arXiv subjects

Martin Haenggi

Publications and source records attributed to Martin Haenggi.

At least 73 records · Page 4Linked to original sources

arXiv2012

Percolation in the Secrecy Graph

The secrecy graph is a random geometric graph which is intended to 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, which, in the model, is determined solely by the locations of the nodes and 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 locations of the nodes and eavesdroppers are given by Poisson point processes, and present bounds for different types of percolation, including in-, out- and undirected percolation.

math.PR↗

arXiv2012

Diversity Loss due to Interference Correlation

Interference in wireless systems is both temporally and spatially correlated. Yet very little research has analyzed the effect of such correlation. Here we focus on its impact on the diversity in Poisson networks with multi-antenna receivers. Most work on multi-antenna communication does not consider interference, and if it is included, it is assumed independent across the receive antennas. Here we show that interference correlation significantly reduces the probability of successful reception over SIMO links. The diversity loss is quantified via the diversity polynomial. For the two-antenna case, we provide the complete joint SIR distribution.

cs.IT↗

arXiv2012

Path Loss Exponent Estimation in a Large Field of Interferers

In wireless channels, the path loss exponent (PLE) has a strong impact on the quality of links, and hence, it needs to be accurately estimated for the efficient design and operation of wireless networks. In this paper, we address the problem of PLE estimation in large wireless networks, which is relevant to several important issues in networked communications such as localization, energy-efficient routing, and channel access. We consider a large ad hoc network where nodes are distributed as a homogeneous Poisson point process on the plane and the channels are subject to Nakagami-m fading. We propose and discuss three distributed algorithms for estimating the PLE under these settings which explicitly take into account the interference in the network. In addition, we provide simulation results to demonstrate the performance of the algorithms and quantify the estimation errors. We also describe how to estimate the PLE accurately even in networks with spatially varying PLEs and more general node distributions.

cs.IT↗

arXiv2012

Distance Distributions in Finite Uniformly Random Networks: Theory and Applications

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying nodal arrangement is almost universally taken to be an infinite Poisson point process. While this assumption is valid in some cases, there are also certain impracticalities to this model. For example, practical networks are non-stationary, and the number of nodes in disjoint areas are not independent. This paper considers a more realistic network model where a finite number of nodes are uniformly randomly distributed in a general d-dimensional ball of radius R and characterizes the distribution of Euclidean distances in the system. The key result is that the probability density function of the distance from the center of the network to its nth nearest neighbor follows a generalized beta distribution. This finding is applied to study network characteristics such as energy consumption, interference, outage and connectivity.

cs.IT↗

arXiv2011

Mean Interference in Hard-Core Wireless Networks

Matérn hard core processes of types I and II are the point processes of choice to model concurrent transmitters in CSMA networks. We determine the mean interference observed at a node of the process and compare it with the mean interference in a Poisson point process of the same density. It turns out that despite the similarity of the two models, they behave rather differently. For type I, the excess interference (relative to the Poisson case) increases exponentially in the hard-core distance, while for type II, the gap never exceeds 1 dB.

cs.IT↗

arXiv2010

Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity

We analyze the effect of interference on the convergence rate of average consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster with a greater exchange of information (i.e., by increased network connectivity) in every iteration. However, when interference is taken into account, it is no longer clear if the rate of convergence increases with network connectivity. We study this problem for randomly-placed consensus-seeking nodes connected through an interference-limited network. We investigate the following questions: (a) How does the rate of convergence vary with increasing communication range of each node? and (b) How does this result change when each node is allowed to communicate with a few selected far-off nodes? When nodes schedule their transmissions to avoid interference, we show that the convergence speed scales with $r^{2-d}$, where $r$ is the communication range and $d$ is the number of dimensions. This scaling is the result of two competing effects when increasing $r$: Increased schedule length for interference-free transmission vs. the speed gain due to improved connectivity. Hence, although one-dimensional networks can converge faster from a greater communication range despite increased interference, the two effects exactly offset one another in two-dimensions. In higher dimensions, increasing the communication range can actually degrade the rate of convergence. Our results thus underline the importance of factoring in the effect of interference in the design of distributed estimation algorithms.

cs.IT↗

arXiv2010

High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution

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 $\p \sim 1-γη^κ$ for $η\rightarrow 0$, 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.

cs.IT↗

arXiv2010

Outage Probability of General Ad Hoc Networks in the High-Reliability Regime

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 in [1], 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 $γη^κ$ as the density of interferers $η$ goes to zero, and that $κ$ assumes values in the range $1\leq κ\leq α/2$ 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 tightly bounds the outage probability for all interferer densities.

