Generalized Analysis of a Distributed Energy Efficient Algorithm for Change Detection

Abstract

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.

Distributed nonparametric sequential spectrum sensing under electromagnetic interference

“…But the impact of heavy-tailed noise has not been specifically studied. In [24], this was considered in the context of change detection and it was shown that heavy tails can degrade the performance significantly. In this paper, for the distributed hypothesis testing algorithm also, we show that heavy-tailed distributions can significantly impact the performance.…”

“…None of these works studies the effect of EMI or outliers on the detection algorithm. Distributed spectrum sensing has been a recent development in this direction ( [2], [22], [23], [24] and the references therein). See [17], [25], [26], [27], [28], [29], [30] for more recent developments in distributed detection and [30] for distributed estimation.…”

Cooperative robust sequential detection algorithms for Spectrum Sensing in Cognitive Radio

“…We briefly present the main steps of the analysis and discuss the differences for the present setup from [2]. The analysis for GLR-CUSUM and MGLR-CUSUM will follow the same steps but will differ in some detail.…”

“…Let At the fusion node a False Alarm will most likely occur during a batch at some secondary node (when a secondary is falsely transmitting). k F at the fusion center can also cross β due to The analysis in [1], [2] was for sensor networks where it was assumed that each node has the same distribution. However now it is more reasonable to assume that the channel gains l P from the primary to each cognitive radio are different.…”

“…However now it is more reasonable to assume that the channel gains l P from the primary to each cognitive radio are different. This requires some changes in computing the FA P and EDD compared to the analysis in [2] which we now explain.…”