Distributed random signal detection with multibit sensor decisions

Distributed detection of weak random signals in additive, possibly non-Gaussian, noise is considered for cases with multibit sensor decisions. Signal-to-noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent. Analytical expressions are provided that describe the best way to fuse the quantized observations for cases with any given number of sensors. The best schemes for originally quantizing the observations at each sensor are also studied for the case of an asymptotically large number of sensors. These schemes are shown to minimize the mean-squared error between the best weak-signal test statistic based on unquantized observations and the best weak-signal test statistic based on quantized observations. Analytical expressions describing optimum sensor quantizers are provided. The approach used to obtain these expressions insures these sensor quantizers give good performance for cases with a finite number of sensors. A novel iterative technique to search for optimum sensor quantizers efficiently is described. Numerical solutions are presented, some of which involve cases where the best schemes for independent signal observations are shown to be suboptimum.