ON THE EFFECT OF SPATIAL CORRELATION ON DISTRIBUTED ENERGY DETECTION OF A STOCHASTIC PROCESS

JUAN AUGUSTO MAYA; LEONARDO REY VEGA

Toronto

Conferencia; 2021 IEEE International Conference on Acoustics, Speech and Signal Processing; 2021

IEEE

In this article, we consider the problem of fully distributed detection of a localized source emitting a signal. We consider that geographically distributed sensor nodes obtain energy measurements and compute cooperatively and in a distributed fashion a statistic to decide if the source is present or absent without the need of a central node or fusion center (FC). We develop a model for the sensor network in which the measurements of different nodes are correlated and some parameters are unknown and must be positive. Thus, the detection problem can be described as a composite hypothesis testing problem. Under the framework of the Generalized Likelihood Ratio Test (GLRT) theory, the positive constraint on the unknown parameters is a non-standard condition and makes the computation of the GLRT asymptotic performance more involved. Nevertheless, we provide a closed-form formula to characterize the asymptotic distribution of the statistics. However, as this test is not amenable to be implemented in a fully distributed setting, we provide an approximate test using the product of the marginal PDFs with local parameter estimation at each node. The asymptotic distribution of this test is also obtained and shown to be identical to the original GLRT test, which contemplates the full statistic structure through the joint PDF. Furthermore, contrary to the GLRT, the proposed algorithm has a structure that facilitates its computation in a distributed manner in Wireless Sensor Networks (WSNs) with scarce communication and computation resources. We conclude the paper by evaluating the performance of the algorithms in the finite data size regime in the context of spectrum sensing in cognitive radio systems showing that even for not so large data sets, their performances have a very good match with the theoretical asymptotic performance, showing the usefulness of the results in practical problems.