arXiv subjects

Martin Haenggi

Publications and source records attributed to Martin Haenggi.

At least 19 recordsLinked to original sources

arXiv2025

Cross-link RTS/CTS for MLO mm-Wave WLANs

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.

cs.NI↗

arXiv2025

Q Cells in Wireless Networks

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 the Q 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.

cs.NI↗

arXiv2025

Spatial Disease Propagation With Hubs

Physical contact or proximity is often a necessary condition for the spread of infectious diseases. Common destinations, typically referred to as hubs or points of interest, are arguably the most effective spots for the type of disease spread via airborne transmission. In this work, we model the locations of individuals (agents) and common destinations (hubs) by random spatial point processes in $\mathbb{R}^d$ and focus on disease propagation through agents visiting common hubs. The probability of an agent visiting a hub depends on their distance through a connection function $f$. The system is represented by a random bipartite geometric (RBG) graph. We study the degrees and percolation of the RBG graph for general connection functions. We show that the critical density of hubs for percolation is dictated by the support of the connection function $f$, which reveals the critical role of long-distance travel (or its restrictions) in disease spreading.

cs.IT↗

arXiv2025

Higher-Order Meta Distribution Reliability Analysis of Wireless Networks

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.

eess.SY↗

arXiv2024

Dual-Zone Hard-Core Model for RTS/CTS Handshake Analysis in WLANs

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 provide better estimates of interference levels and success probability, which could inform strategies for better interference management and improved performance in future WLAN designs.

cs.NI↗

arXiv2024

Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications

We study street-constrained ($\ell_1$) shortest paths in a Poisson line Cox process (PLCP), where Poisson points of linear intensity $\mu$ lie on the lines of an underlying Poisson line process (PLP) of density $\lambda$. Under a one-turn restriction, we derive closed-form expressions for the distribution of the nearest-neighbor path length from (i) the typical PLCP point and (ii) the typical PLP intersection, by explicitly evaluating the relevant void probabilities via a geometric decomposition of the feasible path-length set. For the intersection case, we further provide analytically tractable upper and lower bounds that capture the impact of $\lambda$ and $\mu$. Allowing two turns from the typical point, we obtain a computable upper bound using a feasible-set shrinking argument and identify regimes in which it is tight. We also delineate parameter ranges where a one-turn route from a typical intersection can outperform a two-turn route from a typical point. Finally, we discuss how the results enable statistical performance characterization of ride-hailing services in terms of service guarantee, trip time, and consequently, derive dimensioning insights. We also illustrate qualitatively, how the results can be employed to study vehicle-to-vehicle communication broadcast messages near intersections.

cs.IT↗

arXiv2024

Impact of Network Geometry on Large Networks with Intelligent Reflecting Surfaces

In wireless networks assisted by intelligent reflecting surfaces (IRSs), jointly modeling the signal received over the direct and indirect (reflected) paths is a difficult problem. In this work, we show that the network geometry (locations of serving base station, IRS, and user) can be captured using the so-called triangle parameter $Δ$. We introduce a decomposition of the effect of the combined link into a signal amplification factor and an effective channel power coefficient $G$. The amplification factor is monotonically increasing with both the number of IRS elements $N$ and $Δ$. For $G$, since an exact characterization of the distribution seems unfeasible, we propose three approximations depending on the value of the product $NΔ$ for Nakagami fading and the special case of Rayleigh fading. For two relevant models of IRS placement, we prove that their performance is identical if $Δ$ is the same given an $N$. We also show that no gains are achieved from IRS deployment if $N$ and $Δ$ are both small. We further compute bounds on the diversity gain to quantify the channel hardening effect of IRSs. Hence only with a judicious selection of IRS placement and other network parameters, non-trivial gains can be obtained.

cs.IT↗

arXiv2023

Analysis of the Age of Information in Age-Threshold Slotted ALOHA

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.

cs.IT↗

arXiv2023

Hausdorff Moment Transforms and Their Performance

Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment sequences are discussed and applied. Also, some of the approximations have been rewritten as linear transforms, and detailed accuracy requirements are analyzed. Our finding shows that the performance of the approximations differs significantly in their convergence properties, accuracy, and numerical complexity and that the decay type of the moment sequence strongly affects the accuracy requirement.

