Locally optimum distributed detection of correlated random signals based on ranks

Distributed signal detection schemes have received significant attention, but most research has focused on cases where the observations at the different sensors are independent and the statistical model for the observations is completely known. If the observations at the different sensors consist of noisy versions of random signals which were produced by the same source, then these observations may not be independent. It is also possible that the noise distribution may not be completely known. Cases where weak random signals are observed in possibly non-Gaussian additive noise are considered. The focus is on cases where the sensor tests are based only on the ranks and signs of the observations. Numerical results are provided which indicate that distributed schemes based on ranks and signs are less sensitive to the exact noise statistics when compared to optimum schemes based directly on the observations. This is especially true for some cases where the actual noise distribution has heavy tails, which can cause the optimum schemes based directly on the observations to perform poorly. Analytical forms are given for the locally optimum sensor test statistics based on the ranks and signs of the observations, and we use these to find the best distributed detection schemes for some cases. In the course of obtaining our results, a general set of necessary conditions is given which provide the analytical forms of the locally optimum distributed sensor tests for cases where the observations are discrete random variables. Conditions of this type have not been given previously.