# 8th International Workshop on Spatial Stochastic Models for Wireless Networks - Program

Time Session

## Monday, May 14

09:00-12:30 Morning session
12:30-13:30 Lunch
13:30-17:00 Afternoon session

## Monday, May 14

### 09:00 - 12:30

#### Morning session

What geometry for wireless networks - when Honeycomb is as Poisson and what if both are not ideal
Bartlomiej Blaszczyszyn (Inria-Ens, France)
An ubiquitous assumption when modeling base stations in cellular networks is to consider deterministic lattices, usually hexagonal ones. On the other hand, mobile users are usually modeled by a Poisson point process. Both the assumptions are too simplistic. In the first part of the lecture we will present a few evidences and consequences of the fact that shadowing, that is signal power loss due to reflection, diffraction, and scattering, "harms" the perfect Honeycomb in such a way that it may be perceived by a typical user as a Poisson network. In reality, patterns of base stations are not perfectly periodic, due to various locational constants, nor mobiles users are completely independent because of various interactions: social, human interactions typically introduce more clustering, while the medium access protocols implemented in mobile wireless devices tend to separate active users. These trivial observations raise fundamental questions about the impact of clustering, that is spatial non-homogeneity of nodes, on the performance of wireless networks. We will try to tackle this problem in the second part of the lecture, showing some models "in-between" Honeycomb and Poisson, as well as "beyond" Poisson, regarding clustering of nodes. We will be interested in theoretical comparisons of coverage, connectivity and routing metrics for these network models.
Estimating Wireless Network Properties with Spatial Statistics and Models
Janne Riihijärvi (RWTH Aachen University, Germany); Petri Mähönen (RWTH Aachen University, Germany)
In this paper we discuss the use of spatial statistics and models for different estimation problems related to wireless networks. We focus specifically on problems of state estimation, in which measurement data on only part of the system is available, and should be used to infer the state of the rest of the system. Such problems are becoming increasingly important for network operations and diagnostics, and are also emerging in the context of resource management of future wireless networks. We provide a concise survey of existing techniques from the spatial statistics literature, show how they can be applied in the context of wireless networks, and outline key research challenges for future work.
Coffee break
A population model based on a Poisson line tessellation
Frederic Morlot (INRIA, France)
In this paper, we introduce a new population model. Taking into account geometry of cities by adding roads, we build a Cox process driven by a Poisson line tessellation. We perform several shot-noise computations according to various generalizations of our original process. This allows us to derive analytical formulas for uplink coverage probability in each case.
Stochastic characterization of the two band two player spectrum sharing game
Ilaria Malanchini (Politecnico di Milano, Italy); Steven Patrick Weber (Drexel University, USA); Matteo Cesana (Politecnico di Milano, Italy)
We consider two pairs of communicating users sharing two-bands of spectrum under a sum band power constraint. Our earlier work proposed a natural spectrum sharing game for this problem and characterized the Nash equilibria as a function of the signal and interference distances, when the positions of the four nodes were assumed fixed. In this work, we derive the joint distribution of the interference distances conditioned on the transmitter separation distance, and the unconditioned interference distance distribution when we place one transmitter at the origin and the second uniformly at random over a disk. Therefore, we compute the distribution of the random Nash equilibria as a function of the random interference distances. We leverage the analysis to give an asymptotic expression for the coupling probability in a game where the transmitter positions form a (low density) PPP, which may be interpreted as the fraction of players playing a two-player game.
Interference Characteristics and Success Probability at the Primary User in a Cognitive Radio Network
Prasanna Madhusudhanan (University of Colorado at Boulder, USA); Timothy Brown (University of Colorado, USA); Youjian (Eugene) Eugene Liu (University of Colorado at Boulder, USA)
We analyze a cognitive radio network where the primary users (PUs) and cognitive radio (CR) devices are distributed over the two-dimensional plane according to two independent homogeneous Poisson processes. Any CR that lies within the detection region of some PU switches to a different channel in order to prevent causing harmful interference at the PU. Using the concepts of stochastic geometry, we study the characteristics of the interference caused by the PUs and the CRs to a given PU. Further, these results are used to obtain tight upper and lower bounds for the success probability at the PU; defined as the probability that the signal-to-interference-plus-noise ratio (SINR) is beyond a certain operating threshold.

