**2. Related work**

This section presents an overview of related work in energy efficiency in multihop wireless communications. Differences with the approach investigated in this Chapter for energy efficient cooperative multihop data transmission are outlined.

Network topology design in order to achieve different requirements in a service-oriented framework is considered in [32]. Requirements include throughput maximization, delay constraints, security, and reliability. Energy minimization constraints are not considered. Topology control is also considered in [22], where energy constraints are taken into account via transmit power adjustments. Connectivity between nodes is determined based on distance considerations. In [23] and [16], energy efficiency is considered by having a minimum energy path between each pair of nodes in a wireless multihop network. Topology is controlled by varying the transmission power at each node, and the transmission power at the antenna is considered as the criterion for energy efficiency. In this Chapter, the energy drained from the sensors' batteries, not only the transmit power at the antenna, is used as the criterion for energy efficiency.

Processing capacity is studied in [25] for wireless sensor networks. A cross-layer collaborative in-network processing approach among sensors is adopted, where, in addition to processing information at the application layer, sensors synchronize their communication activities to exchange partially processed data for parallel processing. Sensor nodes are grouped into clusters, and operations are performed independently inside each cluster. Communications between clusters are performed using channels that are orthogonal to intra-cluster communications. Multihop communications are implemented inside each cluster to perform parallel computing of certain processing tasks. Thus, energy efficiency is considered in the sense of minimizing the processing power during task scheduling and implementation, not in the sense of transmissions and receptions for relaying measurement data of sensors, as is the case in this Chapter.

2 Will-be-set-by-IN-TECH

interfaces: one to communicate with the BS over a long-range (LR) wireless technology (e.g., UMTS/HSPA, WiMAX, or LTE), and one to communicate with other SNs over a short-range (SR) wireless technology (e.g., Bluetooth, ZigBee, or WLAN). In addition to freeing bandwidth at the BS and increasing network throughput [19, 20], SR collaboration between SNs leads to a reduced energy consumption [8, 31]. In fact, higher rates can be achieved over SR communications between SNs that are relatively close from each other in a single cooperating cluster. This leads to shorter transmission and reception times and hence

In this Chapter, SNs are considered to be distributed throughout the cell area and can form several cooperating clusters. The energy minimization problem during cooperative content distribution in the multiple clusters case is formulated and the solution outline is presented. Multihop communications are studied, and remarkable energy savings are achieved even with the 2-hop scenario, corresponding to a clustering framework where a single SN, the cluster head (CH), is in charge of directly receiving the measurement data from each SN in the cluster on the SR, and for transmitting the aggregated data to the BS on the LR. A general formulation that incorporates both multihop and clustering is presented, and energy efficient

The paper is organized as follows. Related work is presented and differences with the proposed approach are outlined in Section 2. The system model is presented in Section 3. The problem formulation and solution are discussed in Section 4. Suboptimal schemes leading to significant energy savings at reduced complexity are proposed in Section 5 for the multihop and clustering scenarios. The simulation results are presented in Section 6. Practical implementation aspects are discussed in Section 7. An application example of a WSN for air quality monitoring is presented in Section 8. Potential research directions for future investigation are described in Section 9. Finally, conclusions are drawn in Section 10.

This section presents an overview of related work in energy efficiency in multihop wireless communications. Differences with the approach investigated in this Chapter for energy

Network topology design in order to achieve different requirements in a service-oriented framework is considered in [32]. Requirements include throughput maximization, delay constraints, security, and reliability. Energy minimization constraints are not considered. Topology control is also considered in [22], where energy constraints are taken into account via transmit power adjustments. Connectivity between nodes is determined based on distance considerations. In [23] and [16], energy efficiency is considered by having a minimum energy path between each pair of nodes in a wireless multihop network. Topology is controlled by varying the transmission power at each node, and the transmission power at the antenna is considered as the criterion for energy efficiency. In this Chapter, the energy drained from the sensors' batteries, not only the transmit power at the antenna, is used as the criterion for

Processing capacity is studied in [25] for wireless sensor networks. A cross-layer collaborative in-network processing approach among sensors is adopted, where, in addition to processing information at the application layer, sensors synchronize their communication

efficient cooperative multihop data transmission are outlined.

less energy consumption from the batteries of the SNs.

suboptimal schemes are proposed.

**2. Related work**

energy efficiency.

Small scale networks where sensor nodes are closely located are studied in [7]. TDMA is assumed as an access method. Both transmission and circuit-based energy consumption are considered. Perfect synchronization between nodes is assumed. The joint design of the physical, MAC, and routing layers to minimize network energy consumption is formulated into a convex optimization problem and the solution is provided. The approach presented in this Chapter does not make any assumptions concerning the channel accessing scheme or the scale of the sensor network.

