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power-level uctuations. When a packet from this node is sent and received by the next-hop node, the next-hop node can do the same adjustment. 11.5.2 Power-Ef cient Topology Control Power-ef cient topology control [19 23, 67, 68] in wireless multihop networks maintains a moderate connectivity by adapting transmission range of nodes. Reducing the transmission range reduces the energy consumed for per-packet transmission, and it also promotes the spatial reuse. The objective of power-ef cient topology control is to minimize the transmit power while maintaining certain connectivity. Ramanathan and Rosales-Hain [23] formulate this problem as a constrained optimization problem under the constraints that the result topology should be connected and bi-connected. Their goal is to minimize the maximum transmit power of all the nodes in the network, and two centralized algorithms are proposed based on a new analytical representation of wireless multihop networks. Haiiaghayi et al. [68] studied the problem of minimizing power while keeping k-fault tolerance; that is, each node has at least k neighboring nodes within its transmission range. Two centralized approximation algorithms are proposed, and the upper bound of the approximation factor is proved. A distributed heuristic for 2- and 3-connectivity is also given based on the Minimum Spanning Tree (MST) algorithm. Li and Sinna [20] designed a framework for evaluating (a) the performance of topology control algorithms using the overall network throughput and (b) total energy consumption per packet delivered as the metrics. Based on this framework, scenarios in which topology control improves the network performance can be identi ed. Besides the efforts on theoretical analysis of power-ef cient topology problem, distributed heuristics are also proposed to improve the network performance in terms of energy and throughput. ElBett and Krishnamurthy [67] proposed a simple distributed algorithm to nd the minimum transmit power for maintaining k-connectivity of each node. The algorithm needs a global signaling channel to facilitate the computation of optimal transmission range, and this range will be dynamically changed in a distributed manner in order to adapt to channel variations. Rodoplu and Meng [19] proposed a distributed position-based topology control algorithm that consists of two phases. Phase one is used for link setup and con guration. Each node broadcasts its position to its neighbors and uses this position information of its neighbors to build a spare and strongly connected graph called enclosure graph. The key point is that all the globally optimal links (for the minimum power consumption for communication to the destination) are included in the enclosure graph. Therefore, in phase two, nodes nd these optimal links on the enclosure graph by applying the distributed Bellman Ford shortest path algorithm with power consumption as the link cost. Each node broadcasts its cost to its neighbors, where the cost of node i is de ned as the minimum power necessary for i to establish a path to destination. Wang et al. [21] proposed a localized algorithm that rst constructs a Gabriel graph from the given unit disk graph and then reduces the total transmit power by allowing each node individually excises some replaceable of links. Wattenhofer et al. [22] followed an opposite approach compared with the method in reference 21. Based on directional
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information, nodes increase their transmit power until they nd at least one neighboring node in each direction. Here, transmit power control is based on local information, while guaranteeing global connectivity. 11.5.3 Power Management Mechanism. In typical wireless networks, terminals have to be powered on at all time to detect possible signals that target them. However, this always on results in signi cant unwanted energy consumption, For example, measurements show that idle listening consumes 50 100% of the energy required for receiving [69]. Therefore, idle listening should be avoided as much as possible. Ideally, the wireless radio is powered on only when there are data waiting to be transmitted or received. Otherwise, the radio is powered off and the node is in the sleep state. In this way, the wasted energy for idle mode is minimized. The energy wasted in idle mode is mainly due to the overhearing in wireless channel. If the radio is powered on in idle mode, the ongoing transmissions in the neighborhood would be overheard by this node, which frequently happens in ad hoc networks. In this case, energy consumed for packets is not directed to them, thereby causing a waste of energy. A large amount of energy can be consumed unnecessarily is this case. For example, If a transmitter i has n neighbors, then the total energy consumed for an m-packet transmission is m (Et + n Er ), where Et is the energy required for transmitting one packet, and Er is the energy required for receiving one packet, and an amount of m (n 1) Er energy is wasted in this case. Based on this observation, a new kind of energy conservation mechanism is proposed in which some nodes are allowed to stay in the sleep state whenever they are not scheduled to transmit or receive. Obviously, this approach can reduce energy consumption, thereby prolonging the battery life of nodes in the ad hoc network. There schemes can be classi ed into three categories: scheduled, on-demand, and asynchronous power managements. In a scheduled scheme [24, 25], nodes switch to the low-power sleeping state periodically. Because all the participating nodes have to synchronize their clocks, this mechanism is most appropriate for single-hop networks, but is not well-suited in multihop ad hoc networks. In on-demand schemes [27], nodes in the sleeping state are wakened by requests from neighboring nodes. Therefore, the power management is very simple. In asynchronous schemes [26], each node follows its own wake-up schedule in idle mode, as long as the wake-up intervals among neighboring nodes overlap. Thus, this type of scheme does not require time synchronization, and it is more suitable than a scheduled scheme for multihop ad hoc networks. Related Protocols. Geographic adaptive delity (GAF) [24] is an energy-aware location-based routing algorithm. It forms a virtual grid of covered area. Each node uses its GPS-indicated location to associate itself with a point in the virtual grid. Nodes associated with the same point on the grid are considered equivalent in terms of the cost of routing. Such equivalence is exploited in keeping some nodes located in a particular grid area in the sleeping state in order to save energy. Thus, GAF can substantially increase the network lifetime if the number of nodes increases.
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