the energy extracted by the individual devices. This paper considers a WEIT-enabled device-to-device (D2D) network with the ambient RF transmitters distributed according to a Poisson point process and focuses on the meta distribution of the transferred energy, which is the distribution of the conditional energy outage probability given the locations of the RF transmitters, to show what fraction of devices in the network satisfy the target energy outage constraint if the required transmission energy is given. Furthermore, we derive the meta distribution of the transmission rate under an energy outage constraint and introduce a new notion of transmission efficiency, termed wirelessly powered spatial transmission efficiency, which is defined as the density of concurrently active links that rely on the wireless energy transfer technique and satisfy a certain reliability constraint that has a rate greater than a predefined threshold. Our analysis provides insightful guidelines for the most efficient way to operate a WEIT-enabled self-sustainable D2D communication network.

In this paper, we lay an analytic framework for computing the downlink success probability of cellular networks, taking into account a frequency reuse distance as an interference mitigation scheme. We model the frequency reuse distance using tools from stochastic geometry, namely, we utilize the Matérn hard-core (MHC) point process to capture the effect of interference protection zones created around base stations. To model the overall cellular network, we introduce a new point process composed of N superimposed MHC processes, where each individual MHC process corresponds to a co-channel base station group; this new point process is called the union-MHC (UMHC) process. We further investigate the resulting performance of the UMHC process and present the link success probability in integral form. The success probability can be evaluated for an arbitrary fading model and an arbitrary number of orthogonal resource groups. We test the newly proposed model against the practical data sets from a network operator and observe a good match of the results.

A network model is considered, where Poisson distributed base stations transmit to N power-domain nonorthogonal multiple access (NOMA) users (TIEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA TIEs and consider two different ordering techniques for the NOMA TIEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical TIE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate Rtot, for general N, constrained to: 1) a minimum throughput T for each TIE, 2) identical throughput for all TIEs. We show the existence of: 1) an optimum N that maximizes the constrained Rtotgiven a set of network parameters and 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters N, the constraints, and the ordering technique to balance the Rtotand fairness requirements. We also show that interference-aware TIE clustering can significantly improve performance.

This paper focuses on the meta distributions of the signal-to-interference-plus-noise ratio (SINR) and user-perceived rate in heterogeneous cellular networks (HCNs) with multiple tiers of base stations. On the one hand, it is desirable to offload users to small cells to alleviate the congestion in macrocells; on the other hand, such offloading would in turn cause an SINR degradation of the offloaded users, which needs to be mitigated through interference avoidance based on resource partitioning. Thus, in consideration of both aspects, we provide a general framework for modeling and analyzing joint spectrum allocation and offloading in an HCN using the K-tier homogeneous-independent Poisson model. With it, we derive the per-tier and overall moments of the conditional SINR and rate distribution given the point process, based on which the exact meta distributions are given. We show that the conventional SINR or rate performance evaluated at the typical user (averaging over all tiers and links in the HCN), by itself, is insufficient, and a much sharper version provided by the meta distribution is required in conjunction with the expected value to give a thorough assessment of the benefits of joint resource partitioning and offloading in HCNs.

Rateless coding is a promising forward error correction technique to meet both delay and reliability requirements of emerging wireless applications. However, existing works on rateless codes mostly considered finite networks or ignored the traffic dynamics. In this paper, we present a comprehensive investigation of the end-to-end performance for rateless codes in Poisson bipolar and cellular networks. Specifically, we propose the notion of theend-to-end success probability, which is the success probability given an end-to-end delay requirement, to jointly evaluate the delay performance and transmission reliability of rateless codes. To fully characterize the end-to-end delay, we divide it into two parts, namely the packet waiting time and the transmission time, and provide tractable yet accurate approximations to their statistical distributions. Compared with the previous works, the proposed general framework and the end-to-end performance metric help obtain insights on the role of scheduling, queueing, and coding scheme in practical radio access networks. The approximations are verified to be effective and reliable through simulations. Overall, the results show the significant benefits of rateless codes relative to the fixed-rate codes in terms of the transmission reliability with an end-to-end delay requirement.

The link quality in cellular networks strongly depends on the location of the users relative to the serving and interfering base stations (BSs). This paper proposes a location-dependent BS cooperation scheme for general cellular networks, where BSs are modeled using a stationary point process and the Voronoi diagram forms the cell structure. The cooperation scheme is based on the relative average received signal strength from the three strongest BSs. For the channel model where Rayleigh fading and power-law path loss are considered, each cell is partitioned into three regions based on the relative distance to the three nearest BSs: the cell center region, cell edge region, and cell corner region. The area fraction of each region is tuned by the so-called cooperation level -y ∈ [0, 1]. We study the scheme where users in the above regions receive the non-coherent joint transmission from one, two, and three nearest BSs, respectively. As such, the scheme primarily helps users vulnerable to interference. We analyze the signal-to-interference ratio (SIR) in Poisson networks and show that a moderate -y jointly improves the average SIR performance and the network fairness.

Compared to the standard success (coverage) probability, the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence, we propose a simple approach to approximate the SIR meta distribution for nonPoisson networks based on the ASAPPP (“approximate SIR analysis based on the Poisson point process”) method. We prove that the asymptotic horizontal gap G0between its standard success probability and that for the Poisson point process exactly characterizes the gap between the bth moment of the conditional success probability, as the SIR threshold goes to 0. The gap G0allows two simple approximations of the meta distribution for general HCNs: 1) the per-tier approximation by applying the shift G0to each tier and 2) the effective gain approximation by directly shifting the meta distribution for the homogeneous independent Poisson network. Given the generality of the model considered and the fine-grained nature of the meta distribution, these approximations work surprisingly well.

This paper develops an analytical framework for multi-cell uplink NOMA systems based on stochastic geometry. We propose two scenarios for the clustering of NOMA UEs and derive the Laplace transform of the inter-cell interference taking into account uplink power control. We utilize two different ordering techniques, namely mean signal power- (MSP-) and instantaneous signal-to-intercell-interference-and-noise-ratio- (ISĨNR-) based, for the successive interference cancellation process at the BSs. For each technique, we present a signal-to-interference-and-noise-ratio (SINR) analysis and derive the transmission success probabilities for the NOMA UEs. We show that uplink power control, which generally reduces the signal power disparity between UEs, does not necessarily degrade the NOMA performance. We discuss how UE clustering and the power control exponent impact this finding. ISĨNR-based ordering, which jointly considers path loss, fading, inter-cell interference, and noise, is generally superior to MSP-based ordering. Moreover, we show that the advantage of NOMA vanishes when the target SINR exceeds a certain threshold. A comparison of the two UE clustering scenarios indicates that excluding the UEs which are relatively far from the serving BS may improve the NOMA performance.

Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (PPP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and the beta approximations are evaluated and compared. Key performance metrics, including the mean success probability, the variance of the conditional success probability, the mean local delay, and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve of the conditional success probability of each tier can be tightly approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

This paper presents analytical expressions for the signal-to-interference ratio and the spectral efficiency in macrocellular networks with massive MIMO conjugate beamforming, both with a uniform and a channel-dependent power allocation. These expressions, which apply to very general network geometries, are asymptotic in the strength of the shadowing. Through Monte-Carlo simulation, we verify their accuracy for relevant network topologies and shadowing strengths. Also, since the analysis does not include pilot contamination, we further gauge through Monte-Carlo simulation, the deviation that this phenomenon causes with respect to our results, and hence the scope of the analysis.

The meta distribution of the signal-to-interference ratio (SIR) provides more fine-grained information about the link performance than the standard success probability. This paper studies the reliability in cellular networks with physical layer security constraints using the meta distribution. We consider a cellular network where the BSs are distributed as Possion point process. We provide the distribution of the opportunistic secure spectrum access probability when connection success and secrecy success occurs simultaneously, taking into account the interference correlation. We gain insights on the links reliability in the network under different security levels and the effect on the link reliability of the distance between legitimate user and eavesdropper.

-Non-orthogonal multiple access (NOMA) is a spectrum reutilization technique that superposes messages in the power domain allowing multiple users to be served in the same time-frequency resource block. Successive interference cancellation (SIC) techniques are used for decoding NOMA. A network model is considered where Poisson distributed base stations transmit toNNOMA users each. We present a signal-to-interference-and-noise-ratio analysis for the coverage of the typical user. Due to SIC, coverage implies the ability to decode the messages of all weaker users in the SIC chain. An efficient algorithm for finding a feasible resource allocation that maximizes the cell sum rate ℛtotsubject to a minimum rate constraintTon the individual users is provided for generalN. We show the existence of an optimumNthat maximizes ℛtotgiven a set of network parameters. We also show that NOMA outperforms orthogonal multiple access if the residual intracell interference is below a certain level. The results highlight the importance in choosing network parametersNandTto balance ℛtotand fairness.

Recently a new fundamental performance metric, called the meta distribution of the signal-to-interference ratio (SIR), has been proposed for cellular networks. Compared to the standard success (coverage) probability, the meta distribution provides much more fine-grained information about the network performance. In this paper, we consider general (non-Poisson) network models. However, the exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence we propose a simple approach to approximate the meta distribution for non-Poisson networks, which is based on the ASAPPP (“approximate SIR analysis based on the Poisson point process”) method. For a stationary and ergodic point process model, we prove that the asymptotic horizontal gap G0between its standard success probability and that of the Poisson point process exactly characterizes the gap between the th moment of the conditional success probability, as the SIR threshold goes to G0. Using detailed simulations, we confirm that the meta distribution of an arbitrary stationary and ergodic point process can be approximated by applying the horizontal shift of G0to the meta distribution of the Poisson point process.

This paper focuses on the meta distribution of the signal-to-interference-plus-noise ratio (SINR) and rate in heterogeneous cellular networks (HCNs) with multiple tiers of base stations, where disjoint frequency bands are allocated among tiers and users are associated with each tier with a biased average received power. The meta distribution provides a much sharper version of the “SINR/rate performance” than that merely considered at the typical user through spatial averaging, which gives deep insight into the impacts of heterogeneity, resource coordination, user association, etc., on the performance of individual users. Using tools of stochastic geometry, we develop a general and tractable framework for a fine-grained analysis for HCNs with joint resource partitioning and offloading. With it, we derive exact analytical expressions as well as their asymptotic behaviors for the overall and per-tier moments of the conditional SINR and rate distribution given the point processes, based on which the exact meta distributions are given. We show that although the offloaded users suffer from SINR degradation, the rate performance of all individual users can be improved via load balancing in conjunction with appropriate resource partitioning.

We consider a vehicular network with an underlying regular street system formed by horizontally and vertically oriented streets. We model vehicle locations on each street using Poisson point processes, and each vehicle transmits with some probability following slotted ALOHA. Each receiving vehicle connects to its partner-transmitting vehicle based on the following schemes: 1) Nearest-transmitter reception (NTR), 2) Nearest-transmitter reception with selective thinning (NTR-II), and 3) Nearest-receiver transmission (NRT). In NTR and NTR-II, each receiver receives from its nearest transmitter, whereas in NRT, each transmitter transmits to its nearest receiver. NTR-II is a modified version of NTR, where the transmitters not closest to any of the receivers remain idle. Under each scheme, we calculate the probabilities of successful reception for the general and intersection users, i.e., vehicles not at intersections and at intersections. We study how the nearest-transmitter/receiver distance properties in each scheme differ for general and intersection users, and in turn, how those properties affect their probabilities of successful reception. Also, we show that we can obtain higher data rates in NTR and NTR-II compared to NRT in the high-reliability regime.

This paper focuses on the success probability (or, equivalently, the signal-to-interference-plus-noise ratio (SINR) distribution) at the typical receiver in millimeter wave (mm-wave) device-to-device (D2D) networks. Unlike earlier works, we consider a more general and realistic case where devices in the network are equipped with heterogeneous antenna arrays so that the concurrent transmission beams are varying in width. Specifically, we first establish a general and tractable framework for the target network with Nakagami fading and directional beamforming. Next, we investigate the interactions among beams with different widths and their sensitivities to the adopted model for the antenna pattern. In addition, to show the impact of heterogeneous antenna arrays on the link performance, we derive the success probability of the typical receiver as well as its bounds to get deep insights on the performance of the network.

