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Generalized Analysis of a Distributed Energy Efficient Algorithm for Change Detection

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4 Author(s)
Banerjee, T. ; Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA ; Sharma, V. ; Kavitha, V. ; JayaPrakasam, A.K.

We propose an energy efficient distributed cooperative Change Detection scheme called DualCUSUM based on Page's CUSUM algorithm. In the algorithm, each sensor runs a CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a Multiple Access Channel (MAC) corrupted with noise. The fusion center performs another CUSUM to detect the change. The algorithm performs better than several existing schemes when energy is at a premium. We generalize the algorithm to also include nonparametric CUSUM and provide a unified analysis. Our results show that while the false alarm probability is smaller for observation distribution with a lighter tail, the detection delay is asymptotically the same for any distribution. Consequently, we provide a new viewpoint on why parametric CUSUM performs better than nonparametric CUSUM. In the process, we also develop new results on a reflected random walk which can be of independent interest.

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Wireless Communications, IEEE Transactions on  (Volume:10 ,  Issue: 1 )