On The Effect of Spatial Correlation on Distributed Energy Detection of a Stochastic Process

We consider the problem of distributed detection over a network of sensors using energy measurements. Assuming that the problem is to detect the presence of stochastic signal with arbitrary temporal correlation, we exactly compute the characteristic function of the energy measurement at each sensing node. As it is shown, when the time-bandwidth product W T is large enough, the exact joint probability density function of the measurements at the sensor sites can be closely approximated by a product of non-trivial density functions that depend of some unknown parameters of the source signal and the sensor network. As those parameters can be easily estimated at each sensor node, we propose a modified generalized likelihood ratio test (GLRT). Through numerical experiments we show that this proposal has performance close to the optimal one which use the exact joint density function and with a significant reduction in the consumption of network resources as bandwidth and transmission power.