Device caching has recently been proposed as an efficient way to offload traffic from congested cellular networks. However, previous works usually ignore the fact that, in practice, the user device may not be willing to help others due to the limited battery capacity. In this paper, we introduce cooperation among the device-to-device (D2D) transmitters and propose two novel hybrid caching strategies-single-point caching combined with two-point cooperative caching with joint transmission (SPC-CCJT) or multi-stream transmission (SPC-CCMT)-aiming at saving the energy cost of content deliverers. Using tools from stochastic geometry, we propose an analytical framework of the hybrid caching strategies by modeling the locations of the D2D transmitters as a Gauss-Poisson process (GPP) to accurately capture the clustering and cooperative behaviors. First, we consider a probabilistic caching placement and optimize the caching distribution to maximize the cache hit probability. Second, to compare the performance between different content delivery strategies, we derive the success probability and per-user capacity for SPC, CCJT, and CCMT, respectively. These results are then applied to evaluate the offloading gain and the distribution of the content retrieval delay for SPC-CCJT and SPC-CCMT in the GPP-based D2D networks. It turns out that significant offloading gain and delay improvement can be achieved by hybrid caching with cooperation while the energy cost of each cooperator is kept low.

For buffer-aided tandem networks consisting of relay nodes and multiple channels per hop, we consider two traffic allocation schemes, namely local allocation and global allocation, and investigate the end-to-end latency of a file transfer. We formulate the problem for generic multi-hop queuing systems and subsequently derive closed-form expressions of the end-to-end latency. We quantify the advantages of the global allocation scheme relative to its local allocation counterpart, and we conduct an asymptotic analysis on the performance gain when the number of channels in each hops increases to infinity. The traffic allocations and the analytical delay performance are validated through simulations. Furthermore, taking a specific two-hop network with millimeter-wave (mm-wave) as an example, we derive lower bounds on the average end-to-end latency, where Nakagami-m fading is considered. Numerical results demonstrate that, compared with the local allocation scheme, the advantage of global allocation grows as the number of relay nodes increases, at the expense of higher complexity that linearly increases with the number of relay nodes. It is also demonstrated that a proper deployment of relay nodes in a linear mm-wave network plays an important role in reducing the average end-to-end latency, and the average latency decays as the mm-wave channels become more deterministic. These findings provide insights for designing multi-hop mm-wave networks with low end-to-end latency.

This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the transmitters in a confined region as a single-cluster wireless network. We study the coverage probability for a reference receiver for two strategies; closest-selection, where the receiver is served by the closest transmitter among all transmitters, and uniform-selection, where the serving transmitter is selected randomly with uniform distribution. Second, using Matern cluster processes, we extend our model and analysis to multi-cluster wireless networks. Here, two types of receivers are modeled, namely, closed- and open-access receivers. Closed-access receivers are distributed around the cluster centers of the transmitters according to a symmetric normal distribution and can be served only by the transmitters of their corresponding clusters. Open-access receivers, on the other hand, are placed independently of the transmitters and can be served by all transmitters. In all cases, the link distance distribution and the Laplace transform (LT) of the interference are derived. We also derive closed-form lower bounds on the LT of the interference for single-cluster wireless networks. The impact of different parameters on the performance is also investigated.

The meta distribution provides fine-grained information on the signal-to-interference ratio (SIR) compared with the SIR distribution at the typical user. This paper first derives the meta distribution of the SIR in heterogeneous cellular networks with downlink coordinated multipoint transmission/reception, including joint transmission (JT), dynamic point blanking (DPB), and dynamic point selection/dynamic point blanking (DPS/DPB), for the general typical user and the worst-case user (the typical user located at the Voronoi vertex in a single-tier network). A more general scheme called JT-DPB, which is the combination of JT and DPB, is studied. The moments of the conditional success probability are derived for the calculation of the meta distribution and the mean local delay. An exact analytical expression, the beta approximation, and simulation results of the meta distribution are provided. From the theoretical results, we gain insights on the benefits of different cooperation schemes and the impact of the number of cooperating base stations and other network parameters.

Millimeter-wave (mm-wave) device-to-device (D2D) communication is considered one of the most promising enabling technologies to meet the demanding requirements of future networks. Previous works on mm-wave D2D network analysis mostly considered the case that all devices were equipped with exactly the same number of antennas, whereas real networks are more complicated due to the coexistence of diverse devices. In this paper, we present a comprehensive investigation on the interference characteristics and link performance in mm-wave D2D networks where the concurrent transmission beams are varying in width. First, we establish a general and tractable framework for the target network with Nakagami fading and directional beamforming. To fully characterize the interference, we derive the mean and variance of the interference and then provide an approximation of the interference distribution by a mixture of the inverse gamma and the log-normal distributions. More importantly, the coexistence of varied beamwidths renders their interactions and thus the interference quite complicated and sensitive to the antenna pattern, highlighting the significance of adopting an accurate model for the antenna pattern. Second, to show the impact of heterogeneous antenna arrays on the link performance, we derive the signal-to-interference-plus-noise ratio and rate distributions of the typical receiver as well as their asymptotics, bounds, and approximations to get deep insights on the performance of the network.

The meta distribution of the signal-to-interference ratio (SIR) provides fine-grained information about the performance of individual links in a wireless network. This paper focuses on the analysis of the meta distribution of the SIR for both the cellular network uplink and downlink with fractional power control. For the uplink scenario, an approximation of the interfering user point process with a non-homogeneous Poisson point process is used. The moments of the meta distribution for both scenarios are calculated. Some bounds, the analytical expression, the mean local delay, and the beta approximation of the meta distribution are provided. The results give interesting insights into the effect of the power control in both the uplink and downlink. Detailed simulations show that the approximations made in the analysis are well justified.

We address a fundamental question in wireless networks that, surprisingly, has not been studied before: what is the maximum density of concurrently active links that satisfy a certain outage constraint? We call this quantity the spatial outage capacity (SOC), give a rigorous definition, and analyze it for Poisson bipolar networks with ALOHA. Specifically, we provide exact analytical and approximate expressions for the density of links satisfying an outage constraint and give simple upper and lower bounds on the SOC. In the high-reliability regime where the target outage probability is close to zero, we obtain an exact closed-form expression of the SOC, which reveals the interesting and perhaps counter-intuitive result that all transmitters need to be always active to achieve the SOC, i.e., the transmit probability needs to be set to 1 to achieve the SOC.

Densifying networks and deploying more antennas at each access point are two principal ways to boost the capacity of wireless networks. However, the complicated distributions of the signal power and the accumulated interference power, largely induced by various space-time processing techniques, make it highly challenging to quantitatively characterize the performance of multi-antenna networks. In this paper, using tools from stochastic geometry, a unified framework is developed for the analysis of such networks. The major results are two innovative representations of the coverage probability, which make the analysis of multi-antenna networks almost as tractable as the single-antenna case. One is expressed as an ℓ1-induced norm of a Toeplitz matrix, and the other is given in a finite sum form. With a compact representation, the former incorporates many existing analytical results on single- and multi-antenna networks as special cases and leads to tractable expressions for evaluating the coverage probability in both ad hoc and cellular networks. While the latter is more complicated for numerical evaluation, it helps analytically gain key design insights. In particular, it helps prove that the coverage probability of ad hoc networks is a monotonically decreasing convex function of the transmitter density and that there exists a peak value of the coverage improvement when increasing the number of transmit antennas. On the other hand, in multi-antenna cellular networks, it is shown that the coverage probability is independent of the transmitter density and that the outage probability decreases exponentially as the number of transmit antennas increases.

The uncertainty in the locations of vehicles on streets induced by vehicles passing and queueing make the spatial modeling of vehicles a difficult task. To analyze the performance of vehicle-to-vehicle (V2V) communication for vehicular ad hoc networks (VANETs), accurate spatial modeling is of great importance. In this paper, we concentrate on spatial point process modeling for random vehicle locations in large and small cities, performing empirical experiments with real location data of mobile taxi trajectories recorded by the global positioning system (GPS) in Beijing city of China and Porto city of Portugal. We find that the empirical probability mass functions (PMFs) of the number of taxis in test sets in different regions of Beijing or in Porto all follow a negative binomial (NB) distribution. Based on the above, we show that the Log Gaussian Cox Process (LGCP) model, whose empirical PMF nicely fits the NB distribution, accurately characterizes diverse spatial point patterns of random vehicle location in both large and small cities. This is verified by the minimum contrast method. The LGCP model can be applied to analyze performance metrics (i.e., connectivity, coverage, and capacity) and optimize the practical deployments of VANETs.

In this paper, the meta distribution of the signal-to- interference-plus-noise ratio (SINR) in millimeter wave (mm-wave) device-to-device (D2D) networks is studied, which is the distribution of the conditional SINR distribution given a realization of the point process modeling the network. This analysis provides much more fine-grained information on the performance of individual links than just the mean that is usually evaluated. Modeling the D2D transmitters as a Poisson point process (PPP) and considering the unique mm-wave features, moments of the conditional SINR distribution given the point process are derived in order to calculate analytical expression for the meta distribution. It turns out that when the size of the antenna array tends to infinity, the noise is totally suppressed and the node density becomes the dominating factor affecting the interference in the network. Closed-form approximations of the meta distribution with the beta distribution are also provided. Numerical results give interesting insights into the effects of mm-wave features on the performance of D2D communication.

The analysis of vehicle-to-vehicle communications is generally limited to vehicles on street segments, which are modeled using 1-D point processes. However, it is essential to model the intersections which are crucial for vehicle safety. In this paper, we focus on orthogonal street systems involving intersections with Poisson distributed vehicles on each street. We derive analytical expressions for the success probabilities of two types of users-- the typical general user and the typical intersection user. We show that the the orthogonal street system shares some properties of both 1-D and 2-D Poisson networks. Specifically, the vehicles on the street system behave like 1-D and 2-D Poisson point processes of vehicles in the high-reliability and low-reliability regimes, respectively. Also, we deduce that the success probability of the typical general/intersection user is upper bounded by the minimum of the success probabilities of the 1-D and 2-D Poisson networks.

Reliable communication is a key requirement in wireless networks. For ad hoc networks, satisfying this requirement is challenging due to the interference caused by uncoordinated concurrent transmissions. In this regard, we provide a simple distributed way for a transmitter to meet the target reliability in an interference-limited network. Specifically, for the Poisson bipolar network with Rayleigh fading, we propose a method for a transmitter to decide on its rate (or, equivalently, the signal-to-interference ratio threshold) such that each link in the network achieves a certain reliability. Here the distributed means that the transmitter only knows the distance from its receiver to the nearest interferer and the fading statistics. Based on this local information, we present a semi-heuristic approach to find the distribution of the signal-to- interference ratio (SIR) threshold corresponding to the total interference power from all interferers. For this purpose, we use the property of the interference that it follows a stable distribution for the standard path loss model. We show that the SIR threshold follows the Weibull distribution.

The application of stochastic geometry to the analysis of wireless networks is shown to be propelled by (i) a clean separation of time scales, (ii) abstraction of small-scale effects via ergodicity, and (iii) an interference model reflecting the receiver's lack of knowledge of how individual interference terms are faded. These steps render the analysis simpler and more precise, and more amenable to incorporating subsequent features. Specifically, the paper presents easy-to-evaluate expressions for the ergodic spectral efficiency of cellular networks with single-user multiple-input multiple-output (MIMO).

We introduce a new notion of capacity, termed spatial outage capacity (SOC), which is defined as the maximum density of concurrently active links that have a success probability greater than a predefined threshold. For Poisson bipolar networks, we provide exact analytical and approximate expressions for the density of concurrently active links satisfying an outage constraint. In the high-reliability regime, we obtain an exact closed-form expression of the SOC, which gives its asymptotic scaling behavior.

