Martin Haenggi

University of Notre Dame, Electrical Engineering, Faculty Member

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Papers by Martin Haenggi

Effect of Network Geometry and Interference on Consensus in Wireless Networks

Springer Optimization and Its Applications, 2010

We study the convergence of the average consensus algorithm in wireless networks in the presence ... more We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. It is well-known that convergence of the consensus algorithm improves with network connectivity. However, from a networking standpoint, highly connected wireless networks may have lower throughput because of increased interference. This raises an interesting question: What is the effect of increased network connectivity on the convergence of the consensus algorithm, given that this connectivity comes at the cost of lower network throughput? We address this issue for two types of networks: regular lattices with periodic boundary conditions, and a hierarchical network where a backbone of nodes arranged as a regular lattice supports a collection of randomly placed nodes. We characterize the properties of an optimal TDMA protocol that maximizes the speed of convergence on these networks and provide analytical upper and lower bounds for the achievable convergence rate. Our results show that in a interference-limited scenario the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement. In particular, we prove that asymptotically in the number of nodes, forming long-range interconnections improves the convergence rate in one-dimensional tori, while it has the opposite effect in higher dimensions.

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The TASEP: A Statistical Mechanics Tool to Study the Performance of Wireless Line Networks

2010 Proceedings of 19th International Conference on Computer Communications and Networks, 2010

We consider a multihop wireless line network with a single unidirectional data flow and show that... more 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.

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Geometric analysis of distributed power control and Möbius MAC design

Wireless Communications and Mobile Computing, 2014

ABSTRACT This paper presents a geometric analysis of the convergence condition for the Foschini–M... more 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 &amp; Sons, Ltd.

Delay performance of different MAC schemes for multihop wireless networks

GLOBECOM '05. IEEE Global Telecommunications Conference, 2005., 2005

This paper studies the end-to-end (e2e) delay performance of a multihop wireless network fed with... more 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, mphase 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.

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Delay-Reliability Tradeoffs in Wireless Networked Control Systems

Lecture Notes in Control and Information Science, 2006

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Regularization Energy in Sensor Networks

2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, 2006

Regularization energy is defined as the energy required to move the points of a homogeneous point... more Regularization energy is defined as the energy required to move the points of a homogeneous point process in a bounded set to unique points of a lattice. The optimal mapping required for this movement is derived for one dimensional processes, and bounds are derived for the Poisson point process in one and two dimensions. In addition regularization energy is evaluated for well known point processes in one dimension by simulation. Lemma 3.2: Let a, b ∈ φ , a < b and also a, b be neighbors, then for the optimal mapping f ,

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Heterogeneous Cellular Network Models with Dependence

IEEE Journal on Selected Areas in Communications, 2015

Asymptotic Deployment Gain: A Simple Approach to Characterize the SINR Distribution in General Cellular Networks

IEEE Transactions on Communications, 2015

ABSTRACT In cellular network models, the base stations are usually assumed to form a lattice or a... more ABSTRACT 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.

Asymptotic deployment gain: A new approach to characterize coverage probability

2014 IEEE International Conference on Communications (ICC), 2014

ABSTRACT In cellular network models, the base stations are usually assumed to form a lattice or a... more ABSTRACT 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.

Spatiotemporal Cooperation in Heterogeneous Cellular Networks

IEEE Journal on Selected Areas in Communications, 2015

ABSTRACT This paper studies downlink communication in a heterogeneous cellular network where a se... more ABSTRACT 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.

Dynamic Connectivity and Packet Propagation Delay in ALOHA Wireless Networks

2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, 2007

We consider an ad hoc network which uses multihop and slotted ALOHA for its MAC contention. We th... more We consider an ad hoc network which uses multihop and slotted ALOHA for its MAC contention. We then formulate the minimum time required for a packet to reach the destination from the origin. We define this delay as the minimum time required for a causal path to form between the source and destination. We derive the distributional properties of the connection time using ideas from first passage percolation and epidemic processes. We show that the delay scales linearly with the distance and also provide asymptotic results (w.r.t time) for the positions of the nodes which are able to connect to a transmitter located at the origin. We also provide simulation results to support the theoretical results.

