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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 first $n$ moments. 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.

What happens if the points of a point process are repeatedly displaced randomly in their Voronoi cells? This letter shows that the resulting point process, called the stable point process (SPP), is of repulsive nature and characterized only by its density. In contrast to the existing soft-core models, the SPP is easy to simulate in arbitrary dimensions and thus fills a nagging void in the arsenal of repulsive point processes. Several pertinent applications of the SPP to wireless networks are discussed and demonstrate its relevance and versatility.

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.

This work studies the signal-to-interference-plus-noise ratio (SINR) meta distribution (MD) in cellular networks with a focus on the Poisson model. Firstly, we show that for stationary base station point processes, arbitrary fading, and power-law path loss with exponent $\alpha $ , the base station density $\lambda $ and the noise power $\sigma ^{2}$ impact the SINR MD only through $\eta \pmb {\triangleq } \lambda ^{\alpha /2}/\sigma ^{2}$ , termed the network signal-to-noise ratio (NSNR). Next, we show that for Poisson cellular networks, the SINR MD can be written as $g(x)\theta ^{-2/\alpha }$ when the target SINR $\theta $ and the target reliability ${x}$ jointly satisfy a constraint. We derive this constraint and the integral of $g(x)$ . Lastly, we discuss several extensions of the results to more general models and architectures.

Owing to its unparalleled tractability, the Poisson point process (PPP) has emerged as a popular model for the analysis of cellular networks. Considering a stationary point process of users, which is independent of the base station (BS) point process, it is well known that the typical user does not lie in the typical cell and thus may not truly represent the typical cell performance. Inspired by this observation, we present a construction that allows a direct characterization of the downlink performance of the typical cell. For this, we present an exact downlink analysis for the 1-D case and a remarkably accurate approximation for the 2-D case. Several useful insights about the differences and similarities in the two viewpoints (typical user vs. typical cell) are also provided.

The meta distribution (MD) of the signal-to-interference ratio (SIR) provides fine-grained reliability performance in wireless networks modeled by point processes. In particular, for an ergodic point process, the SIR MD yields the distribution of the per-link reliability for a target SIR. Here, we reveal that the SIR MD has a second important application, which is rate control. Specifically, we calculate the distribution of the SIR threshold (equivalently, the distribution of the transmission rate) that guarantees each link a target reliability and show its connection to the distribution of the per-link reliability. This connection also permits an approximate calculation of the SIR MD when only partial (local) information about the underlying point process is available.

We consider the number of users associating with each base station in a cellular network. Extending and unifying the characterizations for certain settings available in the literature, we derive a result that is asymptotic in the strength of the shadowing, yet otherwise universally valid: it holds for every network geometry and shadowing distribution. We then illustrate how this result provides excellent representations in various classes of networks and with realistic shadowing strengths, evidencing broad applicability.

In wireless networks, the distances from a user to its desired transmitters and undesired interferers play a critical role in its channel quality. In this letter, we study this location-dependence in a cellular network, where a user is always served by its nearest base station. For any stationary and ergodic base station process, we partition its associated Voronoi cells into the cell centers and the cell boundaries. We show that in Poisson networks, the top fraction ${x}$ of users enjoy a signal-to-interference ratio (SIR) gain of ${-}{5}{\alpha }\text {log}_{{10}}{x}$ dB relative to the typical user for Rayleigh fading and the power-law path loss with the exponent $\alpha $ . For the cell boundary users, we give both the exact and asymptotic form of the SIR distribution. As such, this letter permits the grouping of users and the analysis of different groups of users.

Meta distributions (MDs) are refined performance metrics in wireless networks modeled using point processes. While there is no known method to directly calculate MDs, the moments of the underlying conditional distributions (given the point process) can often be expressed in exact analytical form. The problem of finding the MD given the moments has several solutions, but the standard approaches are inefficient and sensitive to the choices of a number of parameters. Here we propose and explore the use of a method based on binomial mixtures, which has several key advantages over other methods, since it is based on a simple linear transform of the moments.

The antenna pattern model plays a key role in evaluating the performance benefits of directional antenna arrays. In this letter, we propose a novel antenna pattern, named multi-cosine antenna pattern, to approximate the actual antenna pattern, and apply it to millimeter wave (mm-wave) networks. To get deep insights on the role of directional antenna arrays in mm-wave networks, we derive exact expressions for the success probability of the typical receiver as well as a tight upper bound. The results show that the proposed antenna pattern provides a better tradeoff between the accuracy and the tractability in terms of both antenna pattern and analysis than previous models.