Millimeter wave (mm-wave) communications is considered a promising technology for 5G networks. Exploiting beamforming gains with large-scale antenna arrays to combat the increased path loss at mm-wave bands is one of the defining features. However, previous works on mm-wave network analysis usually adopted oversimplified antenna patterns for tractability, which can lead to significant deviation from the performance with actual antenna patterns. In this paper, using tools from stochastic geometry, we carry out a comprehensive investigation on the impact of directional antenna arrays in mm-wave networks. We first present a general and tractable framework for coverage analysis with arbitrary distributions for interference power and arbitrary antenna patterns. It is then applied to mm-wave ad hoc and cellular networks, where two sophisticated antenna patterns with desirable accuracy and analytical tractability are proposed to approximate the actual antenna pattern. Compared with previous works, the proposed approximate antenna patterns help to obtain more insights on the role of directional antenna arrays in mm-wave networks. In particular, it is shown that the coverage probabilities of both types of networks increase as a non-decreasing concave function with the antenna array size. The analytical results are verified to be effective and reliable through simulations, and numerical results also show that large-scale antenna arrays are required for satisfactory coverage in mm-wave networks.

Enabling device-to-device (D2D) communications in millimeter-wave (mm-wave) networks is of critical importance for the next-generation mobile networks to support very high data rates (multi-gigabits-per-second) for mobile devices. In this paper, we provide a fine-grained performance analysis of the mm-wave D2D communication networks. Specifically, we first establish a general and tractable framework to investigate the performance of mm-wave D2D networks using the Poisson bipolar model integrated with several features of the mm-wave band. To show what fraction of users in the network achieve target reliability if the required signal-to-interference-plus-noise ratio (SINR) (or QoS requirement) is given, we derive the meta distributions of the SINR and the data rate. Interestingly, in mm-wave D2D networks, the standard beta approximation for the meta distribution does not work very well when highly directional antenna arrays are used or the node density is small. To resolve this issue, we provide a modified approximation by using higher moments of the conditional SINR distribution, which is shown to be closer to the exact result. On this basis, we also derive the mean local delay and spatial outage capacity to provide a comprehensive investigation on the impact of mm-wave features on the performance of D2D communication.

Rateless codes have been shown to provide robust error correction over a wide range of binary and noisy channels. Using a stochastic geometry model, this paper studies the performance of rateless codes in the cellular downlink and compares it with the performance of fixed-rate codes. For the case of Rayleigh fading, an accurate approximation is proposed for the distribution of the packet transmission time of K -bit information packets using rateless codes. The two types of channel coding schemes are compared by evaluating the typical user and per-user success probability and the rate. Based on both the analytical results and simulations, the paper shows that rateless coding provides a significant throughput gain relative to fixed-rate coding. Moreover, the benefit is not restricted to the typical user but applies to all users in the cellular network.

We study the performance of device-to-device (D2D) communication underlaying cellular wireless network in terms of the meta distribution of the signal-to-interference ratio (SIR), which is the distribution of the conditional SIR distribution given the locations of the wireless nodes. Modeling D2D transmitters and base stations as Poisson point processes (PPPs), moments of the conditional SIR distribution are derived in order to calculate analytical expressions for the meta distribution and the mean local delay of the typical D2D receiver and cellular downlink user. It turns out that for D2D users, the total interference from the D2D interferers and base stations is equal in distribution to that of a single PPP, while for downlink users, the effect of the interference from the D2D network is more complicated. We also derive the region of transmit probabilities for the D2D users and base stations that result in a finite mean local delay and give a simple inner bound on that region. Finally, the impact of increasing the base station density on the mean local delay, the meta distribution, and the density of users reliably served is investigated with numerical results.

This paper shows how the application of stochastic geometry to the analysis of wireless networks is greatly facilitated by: (i) a clear separation of time scales; (ii) the abstraction of small-scale effects via ergodicity; and (iii) an interference model that reflects the receiver's lack of knowledge of how each individual interference term is faded. These procedures render the analysis both more manageable and more precise, as well as more amenable to the incorporation of subsequent features. In particular, the paper presents analytical characterizations of the ergodic spectral efficiency of cellular networks with single-user multiple-input multiple-output and sectorization. These characterizations, in the form of easy-to-evaluate expressions, encompass the coverage, the distribution of spectral efficiency over the network locations, and the average thereof.

Rateless codes have been shown to provide robust error correction over wireless channels. Using a stochastic geometry model, this paper studies the performance of cellular downlink with packet transmission based on rateless codes. For the case of Rayleigh fading, a novel and accurate approximation is proposed for the distribution of the packet transmission time of rateless codes. The performance of rateless codes is compared to that of fixed rate codes by evaluating the user rate and success probability achievable with the two channel coding schemes. Based on both the proposed analysis and network simulation, the paper shows that rateless coding provides both coverage and throughput gains relative to fixed rate coding, not only for the typical user but for all users in the cellular network.

In this paper, we consider cellular networks with the base station locations modeled by a Poisson point process. However, unlike earlier works, we consider the cases of no fading and partial fading and analyze the asymptotic behavior of the distribution of the downlink signal-to-interference ratio (SIR) of a typical user. This non-fading case has been elusive since the standard Laplace trick cannot be used. We provide the asymptotics of the SIR distribution FSIR(θ) = P(SIR <; θ) as θ → 0 for the cases of no-fading and partial fading, where only the interfering base stations are subject to fading. We also introduce a new point process-the squared relative distance process-that facilitates the asymptotic analysis of the SIR and expedites simulations.

Gauss-Poisson processes (GPPs) are a class of clustered point processes, which include the Poisson point process as a special case and have a simpler structure than the general Poisson cluster point processes. A key property of the GPP is that it is completely defined by its first- and second-order statistics. In this paper, we first show the properties of the GPP and provide an approach to fit the GPP to a given point set. A fitting example is presented. We then propose the GPP as a model for wireless networks that exhibit clustering behavior and derive the signal-to-interference-ratio distributions for different system models: 1) the basic model where the desired transmitter is independent of the GPP and all nodes in the GPP are interferers; 2) the non-cooperative model where the desired transmitter is one of the nodes in the GPP; and 3) the cooperative model, where the nodes in a GPP cluster transmit cooperatively. The simulation results indicate that a significant gain can be achieved with cooperation.

The current cellular networks have evolved to be more randomly, irregularly, and heterogeneously deployed to meet the exponential growth of mobile data traffic and the demand for seamless coverage, making the signal-to-interference ratio (SIR) distribution more challenging to analyze. Therefore, in this paper, we propose two simple approximative approaches to the SIR distribution of general heterogeneous cellular networks (HCNs) based on the ASAPPP method, which stands for “approximate SIR analysis based on the Poisson point process” and the MISR (mean interference-to-signal ratio)-based gain for each individual tier of the HCNs. Specifically, we first establish a per-tier ASAPPP approximation to general HCNs and then present an effective gain ASAPPP method as a further simplification when the path loss exponents are the same for all the tiers, that is, we give an explicit expression for the effective gain Geffof general HCNs such that the SIR distribution is obtained by scaling the SIR threshold θ to θ/Geff. The asymptotic behavior for the tail of the SIR distribution is also given. Furthermore, to highlight the simplicity and effectiveness of the approximative approaches, we derive the exact distribution of the SIR in the two-tier HCNs modeled by β-Ginibre and Poisson point processes and compare it with the approximate results. The results demonstrate that the proposed approaches give a simple yet excellent approximation for the SIR distribution.

We investigate the stable packet arrival rate region of a discrete-time slotted random access network, where the sources are distributed as a Poisson point process. Each of the sources in the network has a destination at a given distance and a buffer of infinite capacity. The network is assumed to be random but static, i.e., the sources and the destinations are placed randomly and remain static during all the time slots. We employ tools from queueing theory as well as point process theory to study the stability of this system using the concept of dominance. The problem is an instance of the interacting queues problem, further complicated by the Poisson spatial distribution. We obtain sufficient conditions and necessary conditions for stability. Numerical results show that the gap between the sufficient conditions and the necessary conditions is small when the access probability, the density of transmitters, or the SINR threshold is small. The results also reveal that a slight change of the arrival rate may greatly affect the fraction of unstable queues in the network.

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem from stochastic geometry. We proceed to apply our result in the calculation of expected values involving interference in wireless Poisson networks. Based on this, we derive outage probabilities for transmissions in a Poisson network with Nakagami fading. Our results extend the stochastic geometry toolbox used for the mathematical analysis of interference-limited wireless networks.

Vehicle-to-vehicle safety communications based on the dedicated short-range communication technology have the potential to enable a set of applications that help avoid traffic accidents. The performance of these applications, largely affected by the reliability of communication links, stringently ties back to the MAC and PHY layer design, which has been standardized as IEEE 802.11p. The link reliabilities depend on the signal-to-interference-plus-noise ratio (SINR), which, in turn, depends on the locations and transmit power values of the transmitting nodes. Hence, an accurate network model needs to take into account the network geometry. For such geometric models, however, there is a lack of mathematical understanding of the characteristics and performance of IEEE 802.11p. Important questions such as the scalability performance of IEEE 802.11p have to be answered by simulations, which can be very time consuming and provide limited insights to future protocol design. In this paper, we investigate the performance of IEEE 802.11p by proposing a novel mathematical model based on queuing theory and stochastic geometry. In particular, we extend the Matérn hard-core type-II process with a discrete and nonuniform distribution, which is used to derive the temporal states of backoff counters. By doing so, concurrent transmissions from nodes within the carrier sensing ranges of each other are taken into account, leading to a more accurate approximation to real network dynamics. A comparison with Network Simulator 2 (ns2) simulations shows that our model achieves a good approximation in networks with different densities.

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift (or gain) of the distribution of the most tractable model, the Poisson point process (PPP). To study and explain this behavior, this paper focuses on general single-tier network models with nearest-base station association and studies the asymptotic gain both at 0 and at infinity. We show that the gain at 0 is determined by the so-called mean interference-to-signal ratio (MISR) between the PPP and the network model under consideration, while the gain at infinity is determined by the expected fading-to-interference ratio (EFIR). The analysis of the MISR is based on a novel type of point process, the so-called relative distance process, which is a one-dimensional point process on the unit interval [0,1] that fully determines the SIR. A comparison of the gains at 0 and infinity shows that the gain at 0 indeed provides an excellent approximation for the entire SIR distribution. Moreover, the gain is mostly a function of the network geometry and barely depends on the path loss exponent and the fading. The results are illustrated using several examples of repulsive point processes.

The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward, but it only provides limited information on the success probabilities of the individual links. This paper focuses on the meta distribution of the SIR, which is the distribution of the conditional success probability Ps given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as “What fraction of users in a Poisson cellular network achieve 90% link reliability if the required SIR is 5 dB?” Interestingly, in the bipolar model, if the transmit probability p is reduced while increasing the network density λ such that the density of concurrent transmitters λp stays constant as p → 0, Psdegenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability p, the variance of Psapproaches a non-zero constant when p is reduced to 0 while keeping the mean success probability constant.

ABSTRACT This paper presents a geometric analysis of the convergence condition for the Foschini–Miljanic power control algorithm. The Möbius transform is exploited for the first time to analyze the convergence condition of the power control algorithm. A novel MAC scheme based on the Möbius transform is proposed for the link scheduling problem and proven to improve spatial reuse by scheduling links in pairs if possible. The peak power constraint of wireless networks is analyzed theoretically, and applications to random networks are explored in detail. Observations from the analysis of peak power constraints are also applied to the design of the MAC scheme (Möbius MAC) to improve the convergence speed and system performance. Simulation results show that our Möbius MAC can roughly double the performance of CSMA in terms of transport density. Applications to cognitive networks and heterogeneous networks are discussed. Copyright © 2014 John Wiley & Sons, Ltd.

In all current models for cellular networks, independent randomness in the positions of the base stations (BSs) and the propagation conditions is assumed. In practice, however, in coverage-oriented deployments, where the goal is to achieve good baseline coverage, cellular operators place the base stations further apart if propagation is favorable, and vice versa. We thus propose a new class of cellular model, where BSs are deployed such that all cell edge users achieve a minimum target signal power level from the serving BS. The spatial structure of the BSs is a result of the propagation environment and the target signal power. We call such network models joint spatial and propagation (JSP) models. To formulate such models, we assume the path loss follows a power law with a variable path loss exponent, so that the target signal power is achieved at the cell edges, given the distribution of the BSs. The coverage probability, defined as the probability that the signal-to- interference-plus-noise-ratio (SINR) exceeds a threshold, is evaluated and compared with the standard Poisson and lattice models. Our results show that networks with Poisson distributed BSs appear to the user like lattice networks if the dependence between BS placement and propagation is accounted for.

