SPATIOTEMPORAL CORRELATION THEORY FOR WIRELESS SENSOR NETWORKS in .NET

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SPATIOTEMPORAL CORRELATION THEORY FOR WIRELESS SENSOR NETWORKS
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node to transmit its data to the sink. Instead, a smaller number of sensor measurements might be adequate to communicate the event features to the sink within a certain reliability constraint. As a result, the MAC protocol can reduce the energy consumption of the network by exploiting spatial correlation in the WSNs without compromising on the access latency as well as the distortion achieved. In order to gain more insight to these intuitions, a case study is performed using the distortion function (5.12). In a 500-by-500 grid, 50 sensor nodes are randomly deployed. The Power Exponential model is used with 2 = 1 and 1 = {10, 50, 100, 500, 1000, 5000, 1000} as the covariance model for the covariance function, K ( ) in (5.36). The parameter 1 controls the relation between the distance of the nodes and the correlation coef cient. For each value of 1 , the distortion function (5.12) is calculated varying the number of sensor nodes sending information. Starting from 50 nodes, we decrease the number of nodes that send event information to the sink. We refer to these nodes as the representative nodes. Representative nodes are selected randomly among the 50 nodes for each trial, and the distortion function is calculated according to the locations of these nodes. The average distortion calculated from these simulations and the distribution of the distortion for each number of representative nodes is shown in Figure 5.2. As shown in Figure 5.2, the achieved distortion stays relatively constant when the number of representative nodes is decreased from 50 to 15. This behavior is due to the highly redundant data sent by the sensor nodes that are close to each other. In addition, with increasing 1 , the observed event distortion decreases because close nodes become less correlated with increasing 1 . Based on the results shown in Figure 5.2 and the distortion function (5.12), the following discussions about the observed distortion at the sink can be made:
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13 12 Observed Event Distortion 11 10 9 8 7 6 5 4 3 2 0 5 10 15 20 25 30 35 40 45 Number of Representative Nodes 50
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10 50 100 500 1000 5000 10000
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Figure 5.2. Observed event distortion for different 1 values according to changing number of representative nodes.
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COROLLARIES AND EXPLOITING CORRELATION IN WIRELESS SENSOR NETWORKS
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Remark 1. The minimum distortion is achieved when all the nodes in the event area send information to the sink. However, the achieved distortion at the sink can be preserved even though the number of the representative nodes decreases. As a result, signi cant energy saving is possible by allowing a smaller number of nodes to send information to the sink about an event. Remark 2. Based on (5.12), there are two factors affecting the distortion other than the number of representative nodes. 1. The correlation coef cient, (s,i) , between a node ni sending information and the event source S affects the distortion function negatively. The distortion increases as the distance between the event source S and the node ni increases. Intuitively, if a representative node is chosen apart from the source, it observes relatively inaccurate data resulting in higher distortion at the sink. 2. The correlation coef cient, (i,j) , between each representative node ni and nj affects the distortion positively. As the distance between nodes increases, distortion decreases. Since nodes that are further apart observe less correlated data, the distortion is decreased if these nodes are chosen as the representative nodes. Consequently, due to the spatial correlation between sensor observations, significant energy saving can be achieved by choosing representative nodes among the nodes in the event area without degrading the achieved distortion at the sink. It is clear that smaller number of nodes transmitting information reduces contention in the wireless medium, resulting in decreased energy consumption. Energy consumed from both transmission of packets and collision penalties can be reduced drastically if the spatial correlation is exploited. As a result, it is important to nd the minimum number of representative nodes that achieve the distortion constraint given by the sensor application. This minimum number can be given as M = arg (min {D(M) < Dmax }) M where Dmax is the maximum distortion allowed by the sensor application. It is important to note that the minimum number of representative nodes, M , depends on the locations of the representative nodes. It follows from our previous discussions that, for a xed number of representative nodes, the minimum distortion can be achieved by choosing these nodes such that (i) they are located as close to the event source as possible and (ii) they are located as farther apart from each other as possible. As an example, as illustrated in Figure 5.3, choosing representative nodes such that they are spread over the event area results in a decrease in distortion, due to less redundant data sent by these nodes. Note that such a formation also improves the medium access performance during the transmission of the information. Since the representative nodes are not located close to each other, the probability of collision in the wireless medium decreases. As a result, exploiting spatial correlation not only improves the distortion but also utilizes the wireless channel due to the spatial reuse property of the wireless medium.
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