cs.IT↗

arXiv2010

Interference in Lattice Networks

Lattices are important as models for the node locations in wireless networks for two main reasons: (1) When network designers have control over the placement of the nodes, they often prefer a regular arrangement in a lattice for coverage and interference reasons. (2) If nodes are randomly distributed or mobile, good channel access schemes ensure that concurrent transmitters are regularly spaced, hence the locations of the transmitting nodes are well approximated by a lattice. In this paper, we introduce general interference bounding techniques that permit the derivation of tight closed-form upper and lower bounds for all lattice networks, and we present and analyze optimum or near-optimum channel access schemes for one-dimensional, square, and triangular lattices.

cs.IT↗

arXiv2010

Dynamic Connectivity in ALOHA Ad Hoc Networks

In a wireless network the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Previously, connectivity in wireless networks was analyzed using static geometric graphs, and as we show leads to an overly constrained design criterion. The dynamic nature of the transmitting set introduces additional randomness in a wireless system that improves the connectivity, and this additional randomness is not captured by a static connectivity graph. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the 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 consider the giant component of the network formed when communication is noise-limited (by neglecting interference). Then, in the presence of interference, we prove that the delay scales linearly with the source-destination distance on this giant component. We also provide simulation results to support the theoretical results.

cs.IT↗

arXiv2009

Spatial Analysis of Opportunistic Downlink Relaying in a Two-Hop Cellular System

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 node locations of the base stations and the mobile stations as a point process on the plane and then analyze the performance of two different two-hop schemes in the downlink. In one scheme the node nearest to the destination that has decoded information from the base station in the first hop is used as the relay. In the second scheme the node with the best channel to the relay that received information in the first hop acts as a relay. In both these schemes we obtain the success probability of the two hop scheme, accounting for the interference from all other cells. We use tools from stochastic geometry and point process theory to analyze the two hop schemes. 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. Some of the main contributions of this paper are the analytical techniques introduced for the inclusion of the spatial locations of the nodes into the mathematical analysis.

cs.IT↗

arXiv2009

Random Access Transport Capacity

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 as well. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability.

cs.IT↗

arXiv2009

Spatial and Temporal Correlation of the Interference in ALOHA Ad Hoc Networks

Interference is a main limiting factor of the performance of a wireless ad hoc network. The temporal and the spatial correlation of the interference makes the outages correlated temporally (important for retransmissions) and spatially correlated (important for routing). In this letter we quantify the temporal and spatial correlation of the interference in a wireless ad hoc network whose nodes are distributed as a Poisson point process on the plane when ALOHA is used as the multiple-access scheme.

cs.IT↗

arXiv2009

Analysis of Uncoordinated Opportunistic Two-Hop Wireless Ad Hoc Systems

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.

cs.IT↗

arXiv2008

The Transport Capacity of a Wireless Network is a Subadditive Euclidean Functional

The transport capacity of a dense ad hoc network with n nodes scales like \sqrt(n). We show that the transport capacity divided by \sqrt(n) 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.

cs.IT↗

arXiv2008

Outage and Local Throughput and Capacity of Random Wireless Networks

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 (set of transmitting nodes). For the performance analysis, a new parameter, the so-called {\em 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.

cs.IT↗

arXiv2008

The Secrecy Graph and Some of its Properties

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.

cs.IT↗

arXiv2007

Rethinking Information Theory for Mobile Ad Hoc Networks

The subject of this paper is the long-standing open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks (MANETs). A MANET is a peer-to-peer network with no pre-existing infrastructure. MANETs are the most general wireless networks, with single-hop, relay, interference, mesh, and star networks comprising special cases. The lack of a MANET capacity theory has stunted the development and commercialization of many types of wireless networks, including emergency, military, sensor, and community mesh networks. Information theory, which has been vital for links and centralized networks, has not been successfully applied to decentralized wireless networks. Even if this was accomplished, for such a theory to truly characterize the limits of deployed MANETs it must overcome three key roadblocks. First, most current capacity results rely on the allowance of unbounded delay and reliability. Second, spatial and timescale decompositions have not yet been developed for optimally modeling the spatial and temporal dynamics of wireless networks. Third, a useful network capacity theory must integrate rather than ignore the important role of overhead messaging and feedback. This paper describes some of the shifts in thinking that may be needed to overcome these roadblocks and develop a more general theory that we refer to as non-equilibrium information theory.

cs.IT↗