In [1], it was conjectured that the permanent of a P-lifting θ↑Pof a matrix θ of degree M is less than or equal to the Mth power of the permanent perm(θ), i.e., perm(θ↑P) ≤ perm(θ)Mand, consequently, that the degree-M Bethe permanent permM,B(θ) of a matrix θ is less than or equal to the permanent perm(θ) of θ, i.e., permM,B(θ) ≤ perm(θ). In this paper, we prove these related conjectures and show some properties of the permanent of block matrices that are lifts of a matrix. As a corollary, we obtain an alternative proof of the inequality permB(θ) ≤ perm(θ) on the Bethe permanent of the base matrix θ, which, in contrast to the one given in [2], uses only the combinatorial definition of the Bethe-permanent. The results have implications in coding theory. Since a P-lifting corresponds to an M-graph cover and thus to a protograph-based LDPC code, the results may help explain the performance of these codes.

This paper proposes an adaptive and distributed MAC scheme for wireless networks with full-duplex radios. Full-duplex (FD) radios can exchange data simultaneously using the same frequency band and potentially double the throughput. On the other hand, it will inevitably cause extra interference to the network to use FD transmission instead of half-duplex (HD) transmission. Hence, there is a tradeoff between interference and throughput for wireless networks with FD radios. In order to mitigate the interference and maximize the network throughput, we propose the Optimum Adaptive ALOHA (OA-ALOHA) MAC scheme based on the nodes' local information about their neighbors. We derive each node's optimal transmit probability that maximizes the throughput and achieves proportional fairness. Our numerical results show that if the network is using the proposed adaptive MAC scheme, significantly better network throughput can be achieved than with the non-adaptive MAC schemes. HD can achieve around 50% maximum throughput gain using adaptive ALOHA while FD more than 70%. Moreover, a Simplified Adaptive ALOHA (SA-ALOHA) MAC scheme is also included that is based on an approximation of the optimum transmit probability and achieves comparable performance.

The crushing demands for mobile data traffic drive the current cellular networks to become more heterogeneous, making the signal-to-interference ratio (SIR) distribution more difficult to analyze. In this paper we propose a simple approximative approach to the SIR distribution of heterogeneous cellular networks (HCNs) based on the ASAPPP method which stands for ``approximate SIR analysis based on the Poisson point process'' and the MISR (mean interference-to-signal ratio)-based gain for each individual tier of the HCN. The results demonstrate that this approach gives a tight approximation and asymptotically a lower bound for the coverage probability.

It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift of the distribution of the most tractable model, the Poisson point process. This paper makes a first step towards explaining this remarkable property by showing that the asymptotics of the SIR distribution near 0 and near infinity can only differ by a constant.

The stable packet arrival rate region of the discrete-time slotted ALOHA network with the sources distributed as a static Poisson point process is investigated here. The problem is a generalization and extension of interacting queues problem, in which the physical layer is abstracted. Employing tools from queueing theory as well as point process theory, we obtain sufficient conditions and necessary conditions for stability by the concept of dominance. Numerical results show that the gap between sufficient conditions and necessary conditions is small, and the results also reveal how these conditions vary with system parameters.

This paper investigates the throughput for wireless network with full-duplex radios using stochastic geometry. Full-duplex (FD) radios can exchange data simultaneously with each other. On the other hand, the downside of FD transmission is that it will inevitably cause extra interference to the network compared to half-duplex (HD) transmission. In this paper, we focus on a wireless network of nodes with both HD and FD capabilities and derive and optimize the throughput in such a network. Our analytical result shows that if the network is adapting an ALOHA protocol, the maximal throughput is always achieved by scheduling all concurrently transmitting nodes to work in FD mode instead of a mixed FD/HD mode or HD mode regardless of the network configurations. Moreover, the throughput gain of using FD transmission over HD transmission is analytically lower and upper bounded.

Transmission of layered source information, such as scalable video coding (SVC), over heterogenous wireless networks is considered in this work. Scalable transmission enables dynamic adaption of source information to the condition of user equipments, and thus is suitable for heterogenous networks in which the transmission link quality varies substantially. Leveraging tools in stochastic geometry, a comprehensive analysis is conducted for several different transmission protocols, focusing on two key performance metrics, Standard-Definition outage probability and High-Definition probability. The proposed transmission protocols are compared in different aspects, and the benefit of interference cancellation is shown to be significant.

Due to its tractability, a multitier model of mutually independent Poisson point processes (PPPs) for heterogeneous cellular networks (HCNs) has recently been attracting much attention. However, in reality, the locations of the BSs, within each tier and across tiers, are not fully independent. Accordingly, in this paper, we propose two HCN models with inter-tier dependence (Case 1) and intra-tier dependence (Case 2), respectively. In Case 1, the macro-base station (MBS) and the pico-base station (PBS) deployments follow a Poisson point process (PPP) and a Poisson hole process (PHP), respectively. Under this setup and conditioning on a fixed serving distance (distance between a user and its nearest serving BS), we derive bounds on the outage probabilities of both macro and pico users. We also use a fitted Poisson cluster process to approximate the PHP, which is shown to provide a good approximation of the interference and outage statistics. In Case 2, the MBSs and the PBSs follow a PPP and an independent Matern cluster process, respectively. Explicit expressions of the interference and the outage probability are derived first for fixed serving distance and second with random distance, and we derive the outage performance, the per-user capacity, and the area spectral efficiency (ASE) for both cases. It turns out that the proposed Case 2 model is a more appropriate and accurate model for a HCN with hotspot regions than the multitier independent PPP model since the latter underestimates some key performance metrics, such as the per-user capacity and the ASE, by a factor of 1.5 to 2. Overall, the two models proposed provide good tradeoffs between the accuracy, tractability, and practicability.

This paper studies downlink communication in a heterogeneous cellular network where a set of geographically separated base stations (BSs) cooperates in transmitting data to a common receiver. If a decoding error occurs, data is cooperatively retransmitted by a possibly different set of BSs, such that the receiver can benefit from spatiotemporal BS cooperation. Specific cooperation techniques studied in this paper include joint transmission, base station silencing, and the Alamouti space-time code. Using tools from stochastic geometry, the coverage probability at the typical user is characterized as an integral function of the network parameters and the sets of cooperating BSs. The expressions derived reveal the existence of two qualitatively different operating regimes. In the high-coverage regime, the typical user is diversity-limited, so cooperation techniques exploiting spatiotemporal diversity are highly effective in increasing coverage. It is shown that retransmissions always yield time diversity, while channel state information at the transmitters is required to harvest spatial diversity via joint transmission. In the low-coverage regime, on the other hand, the typical user is interference-limited, so cooperation techniques such as joint transmission and base station silencing are effective in increasing coverage as they suppress part of the interference power.

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the outage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) is smaller than a threshold) as the threshold goes to zero. We show that, remarkably, the slope of the outage probability (in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the success probabilities of the PPP and another point process in the high-reliability regime (where the success probability is near 1). To demonstrate the usefulness of the ADG for the characterization of the SINR distribution, we investigate the outage probabilities and the ADGs for different point processes and fading statistics by simulations.

Small cell networks are regarded as a promising candidate to meet the exponential growth of mobile data traffic in cellular networks. With a dense deployment of access points, spatial reuse will be improved, and uniform coverage can be provided. However, such performance gains cannot be achieved without effective intercell interference management. In this paper, a novel interference coordination strategy, called user-centric intercell interference nulling, is proposed for small cell networks. A main merit of the proposed strategy is its ability to effectively identify and mitigate the dominant interference for each user. Different from existing works, each user selects the coordinating base stations (BSs) based on the relative distance between the home BS and the interfering BSs, called the interference nulling (IN) range, and thus interference nulling adapts to each user's own interference situation. By adopting a random spatial network model, we derive an approximate expression of the successful transmission probability to the typical user, which is then used to determine the optimal IN range. Simulation results shall confirm the tightness of the approximation, and demonstrate significant performance gains (about 35-40%) of the proposed coordination strategy, compared with the non-coordination case. Moreover, it is shown that the proposed strategy outperforms other interference nulling methods. Finally, the effect of imperfect channel state information (CSI) is investigated, where CSI is assumed to be obtained via limited feedback. It is shown that the proposed coordination strategy still provides significant performance gains even with a moderate number of feedback bits.

This paper investigates the throughput for wireless network with full-duplex radios using stochastic geometry. Full-duplex (FD) radios can exchange data simultaneously with each other. On the other hand, the downside of FD transmission is that it will inevitably cause extra interference to the network compared to half-duplex (HD) transmission. Moreover, the residual self-interference has negative effects on the network throughput. In this paper, we focus on a wireless network of nodes with both HD and FD capabilities and derive and optimize the throughput in such a network. Our analytical result shows that if the network is adopting an ALOHA protocol, the maximal throughput is achieved by scheduling all concurrently transmitting nodes to work in either FD mode or HD mode depending on one simple condition. Moreover, the effects of imperfect self-interference cancellation on the signal-to-interference ratio (SIR) loss and throughput are also analyzed based on our mathematical model. We rigorously quantify the impact of imperfect self-interference cancellation on the throughput gain, transmission range, and other metrics, and we establish the minimum amount of self-interference suppression needed for FD to be beneficial.

We design and implement a software-radio system for rapid on-off-division duplex (RODD), a scheme to achieve virtual full-duplex communication at the level of a transmission frame. RODD is based on the insight that it is not necessary to separate a node's transmission and reception at the timescale of a frame. Instead, RODD allows each node in a network to follow a different random on-off signaling signature to transmit during its own on-slots and listen to its neighbors through its own off-slots. Over one frame interval, each node broadcasts its message to its neighbors while recovering its neighbors' messages from the superposed signals received via its own off-slots. In this paper, we describe an RODD prototype to prove its key concepts, including redesigned synchronization and coding schemes. Simulation results are presented for comparison with the measurements obtained from a software-defined radio implementation of RODD. The effects of on-off signaling on the performance are investigated experimentally. In particular, the bit error rate is measured and compared with the simulation results. Our results indicate that virtual full duplex is feasible on a USRPs/LabVIEW platform via RODD.

The spatial structure of transmitters in wireless networks plays a key role in evaluating mutual interference and, hence, performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability, and practicability tradeoffs, we introduce and promote the β-GPP, which is an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second-moment approach, and then provide approximations of the interference distribution by three known probability density functions. In addition, to show that the model is relevant for cellular systems, we derive the coverage probability of a typical user and find that the fitted β-GPP can closely model the deployment of actual base stations in terms of coverage probability and other statistics.

In heterogeneous cellular networks (HCNs), the macrocell network is usually assumed to be overlaid by multiple independent tiers of small cells. However, in reality, the locations of the base stations (BSs) belonging to different tiers are not fully independent. Accordingly, in this paper, we propose a two-tier HCN model with inter-tier dependence, where the macro-BS (MBS) and the pico-BS (PBS) deployments follow a Poisson point process (PPP) and a Poisson hole process (PHP), respectively. Under this setup, we derive bounds on the outage probabilities of both macro users and pico users, and then use a fitted Poisson cluster process to approximate the PHP, which is shown to provide a good approximation of the interference and outage. The results show that the model with inter-tier dependence appears closer to the real deployment than the two extremes with full regularity (the triangular lattice) and complete randomness (the PPP). An important conclusion is that significant gains can be obtained if PBSs are deployed smartly (away from MBSs).

