An Asymptotically Equivalent GLRT Test for Distributed Detection in Wireless Sensor Networks

Abstract

In this article, we tackle the problem of distributed detection of a radio source emitting a signal. We consider that geographically distributed sensor nodes obtain energy measurements and compute cooperatively a statistic to decide if the source is present or absent. We model the radio source as a stochastic signal and work with spatially statistically dependent measurements. We consider the Generalized Likelihood Ratio Test (GLRT) approach to deal with an unknown multidimensional parameter from the model. We analytically characterize the asymptotic distribution of the statistic when the amount of sensor measurements tends to infinity. Moreover, as the GLRT is not amenable for distributed settings because of the spatial statistical dependence of the measurements, we study a GLRT-like test where the statistical dependence is completely discarded for building this test. Nevertheless, its asymptotic performance is proved to be identical to the original GLRT, showing that the statistical dependence of the measurements has no impact on the detection performance in the asymptotic scenario. Furthermore, the GLRT-like algorithm has a low computational complexity and demands low communication resources, as compared to the GLRT.