Efficient Geometric Algorithms for Wireless Networks

Abstract

Wireless communications has a wide range of applications including cellular telephones, wireless networking and security systems. Typical systems work through radio frequency communication and this is heavily dependent on the geographic characteristics of the environment. This dissertation discusses the application of geometric optimization in wireless networks where the communication \links" are not static but may be dynamically changing. We show how to exploit the geometric properties of these networks to model their behavior. In the first part of the dissertation, we consider the problem of interference-aware routing in Multi-channel mesh networks employing directional antennas to improve spatial throughput. In such networks, optimal routes are paths with a channel assignment for the links such that the path and link bandwidths are the same. We develop a method to perform topology control while taking into account interference by constructing a spanner; a sub-network containing O(n= θ) links, where n is the network size and θ is a tunable parameter, such that path costs increase by at most a constant factor. In second part, we study the problem of base-station positioning in Sensor Net- works such that we achieve energy-efficient data transmission from the sensors. Given the battery limitations of the sensors, our objective is to maximize the network lifetime. First, we present efficient algorithms for computing a transmission scheme given a fixed base-station and also provide a distributed implementation. Next, we present efficient algorithms for the problem of locating the base-station and simultaneously finding a transmission scheme. We compare our algorithms with linear-programming based algorithms through simulations. In the third part, we study strategies for managing friendly jammers to create virtual barriers preventing eavesdroppers from tapping sensitive RFID communication. Our scheme precludes the use of encryption. Applications domains include (i) privacy of inventory management systems, (ii) credit card communications, (iii) secure communication in any wireless networks without encryption. By carefully managing jammers producing noise, we show how to degrade the signal at eavesdroppers sufficiently, without jeopardizing network performance. We present algorithms targeted towards optimizing the number and power of jammers. Experimental simulations back up our results.