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Understanding Performance Limits in Wireless Sensor Networks

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Title: Understanding Performance Limits in Wireless Sensor Networks
Author(s): Zhang, Honghai
Subject(s): wireless sensor networks
Abstract: In this PhD thesis, we study the fundamental limits of the network performance with respect to coverage, connectivity, lifetime, power, energy, and capacity in wireless sensor networks. An interesting finding is that many of the performance limits are related to the power level chosen by each node to perform sensing and communication tasks. For example, the choice of sensing power and transmission power determines network coverage, connectivity, and the drain of the battery energy, which in turn decide the network lifetime and capacity. Therefore, most of the performance limits are linked at heart by the power consumption of sensor nodes and sensor networks. We first address the problem of maintaining sensing coverage and connectivity in large scale wireless sensor networks. We prove a necessary and sufficient condition under which coverage infers connectivity: the radio range is at least twice the sensing range. In addition, we derive a set of optimality conditions that minimize the overlap while maintaining complete coverage. Based on the optimality conditions, we design a localized algorithm OGDC that can form a connected coverage set of sensors using a small number of sensors. We next analyze the lifetime upper bounds for a wide class of algorithms that maintain coverage and connectivity in sensor networks. Based on the theory of coverage processes, we derive the asymptotic lifetime upper bound in an infinitely large region under several different model assumptions (such as with and without Torus convention) and several different types of node deployment methods (such as Poisson deployment, uniformly random deployment, and regular grid deployment). In addition, we investigate the lifetime upper bound for which only alpha portion of the area is covered and also devise an algorithm that can approach the derived lifetime upper bound. We also study the minimum total power required for maintaining k-connectivity. We show that under the assumption that nodes are distributed as a Poisson point process with density lambda, the minimum total power required for maintaining k-connectivity is \Theta(\frac{\Gamma(c/2 + k)}{(k-1)!} \lambda^{1-c/2}), where 2 <= c <= 4 is the path loss exponent. We find that by allowing each node to choose different transmission ranges, the average power consumption can be reduced by an order of \Theta((\log \lambda)^{c/2}), compared with the case when all nodes choose a common minimum power to ensure k-connectivity. Finally, we study the minimum energy required for transporting packets between two arbitrarily chosen source and destination in a random wireless network. We prove that under the assumption that nodes are distributed as a Poisson point process with density lambda, the minimum energy is \Theta(\lambda^{(1-c)/2}), where c is the path loss exponent. This result can be used to show several network transport capacities. For example, we prove that the network transport capacity with ultra wide band is \Theta(\lambda^{(c-1)/2}) under the assumption that nodes are distributed as a Poisson point process and source destination pairs are randomly chosen. Our simulation results show that the minimum energy converges to d \lambda^{(1-c)/2}, where d is the distance between the source and destination.
Issue Date: 2005-08
Genre: Technical Report
Type: Text
URI: http://hdl.handle.net/2142/11064
Other Identifier(s): UIUCDCS-R-2005-2593
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-20
 

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