This paper studies spatiotemporal cooperation between base stations in the presence of interference in a heterogeneous cellular network. The focus of the paper is the cooperative retransmission scenario, where a set of randomly located base stations that are selected based on their average received powers, possibly belonging to different network tiers, jointly transmit data in each transmission. If a decoding error occurs in the first transmission, data is cooperatively retransmitted by a possibly different set of BSs, such that the receiver can benefit from spatiotemporal BS cooperation. Using tools from stochastic geometry, the coverage probability at the typical user is characterized as an integral function of the network parameters and the sets of cooperating BSs. An integral expression for the coverage probability is also derived for the case when the typical user is able to perform maximum ratio combining (MRC) of the received copies in two transmissions. Numerical evaluation shows that in the high coverage regime spatiotemporal cooperation outperforms joint transmission with no retransmissions and that the gains extend to all regimes if the user has MRC capability.

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the coverage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) exceeds a threshold) as the threshold goes to zero. We show that, surprisingly, the slope of the outage probability (complementary to the coverage probability, in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the coverage probability of the PPP and another point process in the high-reliability regime (where the coverage probability is near 1). To demonstrate the usefulness of the ADG for the characterization of coverage probabilities, we investigate the coverage properties and the ADGs for different point processes and fading statistics by simulations.

In cellular networks, cell size reduction is an important technique for improving the spectral reuse and achieving higher data rates. In addition, it results in power savings as it leads to a decrease in transmit power. However, it is not clear if the transmit power can be indefinitely decreased with the cell sizes. In this paper, we analyze the impact of transmit power reduction (cell size reduction) on the performance of the network. More precisely, we obtain a lower bound on the transmit power such that a minimum coverage and a minimum data rate can be guaranteed. We then analyze the area power consumption metric, which denotes the total power consumed per unit area. Under the constraints of target coverage and target data rate, the area power consumption is minimized and the optimal base station density is obtained. For a path loss exponent α > 4, we observe the existence of a minimum cell size below which shrinking the cell would result in an overall increase of power. However, for α ≤ 4, there exists no such optimal cell-size, as the area power consumption increases with base station density.

The RTS/CTS handshake mechanism in WLAN is studied using stochastic geometry. The effect of RTS/CTS is treated as a thinning procedure for a spatially point process that models the potential transceivers in a WLAN, and the resulting concurrent transmitter processes are described. Exact formulas for the intensity of the concurrent transmitter processes and the mean interference are established. The analysis yields useful results for understanding how the design parameters of RTS/CTS affect the interference in the network.

Gauss-Poisson processes (GPPs) are a class of clustered point processes, which include the Poisson point process as a special case and have a simpler structure than general Poisson cluster point processes. In this paper, we propose the GPP as a model for wireless networks that exhibit clustering behavior. We calculate the success probabilities and provide bounds for three kinds of GPP networks: (1) the basic model where the desired transmitter is independent of the GPP and all nodes in the GPP are interferers; (2) the non-cooperative model where the desired transmitter is one of the nodes in the GPP; (3) the cooperative model where both nodes in a two-node cluster of the GPP serve a receiver cooperatively using non-coherent joint transmission. Our results show that the bounds, especially the upper bounds, provide good approximations for different operating regimes.

Modeling cellular base stations (BSs) as a homogeneous Poisson point process (PPP), this paper provides exact expressions, in terms of a finite integral, for the coverage probability with inter-cell interference coordination (ICIC) and intra-cell diversity (ICD). Despite the fact that both ICIC and ICD can significantly improve the coverage probability, they improve coverage in drastically different ways in the high-reliability regime, where the user outage probability goes to zero. In particular, we show that ICD can provide order gain while ICIC only offers linear gain. This finding contrasts the recent result showing the absence of diversity gain in retransmission in ad hoc networks.

In a network application, channel coding alone is not sufficient to reliably transmit a message of finite length K from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. In this scenario RLNC has been shown to have a throughput advantage over TDMA schemes as K→∞ and q→∞. In this paper we focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel code rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small message lengths K and small q.

Motivated by the ongoing discussion on coordinated multipoint in wireless cellular standard bodies, this paper considers the problem of base station cooperation in the downlink of heterogeneous cellular networks. The focus of this paper is the joint transmission scenario, where an ideal backhaul network allows a set of randomly located base stations, possibly belonging to different network tiers, to jointly transmit data, to mitigate intercell interference and hence improve coverage and spectral efficiency. Using tools from stochastic geometry, an integral expression for the network coverage probability is derived in the scenario where the typical user located at an arbitrary location, i.e., the general user, receives data from a pool of base stations that are selected based on their average received power levels. An expression for the coverage probability is also derived for the typical user located at the point equidistant from three base stations, which we refer to as the worst case user. In the special case where cooperation is limited to two base stations, numerical evaluations illustrate absolute gains in coverage probability of up to 17% for the general user and 24% for the worst case user compared with the noncooperative case. It is also shown that no diversity gain is achieved using noncoherent joint transmission, whereas full diversity gain can be achieved at the receiver if the transmitting base stations have channel state information.

This paper provides a unified framework to study the performance of successive interference cancellation (SIC) in wireless networks with arbitrary fading distribution and powerlaw path loss. An analytical characterization of the performance of SIC is given as a function of different system parameters. The results suggest that the marginal benefit of enabling the receiver to successively decode k users diminishes very fast with k, especially in networks of high dimensions and small path loss exponent. On the other hand, SIC is highly beneficial when the users are clustered around the receiver and/or very low-rate codes are used. In addition, with multiple packet reception, a lower per-user information rate always results in higher aggregate throughput in interference-limited networks. In contrast, there exists a positive optimal per-user rate that maximizes the aggregate throughput in noisy networks. The analytical results serve as useful tools to understand the potential gain of SIC in heterogeneous cellular networks (HCNs). Using these tools, this paper quantifies the gain of SIC on the coverage probability in HCNs with nonaccessible base stations. An interesting observation is that, for contemporary wireless systems (e.g., LTE and WiFi), most of the gain of SIC is achieved by canceling a single interferer.

In mobile networks, distance variations caused by node mobility generate fluctuations in the channel gains. Such fluctuations can be treated as another type of fading besides multipath effects. In this paper, the interference statistics in mobile random networks are characterized by incorporating the distance variations of mobile nodes to the channel gain fluctuations. The mean interference is calculated at the origin and at the border of a finite mobile network. The network performance is evaluated in terms of the outage probability. Compared to a static network, the interference in a single snapshot does not change under uniform mobility models. However, random waypoint mobility increases (decreases) the interference at the origin (at the border). Furthermore, due to the correlation of the node locations, the interference and outage are temporally and spatially correlated. We quantify the temporal correlation of the interference and outage in mobile Poisson networks in terms of the correlation coefficient and conditional outage probability, respectively. The results show that it is essential that routing, MAC, and retransmission schemes need to be smart (i.e., correlation-aware) to avoid bursts of transmission failures.

We evaluate the end-to-end delay of a multihop transmission scheme that includes a source, a number of relays, and a destination, in the presence of interferers located according to a Poisson point process. The medium access control (MAC) protocol considered is a combination of TDMA and ALOHA, according to which nodes located a certain number of hops apart are allowed to transmit with a certain probability. Based on an independent transmissions assumption, which decouples the queue evolutions, our analysis provides explicit expressions for the mean end-to-end delay and throughput, as well as scaling laws when the interferer density grows to infinity. If the source always has packets to transmit, we find that full spatial reuse, i.e., ALOHA, is asymptotically delay-optimal, but requires more hops than a TDMA-ALOHA protocol. The results of our analysis have applications in delay-minimizing joint MAC/routing algorithms for networks with randomly located nodes. We simulate a network where sources and relays form a Poisson point process, and each source assembles a route to its destination by selecting the relays closest to the optimal locations. We assess both theoretically and via simulation the sensitivity of the end-to-end delay with respect to imperfect relay placements and route crossings.

Inter-cell interference coordination (ICIC) and intra-cell diversity (ICD) play important roles in improving cellular downlink coverage. By modeling cellular base stations (BSs) as a homogeneous Poisson point process (PPP), this paper provides explicit finite-integral expressions for the coverage probability with ICIC and ICD, taking into account the temporal/spectral correlation of the signal and interference. In addition, we show that, in the high-reliability regime, where the user outage probability goes to zero, ICIC and ICD affect the network coverage in drastically different ways: ICD can provide order gain, whereas ICIC only offers linear gain. In the high-spectral efficiency regime where the SIR threshold goes to infinity, the order difference in the coverage probability does not exist; however, a linear difference makes ICIC a better scheme than ICD for realistic path loss exponents. Consequently, depending on the SIR requirements, different combinations of ICIC and ICD optimize the coverage probability.

The capacity of wireless networks is fundamentally limited by interference. However, little research has focused on the interference correlation, which may greatly increase the local delay (namely the number of time slots required for a node to successfully transmit a packet). This paper focuses on the question whether increasing randomness in the MAC, specifically frequency-hopping multiple access (FHMA) and ALOHA, helps to reduce the effect of interference correlation. We derive closed-form results for the mean and variance of the local delay for the two MAC protocols and evaluate the optimal parameters that minimize the mean local delay. Based on the optimal parameters, we identify two operating regimes, the correlation-limited regime and the bandwidth-limited regime. Our results reveal that while the mean local delays for FHMA with N sub-bands and for ALOHA with transmit probability p essentially coincide when p=1/N, a fundamental discrepancy exists between their variances. We also discuss implications from the analysis, including an interesting mean delay-jitter tradeoff, and convenient bounds on the tail probability of the local delay, which shed useful insights into system design.

The local delay, defined as the mean time it takes a node to connect to its nearest neighbor, is a fundamental performance metric in a wireless network. For a network with Poisson distributed nodes, we find its scaling behavior (as a function of the rate of transmission) for different types of nearest-neighbor and the two extreme cases of mobility (infinite mobility and no mobility). Remarkably, it turns out that the level of mobility has hardly any effect on the scaling behavior of the local delay; it affects the pre-constant only.

Channel coding alone is not sufficient to reliably transmit a message of finite length from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. We focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel coding rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small K and small q.

The feasibility of successive interference cancellation (SIC) depends on the received power ordering from different users, which, in turn, depends on the fading distribution, path loss function and network geometry. Using a framework based on stochastic geometry, this paper studies the aggregate throughput in d-dimensional random wireless networks with SIC capability. We consider networks with arbitrary fading distribution, power-law path loss; the network geometry is governed by a non-uniform Poisson point process (PPP). Our results demonstrate how the performance of SIC changes as a function of the network geometry, fading distribution, and the path loss law. An important observation is that, in interference-limited networks, lower per-user information rate always results in higher aggregate throughput, while in noisy networks, there exists a positive optimal per-user rate at which the aggregate throughput is maximized.

Communication between two neighboring nodes is a very basic operation in wireless networks. Yet very little research has focused on the local delay in networks with randomly placed nodes, defined as the mean time it takes a node to connect to its nearest neighbor. We study this problem for Poisson networks, first considering interference only, then noise only, and finally and briefly, interference plus noise. In the noiseless case, we analyze four different types of nearest-neighbor communication and compare the extreme cases of high mobility, where a new Poisson process is drawn in each time slot, and no mobility, where only a single realization exists and nodes stay put forever. It turns out that the local delay behaves rather differently in the two cases. We also provide the low- and high-rate asymptotic behavior of the minimum achievable delay in each case. In the cases with noise, power control is essential to keep the delay finite, and randomized power control can drastically reduce the required (mean) power for finite local delay.

For communication between two neighboring nodes in wireless networks, the local delay is defined as the time it takes a node to successfully transmit a packet. Previous research focuses on the local delay in static or infinitely mobile Poisson networks with ALOHA. In this paper, we extend the local delay results to Poisson networks with finite mobility. The results obtained show that mobility helps reduce the local delay. Bounds of the local delay in mobile Poisson networks are derived for different mobility and transmission models. The phase transition that marks the jump of the local delay from finite to infinite is also characterized.

The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set.

The interference in wireless networks is temporally correlated, since the node or user locations are correlated over time and the interfering transmitters are a subset of these nodes. For a wireless network where (potential) interferers form a Poisson point process and use ALOHA for channel access, we calculate the joint success and outage probabilities of n transmissions over a reference link. The results are based on the diversity polynomial, which captures the temporal interference correlation. The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links. We also determine the complete joint SIR distribution for two transmissions and the distribution of the local delay, which is the time until a repeated transmission over the reference link succeeds.

