Favor the Tortoise Over the Hare: An Efficient Detection Algorithm for Cooperative Networks
Pages 3153 - 3170
Abstract
We develop a low-cost algorithm to decide the current state of an environment being monitored by a cooperative and fully distributed wireless network of intelligent sensors, with a low time to reach a given performance. We consider WSNs (<italic>Wireless Sensor Networks</italic>) deployed under stringent power conditions, a situation for which low computational complexity and low power consumption is highly desired. We model a multiple hypothesis test using the <italic>diffusion Least Mean Square</italic> (dLMS) algorithm, a well known estimation technique used in distributed networks, to process data and also share information among nodes across the network. Our first contribution is showing that the performance of this theoretical detector, given in terms of the average probability of error, approximates the optimal performance if the underlying estimator operates at a slow learning rate, which is achieved by a sufficiently small step size. Notably, the detector performance improves as the value of the this step size is reduced, without any reduction in the detection error convergence rate, despite the slower estimation convergence rate. This somewhat counter-intuitive behavior is explained theoretically and confirmed by simulations. From this theoretical formulation, we devise a new detector with low computational complexity whose performance also closely matches that of the optimal and shows the same aforementioned behavior, where the slowest learning rate provides the best detection performance in terms of both the probability of error and convergence rate. We also show that this performance can be easily achieved provided that an adequate initialization of the estimation algorithm is chosen.
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