1. Event Detection From Mobile, Wireless, and Sensor Networks (Technology, Applications, and Future Directions), Chapter 6, Wiley and IEEE Press

2. MODEL DESCRIPTION A typical wireless sensor network consists of a number of sensor nodes and a control center. To perform a detection function, each sensor node collects observation data from the surrounding environment, does some processing locally if needed, and then routes the processed data to the control center. The control center is responsible for making a final decision based on all the data it receives from the sensor nodes.

4. Practical Wireless Sensor Network Model For a wireless sensor network to perform a detection function, routing usually is needed to transmit data from faraway nodes to the control center Spatial and temporal correlations exist among measurements across or at sensor nodes Noise interference must be considered as well.

5. Simplified Wireless Sensor Network Model No cooperations among sensor nodes — each sensor node independently observes, processes, and transmits data. No spatial or temporal correlation among measurements — observations are independent across sensor nodes, and at each single node. No routing — each sensor node sends data directly to the control center. No noise or any other interference — data are transmitted over an error-free communication channel.

6. Simplified Wireless Sensor Network Model

7. Random variable H: indicates whether an event occurs (H =H1) or does not occur (H =H0) Prior probabilities: P[H=H1]=p and P[H =H0]=1- p (0 < p < 1). We have K sensor nodes, {S1, S2,...,SK} Each node makes T binary observations Yi(j) is the jth observation at sensor Si, Yi(j)=0 or 1, i =1, 2,..., K; j =1, 2,..., T. Observations are independently and identically distributed (i.i.d.) Observations have the identical conditional pmf of P[Yi(j)=1|H0]=p0 (false alarm) and P[Yi(j)=1| H1]=p1 (detection prob.), with 0 < p0 < p1<1. ni: the number of 1s out of T observations at sensor Si The processed data are transmitted to the control center, where a final decision Ĥ is made. Our objective is to minimize the overall probability of error (P[ Ĥ  H] ) at the control center.

8. Three Operating Options 1.Centralized Option 2.Distributed Option 3.Quantized Option

9. Three Operating Options 1.Centralized Option: –At each sensor node, the observation data are transmitted to the control center without any loss of information. –The control center bases its final decision on the comprehensive collection of information.

10. Three Operating Options

11. 3. Quantized Option –Instead of sending all the information or sending a one-bit decision, each sensor node processes the observation data locally and sends a quantized M-bit quantity (qi for Si, qi  {0, 1,..., 2 M - 1}, 1  M  T) to the control center –The control center makes the final decision based on the basis of the k quantized quantities {q1; q2;... ; qk}.

12. Analysis – Centralized Option

15. Analysis – Distributed Option For the distributed option we consider the local decision rule at the sensor nodes and the final decision rule at the control center, respectively. 1. Local Decision Rule. As we have specified before, each sensor node applies a local decision rule to make a binary decision based on the T observations. –A question yields naturally whether we should have an identical local decision rule for all the sensor nodes. –Generally, an identical local decision rule does not result in an optimum system from a global point of view. However, it is still a suboptimal scheme if not the optimal one, which has been observed by some previous work. –Irving and Tsitsiklis [9] showed that for the binary hypothesis detection, no optimality is lost with identical local detectors in a two-sensor system –Chen and Papamarcou [3] showed that identical local detectors are asymptotically optimum when the number of sensors tends to infinity.

16. Analysis – Distributed Option –Identical local decision rule is assumed. –Each sensor node does not have any information about other nodes, which means that the identical local decision rule would depend only on {T, p, p0, p1} –The number of sensor nodes K is considered as global information and not available for decision making of sensor nodes. –Eventually the problem is simplified to a similar case for the centralized option, where the only difference is the number of observations changes from KT to T.

17. Analysis – Distributed Option

22. Analysis – Quantized Option For the quantized option, we develop the optimal quantization algorithm as well as the suboptimal quantization algorithm for different application scenarios.

23. Analysis – Quantized Option

25. The optimal quantization algorithm can be obtained by exhaustive search. The one producing the minimal probability of error is the desired optimal quantization algorithm.

26. Comparisons We evaluate the detection performance of the three operating options in terms of Pf, Pd, and Pe. Here we adopt the optimal quantization algorithm for the quantized option. We fix K=4, M=2, p =0.5, p0=0.2, and p1=0.7 and vary T from 3 to 10. Figures 6.3–6.5 show Pf, Pd, and Pe versus T for three options. As we see in general, the centralized option has the best detection performance in the sense that it achieves the highest Pd and lowest Pf and Pe, while the distributed option has the worst performance. This is consistent with our expectation since the centralized option has a complete information of the observation data at the control center, while the distributed option has the least information at the control center.

27. Comparisons

30. Conclusion We have constructed a simplified wireless sensor network model that performs an event detection mission. We have implemented three operating options on the model, developed the optimal decision rules and evaluated the corresponding detection performance of each option. As we expected, the centralized option performs best while the distributed option is the worst regarding the accuracy of the detection. However, it is shown that the distributed option needs fewer than twice the sensor nodes for the centralized option to achieve the same detection performance.

31. Conclusion We have modeled the energy consumption at the sensor nodes. The energy efficiency as a function of system parameters has been compared for the three options. The distributed option has the best performance for low values of Ec and high values of Et. (Ec represents the energy consumed for one comparison or one counting, and Et represents the energy consumed for transmitting one bit of data over a unit distance) For high Ec and low Et, the centralized option is the best for relatively short distances from sensor nodes to the control center, while the distributed option is the best for long distances.

32. Conclusion Furthermore, we have examined the robustness of the wireless sensor network model by implementing two attacks. For both of them, the distributed option shows the least loss of performance in terms of ratio while the centralized option has the highest loss.

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