This paper provides a unified framework to study the performance gain of successive interference cancellation (SIC) in d-dimensional interference-limited networks with arbitrary fading distribution and power-law path loss. We derive bounds on the mean number of users that can be successively decoded and the probability of successively decoding k users. Our results suggest that, without power control, the marginal benefit of enabling the receiver to successively decode k users diminishes very fast with k, especially in networks of high dimensions and small path loss exponent. On the other hand, SIC is more beneficial when the users are clustered around the receiver, or very low-rate codes are used.

We propose and experimentally demonstrate a novel approach to improve the packet delivery efficiency on a vulnerable downlink (e.g., from a transmitter to a far-away receiver) using superposition coding, a multiuser transmission scheme that forgoes orthogonal transmission and deliberately introduces interference among signals at the transmitter. On a software radio platform that uses off-the-shelf point-to-point channel codes, we show that a transmitter serving multiple links can use simple two-user superposition codes to dramatically improve (compared to time division multiplexing) the packet delivery efficiency on its most vulnerable links. Interestingly, our results suggest that superposing signals of far-away users on to those of high-traffic users yields the maximum benefits - implying that the degrees-of-freedom gain in doing so can more than compensate for the increased interference from signal superposition.

This paper first presents a geometric analysis of the convergence condition for the Foschini-Miljanic power control algorithm. Then, based on the analysis, the Dynamic Distributed Power Control MAC (D2PC-MAC) scheme is proposed for wireless networks. D2PC-MAC achieves high spatial reuse, since power control enables nesting of concurrent links, thereby achieving a high density of successful links. The MAC scheme starts by trying to accommodate all links and then eliminating transmitters causing too much interference in two stages, a local stage and a global stage. Both stages operate in a fully distributed manner. Simulation results confirm the expected gains relative to standard MAC schemes: the spatial density of successful links is increased by about a factor of 4 compared to CSMA and about a factor of 8 compared to ALOHA.

We consider a two-hop cellular system in which the mobile nodes help the base station by relaying information to the dead spots. While two-hop cellular schemes have been analyzed previously, the distribution of the node locations has not been explicitly taken into account. In this paper, we model the base station locations deterministically and the mobile stations by a point process on the plane. The node with the best channel to the destination that received information in the first hop acts as a relay to the destination (selection cooperation), and we obtain the success probability of this two-hop scheme, accounting for the interference from all other cells. We use tools from stochastic geometry and point process theory to analyze this two-hop opportunistic relaying scheme. Besides the results obtained, a main contribution of the paper is to introduce a mathematical framework that can be used to analyze arbitrary relaying schemes.

This paper studies power control strategies in interference-limited wireless networks with Poisson distributed nodes. We concentrate on two sets of strategies: single-node optimal power control (SNOPC) strategies and Nash equilibrium power control (NEPC) strategies. SNOPC strategies maximize the expected throughput of the power-controllable link given that all the other transmitters do not use power control. Under NEPC strategies, no individual node of the network can achieve a higher expected throughput by unilaterally deviating from these strategies. We show that under mean and peak power constraints at each transmitter, the SNOPC and NEPC strategies are ALOHA-type random on-off power control policies, whose transmit powers and transmit probabilities depend on the knowledge about the network at each transmitter. Moreover, the resulting NEPC strategies achieve a higher spatial average throughput of the network than constant power transmission. These results suggest that ALOHA can be viewed not only as a MAC scheme but also as a stable and efficient power control scheme.

Characterizing the performance of ad hoc networks is one of the most intricate open challenges; conventional ideas based on information-theoretic techniques and inequalities have not yet been able to successfully tackle this problem in its generality. Motivated thus, we promote the totally asymmetric simple exclusion process (TASEP), a particle flow model in statistical mechanics, as a useful analytical tool to study ad hoc networks with random access. Employing the TASEP framework, we first investigate the average end-to-end delay and throughput performance of a linear multihop flow of packets. Additionally, we analytically derive the distribution of delays incurred by packets at each node, as well as the joint distributions of the delays across adjacent hops along the flow. We then consider more complex wireless network models comprising intersecting flows, and propose the partial mean-field approximation (PMFA), a method that helps tightly approximate the throughput performance of the system. We finally demonstrate via a simple example that the PMFA procedure is quite general in that it may be used to accurately evaluate the performance of ad hoc networks with arbitrary topologies.

Consider a cognitive radio network with two types of users: primary users (PUs) and cognitive users (CUs), whose locations follow two independent Poisson point processes. The cognitive users follow the policy that a cognitive transmitter is active only when it is outside the primary user exclusion regions. We found that under this setup the active cognitive users form a point process called the Poisson hole process. Due to the interaction between the primary users and the cognitive users through exclusion regions, an exact calculation of the interference and the outage probability seems unfeasible. Instead, two different approaches are taken to tackle this problem. First, bounds for the interference (in the form of Laplace transforms) and the outage probability are derived, and second, it is shown how to use a Poisson cluster process to model the interference in this kind of network. Furthermore, the bipolar network model with different exclusion region settings is analyzed.

We design and implement a software-radio system for Superposition Coding (SC), a multiuser transmission scheme that deliberately introduces interference among user signals at the transmitter, using a library of off-the-shelf point-to-point channel codes. We experimentally determine the set of rate-pairs achieved by this transmission scheme under a packet-error constraint. Our results suggest that SC can provide substantial gains in spectral efficiencies over those achieved by orthogonal schemes such as Time Division Multiplexing. Our findings also question the practical utility of the Gaussian approximation for the inter-user interference in Superposition-Coded systems.

The delay till success (DTS) is the mean number of transmissions needed, averaged over the fading, until a single packet is successfully received (decoded) over a wireless link. This paper shows that under a mean and a peak power constraint, random power control can significantly reduce the DTS. We derive the optimal power control policies that minimize the DTS at one link of given length. For most commonly used fading distributions, these optimal power control policies are random on-off policies, whose parameters depend on the fading statistics and the link distance. We present two applications of this result in the context of noise-limited wireless networks: minimizing the local delay (mean delay for successful nearest-neighbor communication) and minimizing the local anycast delay (mean delay for a transmission to any node).

As a fundamental source of delay in wireless networks, the local delay is defined as the mean time, in number of time slots, until a packet is successfully received (decoded) over a link. This paper shows that with mean power and peak power constraints at each node, power control can significantly reduce the local delay. We show that, for links with Rayleigh fading and random length, there exists a simple power control strategy, which turns out to be optimal in reducing the local delay. This strategy acts as an ALOHA-type random on-off power control policy whose parameters depend on the link distance. The optimal power control policy as well as its variations are compared with constant power transmission and other simple random power control policies.

In wireless networks, interference that is generated by undesired transmitters dominantly limits network performance. The correlation of node locations (in mobile or static networks) makes the interference temporally correlated. Such correlation affects network performance greatly, and hence needs to be quantified. In this paper, we quantify the temporal correlation of the interference in mobile Poisson networks. More specifically, we obtain closed-form expressions for the interference correlation coefficient ρ in Poisson line networks under various mobility models. When the mean speed of nodes v̅ increases, we show that ρ is asymptotically proportional to v̅-1. Moreover, multi-path fading and random MAC schemes reduce the temporal correlation of the interference. These results are extended to higher-dimensional networks.

Most channel access schemes for cognitive radio only consider using the idle periods of the primary users. Such schemes are not using the spectrum efficiently, since transmission opportunities also arise when a primary transmitter is active but its corresponding primary receiver is far away from the cognitive user. By detecting the signal power of the acknowledgments, a cognitive user is able to estimate the distance and channel condition between the primary receiver and itself. Then if the primary receiver is far away, the cognitive user can transmit simultaneously with the primary transmitter without affecting the primary link. Based on this idea, the spatio-temporal channel access scheme, utilizing both idle periods and spatial reuse, can be applied. This paper provides fundamental analysis of the channel access delays and shows the advantage of using the spatio-temporal access scheme in the carrier sense multiple access (CSMA)-based network with bi-directional links.

This paper proposes a location-based MAC (LMAC) scheme for wireless networks with randomly placed nodes. This scheme regulates channel access by sharing local location information among transmitters. A lattice approximation approach is used to derive upper and lower bound for the success probability for a typical transmission attempt. Numerical results show that with the node density and link distance fixed, the optimal LMAC provides a much higher density of successful transmissions than CSMA and ALOHA.

Channel coding alone is not sufficient to reliably transmit a message of finite length from a source to one or more destinations. To ensure that no data is lost, channel coding on the physical layer needs to be combined with rateless erasure correcting schemes such as automatic repeat request (ARQ) or random linear network coding (RLNC) on a higher layer. In this paper we consider channel coding on a binary symmetric channel and random linear network coding for erasure correction. Given a message of length K and network coding over a finite Galois field of size q, we obtain the optimal number of blocks for network coding that minimizes the expected number of transmissions. We consider both a single link and broadcast to n destinations. As the field size of network coding gets large and the expected coding overhead in blocks becomes small, we show that, given our assumptions, the benefit of using a larger channel coded block outweighs the advantage of employing network coding over many blocks and the optimal number of number of blocks tends to one, making RLNC equivalent to simple ARQ.

Secrecy graphs model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the location of the nodes and the eavesdroppers are given by Poisson point processes, with and without power constraints. We present bounds for different types of percolation, including in-, out - and undirected percolation.

In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers η goes to 0. We prove for general node distributions and fading statistics that the success probability Ps~ 1 - γηκfor η → 0, and provide values of γ and κ for a number of important special cases. We show that κ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.

Outage probabilities in wireless networks depend on various factors: the node distribution, the MAC scheme, and the models for path loss, fading, and transmission success. In prior work on outage characterization for networks with randomly placed nodes, most of the emphasis was put on networks whose nodes are Poisson-distributed and where ALOHA is used as the MAC protocol. In this paper, we provide a general framework for the analysis of outage probabilities in the high-reliability regime. The outage probability characterization is based on two parameters: the intrinsic spatial contention γ of the network, introduced by Haenggi in a previous work, and the coordination level achieved by the MAC as measured by the interference scaling exponent κ introduced in this paper. We study outage probabilities under the signal-to-interference ratio (SIR) model, Rayleigh fading, and power-law path loss and explain how the two parameters depend on the network model. The main result is that the outage probability approaches γηκas the density of interferers η goes to zero, and that κ assumes values in the range 1 ≤ κ ≤ α/2 for all practical MAC protocols, where α is the path-loss exponent. This asymptotic expression is valid for all motion-invariant point processes. We suggest a novel and complete taxonomy of MAC protocols based mainly on the value of κ. Finally, our findings suggest a conjecture that bounds the outage probability for all interferer densities.

In wireless networks, distance variations caused by node mobility generate fluctuations of the channel gains. Such fluctuations can be treated as another type of fading besides multi-path effects. In this paper, we characterize the interference statistics in mobile random networks by mapping the distance variations of mobile nodes to the channel gain fluctuations. Network performance is evaluated in terms of the outage probability. A nearest-interferer approximation is employed. This approximation provides a tight lower bound on the outage probability. Comparing to a static network, we show that the interference distribution does not change under high mobility and random walk models, but random waypoint mobility increases interference.

We consider a wireless multi-hop network with sources that are Poisson distributed and relays which are placed on the source-destination line. Given a combined TDMA/ALOHA MAC protocol, we explore the following question of optimal spatial reuse: Increasing the number of nodes that are simultaneously scheduled to transmit in a route allows nodes to transmit more often. At the same time, it results in an increase of intra-route and inter-route interference, which has a negative impact on the end-to-end delay and throughput. In a regime of large source-destination distances R, we find that it is delay-optimal for either only one node, or a number of nodes that increases linearly in R, to be scheduled in each slot, depending on the ALOHA probability. If the transmission probability is also optimized, we find that maximum spatial reuse is delay-optimal. Scaling laws for the end-to-end delay and throughput are derived in all cases.

