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Intensive research has been conducted to improve the network performance in terms of network throughput, delay, and energy ef ciency with transmission power control The rst wave of such approaches is power-controlled MAC protocols for example, BASIC schemes [2 5], PCM [6, 7], PCMA [8], and so on Then other approaches with transmission power control are exploited to improve the network performance These early works only consider the interplay between power control and single layer; hence they may not necessarily lead to performance improvement when combining power-aware algorithms across multiple layers Simulation results in reference 9 show that this phenomenon can be realized under certain conditions Therefore, power control problem should be tackled in a systematic approach [10 15] Energy is a precious resource in wireless ad hoc networks because most nodes in the network are driven by battery and cannot be recharged in most cases.

2.3 SCALABILITY AND SYSTEM LIFETIME It is well known that homogeneous ad hoc networks, which include homogeneous WSNs, suffer poor capacity. Gupta and Kumar [11] were the rst to show that the throughput of a node is (1/ n log n), where n is the number of nodes in the network a very pessimistic result! In addition, as paths between nodes become longer, the probability of packets being lost becomes higher. As the number of nodes in a network grows, the successful end-to-end transmission rate drops signi cantly [12]. Experimentation in simulation [13] and in testbeds [14] has con rmed that the performance of homogeneous ad hoc networks does not scale with increasing n. A primary difference between WSNs and ad hoc networks is that the traf c pattern is many-to-one, from the sensor nodes to the base station. Figure 2.7 shows a homogeneous WSN with a base station at the center. A transmission from any sensor node to the base station goes through one of the nodes within a distance of r of the base station. These critical nodes have the highest burden of relaying traf c. As a result, they are likely to exhaust their energy before other sensor nodes [15]. When the critical nodes die, connectivity of the network is lost. Hence the energy drainage rate of the critical nodes determine the system lifetime. Indeed, Du and Xiao [16] found that when connectivity is lost, more than half of the nodes still have more than 50% of their energy left. This energy is wasted since communication with the sink is no longer viable.

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In order to keep the network functional as long as possible, energy-ef cient algorithms should be devised By reducing transmit power level, energy consumption for packet transmission at each node can be reduced Thus, transmission power control is an important technique to design energy-ef cient algorithms for conserving the battery energy of nodes and prolonging the functional lifetime of the network Techniques such as energy-ef cient routing [16 18], topology control [19 23], and power management [24 27] also help to improve energy ef ciency of wireless ad hoc networks The remaining part of this survey is organized as follows Section 112 describes the impact of power control on the wireless ad hoc networks, and it derives some basic guidelines for transmission power control problem In Section 11.

Adding structure to the network can help improve scalability and also alleviate the problem of nonuniform drainage of energy. Clustering is one way to add structure in a homogeneous WSN. Heinzelman et al. propose LEACH, a clustered network in which each cluster head aggregates data and transmits it directly to the base station [17]. The cluster heads are periodically rotated for ef cient load balancing and a consequent lengthening of network lifetime. In order to minimize the total energy, the number of cluster heads must scale as the square root of the total number of sensor nodes [17]. The LRS [18] and power-aware chessboard-based adaptive routing (PCAR) [19] protocols also aim to balance the energy consumption in a homogeneous sensor network. All of these protocols suffer from overhead associated with frequent cluster-head rotation. While the problem of routing in homogeneous WSNs has been considered in at architectures (see Directed Diffusion [20] as an example), when the architecture is hierarchical, the routing protocol makes use of the hierarchy (see TTDD [21] and LEACH [17] as examples). Hierarchy is shown to help a homogeneous WSN achieve higher total throughput and increase the network lifetime. In heterogeneous WSNs, it is often natural to organize the nodes into a hierarchy. In this section we consider algorithms for heterogeneous WSNs to form hierarchical topologies, and address the related problem of routing, in order to tackle the problems of scalability and nonuniform energy drainage. 2.3.1 A Resource-Oriented Protocol: Topology Formation and Routing In WSN applications in which the sensor nodes are inherently heterogeneous in energy resources, these differences should be considered in order to improve the network capacity and extend the system lifetime.

3, we review the transmission power control problem following a single-layer approach; that is, we only consider interactions between power control and single layer Transmission power control in MAC, network, and transport layer is investigated respectively In Section 114 we consider the transmission power control problem from the holistic perspective, and in Section 115 we review energy ef cient algorithms and protocols joint with power control to improve energy ef ciency Finally, we conclude the survey in Section 116 Open issues are discussed at the end of each section 112 DESIGN PRINCIPLES FOR POWER CONTROL In this section we rst describe the fundamental network architecture of wireless ad hoc networks Then we introduce the problem of power control in wireless ad hoc.

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