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Figure 9.8. Logical view of the assumed two-tier network architecture (redrawn from reference 36). MSN stands for micro-sensor nodes.
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existing AFNs and the best positions for placing the M relays. To ef ciently solve the optimization problem, the formulation was further simpli ed through a two-phase procedure. In the rst phase a heuristic is proposed for optimized placement of the M relay nodes. Given the known positions of the RNs, in the second phase the energy budget is allocated to the combined AFNs and RNs population, which is a linear programming optimization. Data delity is obviously an important design goal of WSNs. A sensor network basically provides a collective assessment of detected objects by fusing the readings of multiple independent, and sometimes heterogeneous, sensors. Data fusion boosts the creditability of the reported incidents by lowering the probability of false alarms and of missing a detectable object. From a signal processing point of view, data fusion tries to minimize the effect of the distortion by considering the readings from multiple sensors so that a high- delity assessment can be made regarding the detected phenomena. Although increasing the number of sensors reporting in a particular region will sure boost the accuracy of the fused data, redundancy in coverage would require an increased node density, which can be undesirable due to cost and other constraints such as the potential of detecting the sensors in a combat eld. Zhang and Wicker [37] looked at the sensor placement problem from a data fusion point of view. The observation that they made is that there is always an estimation distortion associated with a sensor reading which is usually countered by getting many samples. They thus mapped the problem of nding the appropriate sampling points in an area to that of determining the optimal sampling rate for achieving a minimal distortion, which is extensively studied in the signal processing literature. In other words, the problem is transformed from the space to the time domain. The optimal sampling points are actually the best spots where sensors can be placed. The approach is to partition the deployment area into small cells, and then optimal sampling rate per cell is determined for minimal distortion. Assuming that all sensors have the same sampling rate, the number of sensors per cell can be determined. Similar to Zhang and Wicker [37], Ganesan et al. [38] studied sensors placement to meet some application quality goals. The problem considered is to nd nodes positions so that the fused data at the base station meets desired level of delity. Unlike Zhang and Wicker [37], a tolerable distortion bound is imposed as a constraint, and minimizing energy consumption in communication is set as an objective of the optimization formulation. Also, in this work the number of sensors is xed and their position is to be determined. Given the consideration of energy consumption, data paths are modeled in the formulation, making the problem signi cantly harder. The authors rst provided a closed-form solution for the one-dimensional node placement case and used it to propose an approximation algorithm for node placement in a circular region. Extending the approach to handle other regular and irregular structures is noted as future work. Wang et al. [39] also exploited similar ideas for a WSN that monitors a number of points of interest. Practical sensing models indicate that the ability of detecting target/events diminishes with increased distance. One way to increase the creditability of the fused data is to place the sensors so that a point of interest would be in the
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high- delity sensing range of multiple nodes. Given a xed number of sensors, there is a tradeoff between deploying a sensor in the vicinity of one point of interest to enhance the probability of event detection and the need to cover other points of interest. The probability of event detection by a sensor is called the utility. The utility per point of interest is thus the collective utility of all sensors that cover that point. The authors formulate a nonlinear optimization model to identify the locations of the sensors so that the average utility per point of interest is maximized. To limit the search space, the area is represented as a grid with only intersection points considered as candidate positions. Finally we would like to note that the work of Clouqueur et al. [14], which we discussed earlier, can also be classi ed under data- delity-based sensor placement. They estimate the creditability of fused data from multiple sensors and use it to identify the position of sensors for maximizing the probability of target detection. Table 9.1 categorizes the sensor nodes placement mechanisms discussed in this section. 9.2.2 Base-Station Placement A considerable research has been done on optimal initial (i.e., at network setup time) positioning of single or multiple base stations in WSNs. Published work generally differs based on the assumptions made, the considered network model, the available network state information, and the metrics to be optimized. Popular objectives of base-station positioning include maximizing the overall network lifetime, minimizing the longest data path, and achieving maximal data rate. Given the location, onboard energy supply, and number of sensors, such objectives are optimized using techniques like integer linear programming, network ow, and computational geometry. In this section, we categorize prior work on static single and multiple base-station positioning. Optimized Positioning of a Single Base Station. The limited energy supply onboard a sensor node has made network longevity a key performance metric. Some published work exploited the exibility in base station positioning in order to extend the network lifetime. Nonetheless, multiple variants of the base-station positioning were pursued. The difference is due to either the de nition of a network lifespan, the network operation model, and the network state parameters that are included in the formulation. While some considered the network to be functional until the rst sensor node dies [7], many used the failure of a percentage of the deployed sensors [12, 40, 41] as indicative of the network lifespan. Other work strived to extend the network lifetime through minimizing the total power consumed in collecting the readings of all sensors [11]. All these static base-station positioning approaches have assumed a periodic data collection model for the network. That is, each sensor node transmits a certain amount of data at a xed rate. Some schemes also factored in the necessary transmission scheme for the sensor nodes [7]. However, no in-network data aggregation has been considered; that is, each node should transmit the packets it received without any concatenation, suppression, or compression. While most of these
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