This paper studies the value of allowing multiple transmitters to share all of the available bandwidth to concurrently transmit to a single receiver with multi-packet decoding capability. While such coordination can be bandwidth-efficient, it increases the density of interferers when many such multiple-access clusters exist in the network. On the other hand, orthogonal schemes such as FDMA may not be as bandwidth-efficient but operate at lower interferer densities due to orthogonalization. We take the first step towards understanding this trade-off. In particular, we analyze equidistant transmitters sending data using a coordination scheme based on the optimum strategy for a Gaussian multiple access channel. In terms of the throughputs seen in a typical cluster in a Poisson network, this form of coordination has little or no benefit when compared to FDMA. We also find that the increased interference due to multiple coordinated transmissions reduces the efficacy of successive decoding.

Superposition coding is a well-known capacity-achieving coding scheme for stochastically degraded broadcast channels. Although well-studied in theory, it is important to understand issues that arise when implementing this scheme in a practical setting. In this paper, we present a software-radio based design of a superposition coding system on the GNU Radio platform with the Universal Software Radio Peripheral acting as the transceiver frontend. We also study the packet error performance and discuss some issues that arise in its implementation.

Communication between two neighboring nodes is the most basic operation in wireless networks. Yet very little research has focused on the local delay, defined as the mean time it takes a node to connect to its nearest neighbor. In this paper, we derive the local delay in Poisson networks with ALOHA and find the conditions for which the local delay is finite. It turns out that while the local delay is always finite in highly mobile networks, there is a phase transition in static networks, i.e., there is a maximum transmit probability above which the local delay is infinite.

We consider a cognitive radio network with two types of users: primary users (PUs) and cognitive users (CUs), whose locations follow two independent Poisson point processes. The cognitive users follow the policy that a cognitive transmitter is active only when it is outside the primary user exclusion regions. Due to the interaction between the primary users and the cognitive users through exclusion regions, an exact calculation of the interference and the outage probability seems unfeasible. Instead, we derive bounds for the interference (in the form of Laplace transform) and the outage probability. Two network models, the bipolar and the nearest-neighbor model, are considered.

We consider a multihop wireless line network with a single unidirectional data flow and show that by limiting the buffer sizes at the relay nodes to unity, the flow of traffic in the system can be efficiently regulated in a completely distributed fashion. Upon exerting this simple transmission policy, we find that the transport of packets in the wireless network is analogous to the flow of particles in the totally asymmetric simple exclusion process (TASEP). Using existing results from statistical mechanics, we characterize the end-to-end delay and throughput performance of multihop wireless line networks for two different channel access schemes. Additionally, we apply our findings towards the design of long networks. This paper also aims at promoting the TASEP as a powerful tool for analyzing the performance of ad hoc networks.

We study the delay and throughput in a wireless multihop network with sources that form a Poisson point process and relays which are placed equidistantly on the source-destination line. A combined TDMA/ALOHA MAC protocol with intra-route TDMA and inter-route ALOHA is employed. We give bounds on the delay-optimal number of hops and derive the asymptotic delay-throughput tradeoff as the source-destination distance R gets large. The delay includes both the service times and waiting times in the buffers of the typical route. One main finding is that when the transmission probability and number of hops are jointly optimized for minimum delay, the number of hops scales as R2/3while the delay scales as R4over3.

Network-wide adoption of a multipacket transmission scheme such as Superposition Coding (SC) for local “one-to-many” communication results in mutually interfering “broadcast” clusters. We analyze the benefits of SC and traditional Frequency Division (FD) with this interference via a utility function that measures the rate of information transfer per unit area. In particular, we study transmitters forming a Poisson point process and using ALOHA for medium access. For a fixed bandwidth allocation, FD allows spatial reuse to be independently optimized for each frequency band. On the other hand, with SC for a fixed power allocation, the optimal spatial reuse depends on the relative contribution of each link to the utility function. Since optimal spatial reuse is a function of the network geometry, the gains provided by SC depend on the geometry of the receiver node placement.

In data collection applications of low-end sensor networks, a major challenge is ensuring reliability without a significant goodput degradation. Short hops over high-quality links minimize per-hop transmissions, but long routes may cause congestion and load imbalance. Longer links can be exploited to build shorter routes, but poor links may have a high energy cost. There exists a complex interplay among routing performance (reliability, goodput, energy efficiency), link estimation, congestion control, and load balancing; we design a routing architecture, Arbutus, that exploits this interplay, and perform an extensive experimental evaluation on testbeds of 100-150 Berkeley motes.

We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability.

We consider the effect of network throughput on the convergence of a specific class of distributed averaging algorithms, called consensus algorithms. These algorithms rely on iterative computation of the desired average by message passing among the nodes. It is thus assumed that the rate of convergence should benefit from greater network connectivity. However, one must also account for the additional network resources that establishing such a connectivity would entail. In this paper, we study this problem in the context of randomly-placed consensus-seeking nodes that are connected through a dense wireless network, i.e., whose capacity is interference-limited. By analyzing the outage of each communication link along with results from mixing times of Markov chains, we obtain scaling laws for the mixing times of fastest-converging consensus topologies over such networks.

We consider a time-slotted two-hop wireless system in which the sources transmit to the relays in the even time slots (first hop) and the relays forward the packets to the destinations in the odd time slots (second hop). Each source may connect to multiple relays in the first hop. In the presence of interference and without tight coordination of the relays, it is not clear which relays should transmit the packet. We propose four decentralized methods of relay selection, some based on location information and others based on the received signal strength (RSS).We provide a complete analytical characterization of these methods using tools from stochastic geometry. We use simulation results to compare these methods in terms of end-to-end success probability.

In routing protocols for wireless sensor networks energy efficiency is of paramount importance. Reliability-oriented protocols discard lossy links to avoid the significant energy cost of packet loss. The downside is that nodes with a particularly favorable channel tend to be overused: their lifespan is curtailed and the total amount of data delivered by the network may be significantly reduced. This problem is particularly critical for the nodes that provide access to the sink, since they have to carry the weight of the whole network. The use of load balancing schemes can be expected to provide significant lifetime benefits: rather than always using the nodes with the best channel, traffic is redistributed over a larger number of relays. We quantify the benefits of load balancing by comparing a routing protocol with embedded load balancing to a reliability-oriented protocol. We present and interpret experimental evidence of the benefits that stem from load balancing, but at the same time we also show that there are situations in which load balancing does not help.

In a wireless network, the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Analyzing the connectivity of such a network using static graphs would lead to pessimistic performance results. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the network MAC contention and introduce a random dynamic multi-digraph to model its connectivity. We first provide analytical results about the degree distribution of the graph. Next, defining the path formation time as the minimum time required for a causal path to form between the source and destination on the dynamic graph, we derive the distributional properties of the connection delay using techniques from first-passage percolation and epidemic processes.We show that the delay scales linearly with the distance and provide asymptotic results (with respect to time) for the positions of the nodes which are able to receive information from a transmitter located at the origin. We also provide simulation results to support the theoretical results.

We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA/ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized. We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops.

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

The one tutorial and 22 papers in this special issue focus on geometry and random graph for the analysis and design of wireless networks. The papers are organized into five groups: Topology; Outage, throughput, capacity, and scaling laws; Connectivity and coverage; Co-existence of disparate wireless networks and cognitive radio; and Distributed algorithms.

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form aPoissonclusterprocesson the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.

In the above titled paper (ibid., vol 54, no. 12, pp. 5500-5510, Dec 08), the table containing the list of symbols was corrupted during the publication process. The proper symbol table is presented here.

Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access scheme (set of transmitting nodes). For the performance analysis, a new parameter, the so- called spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0. Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unit-distance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.

The multihop spatial reuse Aloha (MSR-Aloha) protocol was recently introduced by Baccelli et aL, where each transmitter selects the receiver among its feasible next hops that maximizes the forward progress of the head of line packet towards its final destination. They identify the optimal medium access probability (MAP) that maximizes the spatial density of progress, defined as the product of the spatial intensity of attempted transmissions times the average per-hop progress of each packet towards its destination. We propose a variant called longest edge routing where each transmitter selects its longest feasible edge, and then identifies a packet in its backlog whose next hop is the associated receiver. The main contribution of this work (and of Baccelli et aL) is the use of stochastic geometry to identify the optimal MAP and the corresponding optimal spatial density of progress.

The analytical end-to-end (e2e) performance of a wireless multihop network is largely unknown, because of the interconnections between several factors involved. Customarily, the nodes are often assumed to be spatially uncorrelated so that they can be analyzed in isolation, which is valid when all the traffic flows are independent. In practice, however, most traffic flows are correlated and cause spatial correlation among nodes. The results based on the assumption of spatially uncorrelated nodes may be far from the performance of real networks. In this paper, we aim to study the impact of the spatial correlation on the e2e delay in a wireless line network (WLN). In particular, we use queueing theory to reveal that the burstiness, the temporal correlation of the traffic flow and the underlying medium access control (MAC), together determine the spatial correlation, from which an analysis of the e2e delay of a WLN is accomplished.

In this paper we derive the tail properties of interference for any stationary and isotropic spatial distribution of transmitting nodes. Previously the properties of interference were known only when the nodes are distributed as a homogeneous Poisson point process on the plane. We show the effect of a singular path loss model on the tail distribution of the interference. When the path loss function has a singularity at the origin, the interference is shown to be a heavy-tailed distribution under very mild conditions. When the path loss is bounded, the distribution of the interference is predominantly dictated by the fading. We also provide asymptotically tight upper and lower bounds on the CDF of the interference, and discuss the effectiveness of using a Gaussian approximation for modelling the interference.

A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The underlying point process models considered are lattices and Poisson point processes. In the lattice case, analogies to standard bond and site percolation can be exploited to determine percolation thresholds. In the Poisson case, the node degrees are determined and percolation is studied using analytical bounds and simulations. It turns out that a small density of eavesdroppers already has a drastic impact on the connectivity of the secrecy graph.

The transport capacity of a dense ad hoc network with n nodes scales like radicn. We show that the transport capacity divided by radicn approaches a non-random limit with probability one when the nodes are i.i.d. distributed on the unit square. We prove that the transport capacity under the protocol model is a subadditive Euclidean functional and use the machinery of subadditive functions in the spirit of Steele to show the existence of the limit.

The hot spot problem is a typical byproduct of the many-to-one traffic pattern that characterizes most wireless sensor networks: the nodes with the best channel to the sink are overloaded with traffic from the rest of the network and experience a faster energy depletion rate than their peers. Routing protocols for sensor networks typically use a reliability metric to avoid lossy links and thus directly exacerbate the problem. Significant advantages can be obtained by embedding a load balancing scheme at the network layer, as we show with the design and implementation of Arbutus, a novel routing protocol for wireless sensor networks with a built-in load balancing scheme. By imposing a special structure on the collection tree, privileging longer hops, and accounting for network load in the route selection process, Arbutus reduces the impact of hot spots on network lifetime without a deterioration of the end-to-end reliability performance. An implementation of Arbutus on Berkeley motes and the MoteLab testbed shows a 30% reduction in the network traffic load needed to achieve the same packet delivery rate as an existing mote-oriented protocol. This provides key benefits such as a significant lifetime gain and increased fault tolerance.

In wireless networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. A unified framework is introduced that permits the geometric characterization of fading by incorporating the fading process into the point process model. Concretely, assuming nodes are distributed in a stationary Poisson point process inRd, the properties of the point processes that describe the path loss with fading are analyzed. The main applications are single-hop connectivity and broadcasting.

This paper applies spectral efficiency as a performance measure for routing schemes and considers how to obtain a good route in a wireless network. The objective for this study is to combine different perspectives from networking and information theory in the design of routing schemes. The problem of finding the optimum route with the maximum spectral efficiency is difficult to solve in a distributed fashion. Motivated by an information-theoretic analysis, this paper proposes two suboptimal alternatives, namely, the approximatelyideal- path routing (AIPR) scheme and the distributed spectrumefficient routing (DSER) scheme. AIPR finds a path to approximate an optimum regular path and requires location information. DSER is more amenable to distributed implementations based on the Bellman-Ford or Dijkstra's algorithms. The spectral efficiencies of AIPR and DSER for random networks approach that of nearest-neighbor routing in the low signal-to-noise ratio (SNR) regime and that of single-hop routing in the high SNR regime. In the moderate SNR regime, the spectral efficiency of DSER is up to twice that of nearest-neighbor or single-hop routing.