math.NA↗

arXiv2023

Binomial Line Cox Processes: Statistical Characterization and Applications in Wireless Network Analysis

The current analysis of wireless networks whose transceivers are confined to streets is largely 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 binomial line process, is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process 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 transmission 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.

cs.IT↗

arXiv2021

The Transdimensional Poisson Process for Vehicular Network Analysis

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.

cs.NI↗

arXiv2021

Stochastic Geometry Analysis of Spatial-Temporal Performance in Wireless Networks: A Tutorial

The performance of wireless networks is fundamentally limited by the aggregate interference, which depends on the spatial distributions of the interferers, channel conditions, and user traffic patterns (or queueing dynamics). These factors usually exhibit spatial and temporal correlations and thus make the performance of large-scale networks environment-dependent (i.e., dependent on network topology, locations of the blockages, etc.). The correlation can be exploited in protocol designs (e.g., spectrum-, load-, location-, energy-aware resource allocations) to provide efficient wireless services. For this, accurate system-level performance characterization and evaluation with spatio-temporal correlation are required. In this context, stochastic geometry models and random graph techniques have been used to develop analytical frameworks to capture the spatio-temporal interference correlation in large-scale wireless networks. The objective of this article is to provide a tutorial on the stochastic geometry analysis of large-scale wireless networks that captures the spatio-temporal interference correlation (and hence the signal-to-interference ratio (SIR) correlation). We first discuss the importance of spatio-temporal performance analysis, different parameters affecting the spatio-temporal correlation in the SIR, and the different performance metrics for spatio-temporal analysis. Then we describe the methodologies to characterize spatio-temporal SIR correlations for different network configurations (independent, attractive, repulsive configurations), shadowing scenarios, user locations, queueing behavior, relaying, retransmission, and mobility. We conclude by outlining future research directions in the context of spatio-temporal analysis of emerging wireless communications scenarios.

cs.NI↗

arXiv2021

Cox Models for Vehicular Networks: SIR Performance and Equivalence

We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of $\mathbb{R}^{2}$. 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.

cs.NI↗

arXiv2021

Joint Spatial-Propagation Modeling of Cellular Networks Based on the Directional Radii of Poisson Voronoi Cells

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.

cs.IT↗

arXiv2020

SIR Analysis via Signal Fractions

The analysis of signal-to-interference ratios (SIRs) in wireless networks is instrumental to derive important performance metrics, including reliability, throughput, and delay. While a host of results on SIR distributions are now available, they are often not straightforwards to interpret, bound, visualize, and compare. In this letter, we offer an alternative path towards the analysis and visualization of the SIR distribution. The quantity at the core of this approach is the signal fraction (SF), which is the ratio of the signal power to the total received power. A key advantage is that the SF is constrained to [0,1]. We exemplify the benefits of the SF-based approach by reviewing known results for Poisson cellular networks. In the process, we derive new approximation and bounding techniques that are generally applicable.

cs.IT↗

arXiv2019

Distance from the Nucleus to a Uniformly Random Point in the 0-cell and the Typical Cell of the Poisson-Voronoi Tessellation

Consider the distances $\tilde{R}_o$ and $R_o$ from the nucleus to a uniformly random point in the 0-cell and the typical cell, respectively, of the $d$-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this paper is to characterize the exact distributions of $\tilde{R}_o$ and $R_o$. First, using the well-known relationship between the 0-cell and the typical cell, we show that the random variable $\tilde{R}_o$ is equivalent in distribution to the contact distance of the Poisson point process. Next, we derive a multi-integral expression for the exact distribution of $R_o$. Further, we derive a closed-form approximate expression for the distribution of $R_o$, which is the contact distribution with a mean corrected by a factor equal to the ratio of the mean volumes of the 0-cell and the typical cell. An additional outcome of our analysis is a direct proof of the well-known spherical property of the PV cells having a large inball.

math.PR↗

arXiv2019

Downlink Analysis for the Typical Cell in Poisson Cellular Networks

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 it 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.

cs.IT↗

arXiv2019

Massive MIMO Forward Link Analysis for Cellular Networks

This paper presents analytical expressions for the signal-to-interference ratio (SIR) 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.

cs.IT↗