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#### Document Type

Open Access Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Degree Program

Electrical and Computer Engineering

#### Year Degree Awarded

Fall 2014

#### First Advisor

Prof. Dennis Goeckel

#### Second Advisor

Prof. Patrick Kelly

#### Third Advisor

Prof. Hossein Pishro-Nik

#### Fourth Advisor

Prof. Don Towsley

#### Subject Categories

Digital Communications and Networking | Systems and Communications

#### Abstract

This thesis work is concerned with communication in large random wireless ad hoc networks. We mathematically model the wireless network as a collection of randomly located nodes, and explore how its performance scales as the network size increases. In particular, we study three important properties: broadcasting ability, rate of information exchange, and secret communication capability. In addition, we study connectivity properties of large random graphs in a more general context, where the graph does not necessarily represent a wireless communication network.

Broadcasting, i.e., delivering a message from a single node to the entire network in a wireless ad hoc network can be achieved by nodes acting as relays. However, due to the random placement of nodes, broadcasting gets more difficult as the network size increases. We study how a stronger form of cooperation where nodes coordinate and transmit at the same time to increase their collective transmit range can improve broadcast ability. We show that, in this case, broadcast performance strongly depends on the type of wireless medium, in particular how fast the signal strength decays with distance. Specifically, we establish that, with increasing network size, broadcast probability goes to zero unless the attenuation in the medium is lower than a certain critical threshold. We consider the case of a wireless ad hoc network that is supported by base stations to improve data rate, which is referred to as a hybrid network. Although the availability of base stations may improve the throughput between the wireless nodes by providing access to an overlaid high-speed wired network, this improvement does not necessarily bring a scaling advantage as the network gets larger. Motivated by work which suggests the capacity increase depends on at what rate the number of base stations scales in comparison to the number of wireless nodes, we study the ultimate constraints on the capacity of hybrid networks. In particular, we prove upper bounds on the capacity scaling benefit the base stations can provide and also show constructions that achieve these bounds in some cases.

We study secret communication capabilities of nodes in a large wireless ad hoc network that also includes eavesdropper nodes. Under an information-theoretic secrecy framework, we investigate whether nodes can exchange data while keeping bits secret from eavesdropper nodes without sacrificing on the data rate, and, most importantly, without location information about the eavesdroppers. We show that this is indeed possible by employing a combination of secret sharing, two-way communications and network coding, where nodes perform simple coding operations on messages instead of simply forwarding them.

Finally, motivated by the results in the theory of random graphs that facilitate the understanding of the behavior of large wireless networks, we study connectivity in general random graphs in more detail. In particular, we study the percolation phenomenon, which refers to the abrupt transition of connectivity in large random graphs from a combination of disconnected islands to a large cluster spanning the whole graph when a critical threshold on the randomness parameter is exceeded. We study the extension of this percolation behavior to the case of a multilayer graph, which is formed by merging different graphs on the same vertex set, each representing a different type of connection between vertices. A multilayer graph, in general, is better connected than its individual layers, as vertices can be connected through paths traversing many layers. We numerically calculate the critical connectivity level on each layer such that the multilayer graph transitions to a well-connected state, i.e., percolates. Furthermore, we study the exact asymptotic behavior of this critical percolation threshold as the number of layers increases.

#### Recommended Citation

Capar, Cagatay, "Asymptotic Analysis of Random Wireless Networks: Broadcasting, Secrecy, and Hybrid Networks" (2014). *Doctoral Dissertations*. 163.

https://scholarworks.umass.edu/dissertations_2/163