This letter presents a theoretical framework for the analysis of the meta distribution of the SIR for Poisson networks with interference cancellation (IC) enabled at the receivers, which gives deep insight into the network performance on a link-wise basis. A simple but insightful IC model named C-IC is studied for which the exact $b$ th moment of the meta distribution and its beta distribution approximation and some useful bounds are validated. The conditions for the mean local delay to be finite are also stated. The results show that IC improves the performance not only in terms of the mean but also in terms of the variance of the meta distribution.

The analysis of the success probability or signal-to-interference ratio (SIR) distribution for coherent joint transmission (JT) based on stochastic geometry is an open issue. In this letter, we study coherent JT in downlink heterogeneous cellular networks and provide an upper bound of the success probability for the general user and the worst-case user (cell-corner user), and an approximation for the general user. Simulation results show that the derived upper bound and approximation are quite accurate and thus provide an analytical approach to quantify the SIR performance of coherent JT.

Recent studies on secure wireless communication have shed light on a scenario where interference has a desirable impact on network performance. Particularly, assuming independent interference power fluctuations at the eavesdropper and the receiver, opportunistic secure information transfer can occur on the legitimate link. However, interference is spatially correlated due to the common set of interfering sources, which may diminish the opportunistic secure spectrum access (OSSA) probability. We study and quantify the effect of spatial interference correlation on OSSA in cellular-networks and investigate the potential of full-duplex jamming (FDJ) solutions. The results highlight the scenarios where FDJ improves OSSA performance.

In this letter, we propose a new coordinated multipoint technique based on mutual information (MI) accumulation using rateless codes. Using a stochastic geometry model for the cellular downlink, we quantify the performance enhancements in coverage probability and rate due to MI accumulation. By simulation and analysis, we show that MI accumulation using rateless codes leads to remarkable improvements in coverage and rate for general users and specific cell edge users.

The point process of concurrent users is critical for the analysis of cellular systems, in particular for the uplink and for full-duplex communication. We analyze the properties of two popular models. For the first one, we provide an accurate characterization of the pair correlation functions from the user and the base station point of view, which are applied to approximate the user process by Poisson and Ginibre point processes. For the second model, which includes the first model asymptotically, we study the cell vacancy probability, the mean area of vacant and occupied cells, the user-base station distance, and the pair correlation function in lightly and heavily loaded regimes.

We study the geometric aspects of the sentry selection problem for a sensor network with randomly distributed sensors, each of which covers a small disc. The problem is to partition the sensors into a predetermined number of groups, so that, for each group, the sensing regions of the sensors in that group together cover the region of interest. After presenting some theoretical results, we include descriptions of two fast partitioning algorithms, together with the results of simulating them on moderate-sized networks.

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.

The local delay characterizes the number of time slots required for a node to successfully transmit a packet to its target receiver. In this letter, we explore the impact of coordinated transmission on the mean local delay and the energy efficiency, in a Poisson network model. Leveraging tools from point process theory, we derive analytical expressions of the mean local delay and the long-term energy efficiency, without and with coordinated transmission. We find that coordinated transmission greatly decreases the mean local delay and also improves the long-term energy efficiency under certain network configurations.

Motivated by information-theoretic secrecy, geometric models for secrecy in wireless networks have begun to receive increased attention. The general question is how the presence of eavesdroppers affects the properties and performance of the network. Previously, the focus has been mostly on connectivity. Here we study the impact of eavesdroppers on the coverage of a network of base stations. The problem we address is the following. Let base stations and eavesdroppers be distributed as stationary Poisson point processes in a disk of area n. If the coverage of each base station is limited by the distance to the nearest eavesdropper, what is the maximum density of eavesdroppers that can be accommodated while still achieving full coverage, asymptotically as n→∞?

It is known that the transport capacity of a dense wireless ad hoc network with nnodes scales like vn. We show that the transport capacity divided by vnapproaches a nonrandom limit with probability 1 when the nodes are uniformly distributed on the unit square. To show the existence of the limit, 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.

We present closed-form expressions of the average link throughput for sensor networks with a slotted ALOHA MAC protocol in Rayleigh fading channels. We compare networks with three regular topologies in terms of throughput, transmit efficiency, and transport capacity. In particular, for square lattice networks, we present a sensitivity analysis of the maximum throughput and the optimum transmit probability with respect to the signal-to-interference ratio threshold. For random networks with nodes distributed according to a two-dimensional Poisson point process, the average throughput is analytically characterized and numerically evaluated. It turns out that although regular networks have an only slightly higher average link 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.

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