### 13:30 - 17:00

#### Afternoon session

The Effect of Caching in Sustainability of Large Wireless Networks
Georgios S. Paschos (CERTH - ITI, Center for Research and Technology, Greece); Savvas Gitzenis (Certh, Greece); Leandros Tassiulas (University of Thessaly, Greece)
We study the scalability of multihop wireless communications, a major concern in networking, for the case that users access content cached across the nodes. In contrast to the standard paradigm of randomly selected communicating pairs, content replication is efficient for certain regimes of content volume and popularity, cache and network size. Assuming the Zipf popularity law, and investigating on the relative ways that the number of files, the cache size and the network nodes can all jointly scale to infinity, we derive asymptotic laws on required link capacity, which range from O(\sqrt{N}) down to O(1), and identify regimes of network operation.
Floating information with stationary nodes
Esa Hyytiä (Aalto University, Finland); Pasi Lassila (Helsinki University of Technology, Finland); Joerg Ott (Aalto University & Helsinki Institute of Information Technology, Finland); Jussi Kangasharju (University of Helsinki, Finland)
In the Floating Content application, mobile nodes collectively store and disseminate messages by using the principles of opportunistic networking. The system operates in best effort fashion relying solely on the nodes located in the given area. Past work has focused on models, where the nodes are moving and the messages are exchanged on-the-fly''. In this paper, we consider the case, where messages are exchanged only when two nodes are stationary within each others' transmission range. Our objective is to characterize when the information is likely to remain available for long periods of time. We find that there exists a certain permanence threshold for the mean node degree above which the expected lifetime of the information increases very rapidly (finite systems) or the information becomes permanent (infinite system). This threshold is about 1.3 for the basic case (a single stop per visit). Additional stops within the zone improve the situation further.
Walking Around in a Changing World: Understanding Random Walks over Dynamic Graphs
Daniel R Figueiredo (UFRJ, Brazil)
The growing interest in understanding how things connect and the importance of connectedness on various processes has lead to a large and multidisciplinary body of work over the past decade. A fundamental aspect is its dynamic nature as all networks constructed by nature or man suffer structural changes over some time-scale. For example, consider online social networks, the Web, a mobile wireless network or the neural network of an individual. Random walks are a fundamental building block for understanding networks and have been applied to problems related to clustering, ranking, searching and routing. Its relatively well-understood behavior on a static network and algorithmic simplicity support its prominent role as a building block for different mechanisms. However, very little is known about their behavior on dynamic networks. In this talk we present a general modeling framework for dynamic networks and continuous time random walks. We then analyze the long-term behavior (steady state) of the walker on dynamic networks and show it to be non-trivial, in striking contrast to the static case. However, we characterize its steady state behavior for three general special cases: (i) walker rate is much faster or slower than network dynamics (time-scale separability); (ii) walker is proportional to the degree of the node it resides on (coupled dynamics); (iii) degrees of nodes in the same connected component are identical (structural restriction). Finally, we apply our framework to mobile wireless networks and show interesting properties in this scenario that could be explored in the design of algorithms. The theoretical findings presented in this talk were obtained in collaboration with other researchers and will be published this year in ACM SIGMETRICS 2012.
Coffee break
Optimizing Practical Adaptive Frequency Hopping and Medium Access Control in Ad Hoc Networks
Ralph Tanbourgi (Karlsruhe Institute of Technology (KIT), Germany); Jens P. Elsner (Karlsruhe Institute of Technology (KIT) & Communications Engineering Lab, Germany); Holger Jäkel (Karlsruhe Institute of Technology (KIT), Germany); Friedrich K. Jondral (Karlsruhe Institute of Technology, Germany)
Adaptive frequency hopping (AFH) as proposed, e.g., in IEEE 802.15.2 aims at increasing system reliability in the presence of quasi-static external interference. Practical approaches require autonomous sensing of the interference environment, with the measurements containing both external interference and network self -interference. In prior work, a simplistic model for AFH-based ad hoc networks was developed to analyze how this issue affects the area spectral efficiency (ASE). It was found that the AFH mechanism severely degrades ASE when self-interference is increased. In this paper, we modify the model to account for the correlation between the nodes' adapted hopping sets. We then address the question of how to design the system parameters to achieve optimal performance and avoid the degradation. We discuss different optimization problems and identify sensing techniques that can cope with increased selfinterference. Among these techniques, carrier detection sensing was found to be robust against self-interference while showing good performance. We further discuss cases where joint optimization of the AFH and CSMA mechanisms is beneficial and cases where there is little to be gained.
Analysis of Multicell Cooperation with Random User Locations Via Deterministic Equivalents
Jakob Hoydis (Alcatel-Lucent Bell Labs, Germany); Axel Müller (Intel, France); Romain Couillet (Supélec & Ecole Centrale Paris, France); Mérouane Debbah (Supelec, France)
We consider the uplink of a one-dimensional 2-cell network with fixed base stations (BSs) and randomly distributed user terminals (UTs). Assuming that the number of antennas per BS and the number of UTs grow infinitely large, we derive tight approximations of the ergodic sum rate with and without multicell processing for optimal and sub-optimal detectors. We use these results to find the optimal BS placement to maximize the system capacity. This work can be seen as a first attempt to apply large random matrix theory to the study of networks with random topologies. We demonstrate that such an approach is feasible and leads to analytically tractable expressions of the average system performance. Moreover, these results can be used to optimize certain system parameters for a given distribution of user terminals and to assess the gains of multicell cooperation.
Power Control in Random Networks: The Effect of Disorder in User Positions
Aris Moustakas (University of Athens, Greece); Nicholas Bambos (Stanford University, USA)
Consider a wireless network of transmitter-receiver pairs. The transmitters adjust their powers to maintain a particular SINR target in the presence of interference from neighboring transmitters. In this paper we analyze the optimal power vector that may achieve this target in the presence of randomness in the network. In particular, we address the scenario where the receiver pairs may be located in one of two distinct distances from their serving transmitter base. We apply concepts from random matrix theory to evaluate the asymptotic mean optimal power per link. Our analytical results show substantial agreement with numerically generated networks, not only in one-dimensional network arrays but also in two dimensional network geometries. Notably, we observe that the optimal power in random networks does not go to infinity in a continuous fashion as in regular grids. Rather, beyond a certain point, no finite power solution exists.