In [13], energy efficiency is studied in wireless sensor networks. Sensors having data to transmit should relay this data to a single source using multihop. Nodes that do not have data to transmit or that are not relaying the data of other nodes can be put to sleep. Energy efficiency is achieved by reducing the number of active nodes. An energy efficient routing technique in multihop wireless sensor networks is presented in [28]. For each node, the energies consumed during reception, transmission, and sensing are considered in the analysis. In the model of [28], frame nodes relay the content of the source to the destination. If the communication fails between the source and a frame node, or between two frame nodes, assistant nodes come into play and relay the data to the next frame node. Hence the use of opportunistic transmissions depending on the fading conditions of the channel. The optimal number of nodes that should be included in a path is determined. The purpose is to reduce the energy consumption by reducing the number of nodes relaying the data from source to destination. In the scenario investigated in this Chapter, all nodes are assumed to have data to transmit, and hence cannot be put to sleep to achieve energy savings. This scenario corresponds, for example, to WSNs deployed for the purpose of air quality monitoring in a given area, where each sensor will periodically send measurement data to a central processing system.

In [3], multipath routing based on spatial relationships among nodes is considered. Stochastic geometric and queueing models are used for the evaluation of different types of scenarios. Energy aware routing with the possibility of energy replenishment of nodes in multihop wireless sensor networks is presented in [17]. An algorithm that only requires short term energy replenishment information is also presented. However, channel conditions are not taken into consideration in the approach of [17], conversely to the work in this Chapter where channel state information (CSI) is exploited in order to build the energy efficient routes from SNs to the BS.

Several papers in the literature consider implementation scenarios related to a particular standard. For short range multihop communications, IEEE 802.11s is receiving significant attention. In [6], a tutorial is presented for multihop communications and mesh capabilities in IEEE 802.11. Task group 802.11s is handling this issue. In the draft 802.11s proposal, the mesh network is implemented at the link layer and relies on MAC addresses instead of IP addresses, which provides layer-2 multihop communication. A survey of the unicast admission control schemes designed for IEEE 802.11-based multi-hop mobile ad-hoc networks (MANETs) is presented in [10], where different admission control protocols are discussed and analyzed. In [27], cooperative rate adaptation in multihop IEEE 802.11 is considered. The problem is formulated as an optimization problem and shown to be NP-hard. Thus, a suboptimal method is presented. Energy efficiency is considered in terms of reducing the transmission power at the SNs' antennas. Enhancements of the performance of IEEE 802.11-based multihop ad hoc wireless networks from the perspective of spatial reuse were surveyed in [2]. Techniques adopting transmit power control, tuning the carrier sensing threshold, performing data rate adaptation, and using directional antennas were discussed. In this Chapter, the presented approach is general and not confined to a particular standard, it does not only consider transmit energy at the antenna, but also the energy drained from the battery during transmission and reception. Compared to mesh networks, not every SN needs to communicate with all other SNs. Instead, each SN needs to transmit the measured data using an optimum energy minimizing path to the BS. This path remains the same as long as the channel conditions remain constant.

In addition to multihop, energy efficient clustering methods are also investigated in the literature. An algorithm is presented in [14] as an improvement on the methods in [12] and [15]. In [12, 14, 15], each node volunteers to be a cluster head in a probabilistic manner, and non-cluster nodes associate themselves with cluster heads based on the announcements received from these cluster heads. The actual energy drained from the battery of the device is considered. However, the problem is not formulated and solved as an optimization problem (as in this Chapter), but rather an efficient clustering algorithm that ensures fairness in energy consumption between nodes, due to the probabilistic selection, is presented. In [15], the use of a proxy node was added to the approach of [12], whereas in [14] the additional use of a main cluster head was implemented, with the main cluster head relaying the data from cluster heads to the BS. The work of [12] was extended in [4] to include multihop communications in addition to clustering. In addition, an approach to determine the optimal number of cluster heads is proposed. Clustering is performed on distance based criteria and a probabilistic random approach is adopted for the election of cluster heads. A cluster head selection based on proximity was adopted in [30], where the residual energy of the node is also considered in the selection process. A multihop time reservation using adaptive control for energy efficiency (MH-TRACE) is presented in [24]. Cluster formation is probabilistic and it is not based on connectivity information. In MH-TRACE, the interference level in the different time-frames is monitored continuously in order to minimize the interference between clusters. MH-TRACE clusters use the same spreading code or frequency and time division is adopted. In this Chapter, cluster head selection is not probabilistic or simply proximity based. Fading is considered in the selection approach since CSI affects the achievable rates and is thus incorporated in the optimization problem.