We consider a hybrid wireless network, in which the low-power nodes collect data and pass it to the data aggregation nodes (base stations). The low-power nodes are assumed to form a Poisson point process and communicate to the base stations using spread spectrum. We derive bounds to the probability of sensor node isolation, when the base stations are arranged randomly or in a regular fashion.

In ad hoc networks with random node distribution, the underlying point process model and the channel fading process are usually considered separately. We provide a unified framework for the geometric characterization of fading by incorporating the fading process into the point process model. Concretely, assuming nodes are distributed in a stationary Poisson point process in Rd, we analyze the properties of the point processes that describe the path loss with fading. Applications include connectivity and broadcasting.

The simple, yet powerful concept of an ldquoerristorrdquo and its ldquoerristancerdquo has recently been introduced for ad hoc networks and applied to scenarios such as retransmission (time diversity), path diversity, or a combination thereof. We extend this formalism to the case of spatial diversity, realized by employing multiple antennas at each node. Based on this framework, one can efficiently analyze and design Rayleigh-faded MIMO ad hoc networks that employ selection combining. The mathematically tractable definition of the erristor term greatly simplifies the study of a multiple-antenna network and helps solve problems based on end-to-end reliability or resource allocation easily, which we illustrate in an example. Moreover, this technique demonstrates the superiority in performance of MIMO over single-antenna routing schemes, particularly at high SNR.

A new fading model is proposed and discussed that combines the uncertainties in the transmission distance as well as small-scale fading. If nodes are assumed to be distributed according to a Poisson point process and the fading is Rayleigh, the joint fading distribution is particularly simple. Interpreting fading as a stochastic mapping, we show that a node cannot infer on the presence of fading by measuring link qualities. Other applications of the fading model include connectivity, opportunistic communication, and probabilistic progress

Multipath fading heavily contributes to the unreliability of wireless links, causing fairly large deviations from link quality predictions based on path loss models; its impact on wireless sensor networks is considerable. Although analytical models provide a probabilistic description, multipath fading is a deterministic phenomenon. Moreover, in the case of static nodes, fading is time-invariant. We illustrate its spatial nature with experimental evidence obtained using lower-end sensing node hardware. We also show the limitations of the supposed immunity of wideband radios to multipath fading in indoor deployments.

Multipath fading heavily contributes to the unreliability of wireless links and is normally seen as a negative phenomenon hindering proper radio communication. However, fading can also improve the chances of reliable communication over channels that would otherwise be unusable, as our experimental evidence shows. In the context of wireless sensor networks, we show that limited motion of the base station may be used to obtain a considerable spatial diversity benefit through the exploitation of induced fading. We compare our limited mobility approach to multi-antenna systems, which are commonly used to achieve spatial diversity, and we illustrate these concepts with the help of experimental results. Moreover, we analyze how spatial diversity relates to network lifetime

We introduce and discuss a novel link model that incorporates both uncertainty in the fading coefficients and the node distances for ad hoc networks with randomly placed nodes. The main result is the complete distribution of the received power for a transmission between a node and its n-th nearest neighbor. Several applications of the proposed fading model are discussed, including connectivity, opportunistic communication, and localization.

The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for power-limited and bandwidth-limited communication regimes. We regard channel state information (CSI) at the receiver and point-to-point capacity-achieving codes for the additive white Gaussian noise (AWGN) channel as practical features, interference cancellation (IC) as possible, but less practical, and synchronous cooperation (CSI at the transmitters) as impractical. We consider a communication network with a single source node, a single destination node, and N-1 intermediate nodes placed equidistantly on a line between them. We analyze the minimum total transmit power needed to achieve a desired end-to-end rate for several schemes and demonstrate that multihop communication with spatial reuse performs very well in the power-limited regime, even without IC. However, within a class of schemes not performing IC, single-hop transmission (directly from source to destination) is more suitable for the bandwidth-limited regime, especially when higher spectral efficiencies are required. At such higher spectral efficiencies, the gap between single-hop and multihop can be closed by employing IC, and we present a scheme based upon backward decoding that can remove all interference from the multihop system with an arbitrarily small rate loss. This new scheme is also used to demonstrate that rates of O(logN) are achievable over linear wireless networks even without synchronous cooperation.

Uniformly random or Poisson distributions are widely accepted models for the location of the nodes in wireless sensor networks if nodes are deployed in large quantities and there is little control over where they are dropped. On the other hand, by placing nodes in regular topologies, we expect benefits both in coverage and efficiency of communication. We describe and analyze a basic localized algorithm and three modifications for topology control that provide a tradeoff between performance and deployment cost. The objective is to regularize the topology for improved energy efficiency. The basic algorithm produces quasiregular networks, which only use nodes as sentries and relays that are approximately evenly spaced, thereby emulating a regular grid topology. It is shown that quasiregular networks have a significant energy and lifetime advantage compared with purely random networks. We consider two specific types of quasiregular networks: the ones that are based on a Gaussian deviation about an ideal grid point (type A), and the ones that consist of a subset of nodes taken from a Poisson point process (type B). We show that the two types are equivalent for a certain density of the Poisson point process and, in particular, that in both cases the deviation from the ideal regular grid follows a Rayleigh distribution, whereas the distance between nearest neighbors is Ricean

For wireless ad hoc networks with stationary and deterministically placed nodes, finding the optimal placement of the nodes is an interesting and challenging problem, especially under energy and QoS constraints. We study and compare the performance of several networks with regular topologies utilizing a Rayleigh fading link model. For nearest neighbor and shortest path routing, analytical expressions of the path efficiency, delay, and energy consumption for a given end-to-end reception probability are derived. For the interference analysis, the maximum throughput and optimum transmit probability are determined, and a simple MAC scheme is compared with an optimum scheduler, yielding lower and upper performance bounds.

This paper studies the end-to-end (e2e) delay performance of a multihop wireless network fed with a single constant bit rate (CBR) source. Two MAC schemes are investigated, m-phase TDMA and probabilistic slotted ALOHA. A delay model is used to analyze the resulting tandem queueing system and derive tight upper bounds on the delay mean. The e2e delay linearly increases with the route length and its distribution converges to a Gaussian distribution. For channels with reception probability greater than 0.5, TDMA significantly outperforms ALOHA. For unreliable channels, the situation is less clear

We derive outage expressions and throughput bounds for wireless networks subject to different sources of nondeterminism. The degree of uncertainty is characterized by the location of the network in the uncertainty cube whose three axes represent the three main sources of uncertainty in interference-limited networks: the node distribution, the channel gains, and the channel access. The range for the coordinates is [0,1], where 0 indicates complete determinism, and 1 a maximum degree of randomness (nodes distributed in a Poisson point process, fading with fading figure 1, and ALOHA channel access, respectively)

Abstract — In this paper, we present closed-form ex-pressions of the average per-node throughput for sensor networks with a slotted ALOHA MAC protocol in Rayleigh fading channels. We compare networks with three regular topologies in terms of per-node throughput, transmit efficiency, and transport capacity. In particular, for square lattice networks, we present an analysis of the dependence of the maximum throughput and optimum transmit proba-bility on the signal-to-interference-ratio threshold required for successful reception. For random networks with nodes distributed according to a two-dimensional Poisson point process, the average per-node throughput is analytically characterized and numerically evaluated. It turns out that although regular networks have an only slightly higher per-node throughput than random networks for the same link distance, regular topologies have a significant benefit when the end-to-end throughput in multihop connections is considered. I.

Diversity schemes permit efficient communication over fading channels but are often hard to analyze and design in networks with many nodes. For Rayleigh-fading channels, there exists an interesting relationship between resistive circuits and time and path diversity mechanisms in wireless ad hoc networks. A resistor-like network element, the erristor, representing the normalized noise-to-signal ratio, is introduced. Given an end-to-end packet delivery probability, the logarithmic mapping from link reception probabilities to erristor values greatly simplifies the problems of power allocation and the selection of time and path diversity schemes, which is illustrated in a number of examples. We focus on transmission strategies with selection combining and simple noncoherent "decode-and-forward" strategies, which is motivated by their practicality. Thanks to its conceptual simplicity, the formalism that is developed provides valuable insight into the benefits of diversity mechanisms.

The distribution of Euclidean distances in Poisson point processes is determined. The main result is the density function of the distance to the n-nearest neighbor of a homogeneous process in Ropfm, which is shown to be governed by a generalized Gamma distribution. The result has many implications for large wireless networks of randomly distributed nodes

This paper addresses the routing problem for large wireless networks of randomly distributed nodes with Rayleigh fading channels. First, we establish that the distances between neighboring nodes in a Poisson point process follow a generalized Rayleigh distribution. Based on this result, it is then shown that, given an end-to-end packet delivery probability (as a quality of service requirement), the energy benefits of routing over many short hops are significantly smaller than for deterministic network models that are based on the geometric disk abstraction. If the permissible delay for short-hop routing and long-hop routing is the same, it turns out that routing over fewer but longer hops may even outperform nearest-neighbor routing, in particular for high end-to-end delivery probabilities.

Traditionally, the routing problem is addressed at the network layer, an approach that has been extended to the wireless realm. In wireless multihop networks, however, strict layer-base protocol design leads to substantial inefficiencies. This paper addresses the routing problem for large wireless ad hoc networks from a fundamental point of view, not constrained by particular protocol implementations or layered architectures, but taking into account the properties of the wireless channel. First, an analytical channel model is presented that is based on Rayleigh fading. It demonstrates how noise and interference effects can be separated, and how each interfering transmission affects the packet reception probability. Second, the distribution of node distances in networks with uniformly randomly placed nodes is derived. These two ingredients are used to discuss the benefits of different routing strategies. In particular, short-hop and long-hop routing schemes are compared. Further, cooperative strategies such as multipath routing and cooperative diversity are briefly discussed as techniques that are enabled by the broadcast nature of the wireless channel.

In this paper, various fast transmission strategies for sending information from a source s over a large distance to a target t in ad hoc wireless networks where the nodes are distributed as a Poisson process of intensity is presented. The existence of an infinite component, i.e., percolation, is not sufficient for our problem since the proportion of vertices in the infinite component may be very low. To achieve connectivity the power must increase with the number of vertices, since there is some positive chance that a vertex is isolated. Result shows that with directional transmissions, even with very low power there exist points at arbitrarily large distance that can communicate.

After deriving the distribution of the distance to the n/sup th/ nearest neighbor in uniformly random networks of any dimension we establish that nearest-neighbor routing schemes perform poorly in random networks. We suggest and analyze an improved scheme that approaches the performance of regular networks.

We consider a wireless communication system with a single source node, a single destination node, and multiple relay nodes placed equidistantly between them. We limit our analysis to the case of coded TDMA multihop transmission, i.e., the nodes do not cooperate and do not try to access the channel simultaneously. Given a global constraint on bandwidth, we determine the number of hops that achieves a desired end-to-end rate with the least total transmission power. Furthermore, we examine how the optimum number of hops changes when an end-to-end delay constraint is introduced using the sphere-packing bound and computer simulations. The analysis demonstrates that the optimum number of hops depends on the end-to-end rate and the path-loss exponent. Specifically, we show the existence of an asymptotic per-link spectral efficiency, which is the preferred spectral efficiency in TDMA multihop transmission.

Power amplifiers for wireless transmission provide a limited radiated power, and their efficiency depends highly on the operating point. We show that power control and routing strategies in multi-hop wireless networks are strongly affected by these non-ideal amplifier characteristics. For the analysis, we prove that the distances in random networks are governed by a generalized Rayleigh distribution, and we determine the power efficiency of different routing schemes. The main result is that nearest-neighbor routing is highly inefficient if the network has to be connected with high probability.

Large-scale networks of integrated wireless sensors become increasingly tractable. Advances in hardware technology and engineering design have led to dramatic reductions in size, power consumption, and cost for digital circuitry, and wireless communications. Networking, self-organization, and distributed operation are crucial ingredients to harness the sensing, computing, and computational capabilities of the nodes into a complete system. This article shows that those networks can be considered as cellular nonlinear networks (CNNs), and that their analysis and design may greatly benefit from the rich theoretical results available for CNNs.