Distributed Discrimination from Correlated Sensor Observations

We address two problems of distributed discrimination between two non-weak signals from dependent observations with fixed-sample-size. In the context of this paper, the decisions are coupled through a common cost function, which consists of the sum of the error probabilities under the two hypotheses. In the first problem, two detectors must decide on the basis of their observations which one of two different non-weak signals is present. The observations of the two detectors obey multivariate probability density functions of ¿-mixing or ¿-mixing type, and they are independent for the two sensors when conditioned on the particular hypothesis being true. In the second problem, the observations of each individual detector still follow multivariate joint pdfs of ¿-mixing or ¿-mixing dependance, but they are now also correlated across sensors. Large sample sizes are necessary to guarantee high quality tests and the asymptotic performance is of interest. In both cases, the detectors employ suboptimal decision tests based on memoryless nonlinearities. To determine the optimal nonlinearities for the two detectors, we identify new performance measures based on two-dimensional Chernoff bounds. The maximization of their exponents (the exponential rates of decrease) implies the minimization of the aforementioned average cost function. This optimization results in integral equations whose solution provides the optimal nonlinearities. Numerical results based on simulation of the performance of the proposed two-sensor schemes are provided for the case of multivariate Rayleigh vs. log-normal observations to support the analysis.