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A search algorithm for the design of multinested cellular neural networks

2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2002

In this paper, we propose a search algorithm that can be used to effectively find multinested cel... more In this paper, we propose a search algorithm that can be used to effectively find multinested cellular neural networks (CNN) implementations for Boolean functions in high dimensional input spaces. For the purposes of this paper, the algorithm is illustrated for the five-dimensional case, although it is completely general and can be applied to find functions with an arbitrary number of

Coordinated Multipoint Joint Transmission in Heterogeneous Networks

IEEE Transactions on Communications, 2014

ABSTRACT Motivated by the ongoing discussion on coordinated multipoint in wireless cellular stand... more ABSTRACT 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.

Coordinated multipoint in heterogeneous networks: A stochastic geometry approach

2013 IEEE Globecom Workshops (GC Wkshps), 2013

ABSTRACT Motivated by the ongoing discussion on coordinated multipoint in wireless cellular stand... more ABSTRACT 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 the paper is the joint transmission scenario, where an ideal back haul network allows a set of randomly located base stations, possibly belonging to different network tiers, to jointly transmit data, so as to mitigate intercell interference and hence improve coverage and spectral efficiency. Using tools from stochastic geometry, an exact integral expression for the network coverage probability is derived in the scenario where a typical user can coherently combine the received signal from a pool of base stations, that are selected based on their average received power strengths or distance from the receiver. In the special case where cooperation is limited to two base stations, numerical evaluations illustrate relative gains in coverage probability of up to about 30% compared to the non-cooperative case.

Throughput-delay-reliability tradeoffs in multihop networks with random access

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010

In ad hoc networks, performance objectives are often in contention with each other. Indeed, due t... more In ad hoc networks, performance objectives are often in contention with each other. Indeed, due to the transmission errors incurred over wireless channels, it is difficult to achieve a high rate of transmission in conjunction with reliable delivery of data and low latency. In order to obtain favorable throughput and delay performances, the system may choose to compromise on its reliability and have nodes forcibly dropping a small fraction of packets. The focus of this paper is on the characterization of tradeoffs between the achievable throughput, end-to-end delay and reliability in wireless networks with random access.

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Traffic management in random cellular networks

2014 Information Theory and Applications Workshop (ITA), 2014

ABSTRACT We consider a cellular network where base stations are randomly deployed according to a ... more ABSTRACT We consider a cellular network where base stations are randomly deployed according to a Poisson point process and new jobs arrive in time and space according to a Poisson space-time point process, and are assigned to base stations according to different assignment schemes with/without base station cooperation. We derive “macroscopic” spatial averages of local base station performance metrics, such as traffic load, utilization factor, and delay, under different models on the service time distribution which include dependence on distance. Moreover, we determine and derive properties of the traffic capacity of the network, defined as the maximum spatio-temporal job density under a given constraint on the percentage of unstable base stations. The proposed model provides a baseline for the study of irregular cellular networks with bursty spatio-temporal data traffic.

WSN08-6: Simplified Analysis and Design of MIMO Ad Hoc Networks

IEEE Globecom 2006, 2006

The simple, yet powerful concept of an "erristor" and its "erristance" has been recently introduc... more The simple, yet powerful concept of an "erristor" and its "erristance" has been recently 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.

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Optimizing spatial reuse by dynamic power control

2012 IEEE International Conference on Communications (ICC), 2012

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Optimal Spatial Reuse in Poisson Multi-Hop Networks

2010 IEEE Global Telecommunications Conference GLOBECOM 2010, 2010

We consider a wireless multi-hop network with sources that are Poisson distributed and relays whi... more 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.

Path loss exponent estimation in large wireless networks

2009 Information Theory and Applications Workshop, 2009

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