Multi-Sensor Correlation and Quantization in Distributed Detection Systems
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Quantization and fusion schemes are derived for multi-sensor correlation in distributed K- sensor systems that are used for the detection of weak signals or general signal discrimination from dependent observations. The dependence in the observations across time and sensors is modeled via stationary m - dependent, f - mixing, or r - mixing processes. The observation sequences of the various sensors have identical individual statistics and identical pairwise statistics (symmetric conditions). Each sensor observation is passed through a memoryless non-linearity or quantizer (the same one for all sensors) to form the sensor test statistic; the decision statistics of the various sensors are then passed to the fusion center in an unquantized or binary quantized manner to form the final decision statistic of the fusion center. Based on a common large sample size for each sensor that is necessary for achieving high-quality performance, an asymptotic analysis is applied for the error probabilities of the fusion center. This provides design criteria for the optimal memoryless nonlinearity and quantizer. Optimization of these design criteria yields the optimal nonlinearity or quantizer as solutions to linear integral equations involving the first - and second-order pdfs of the sensor observations describing the individual and pairwise dependence. the analytical results obtained are valid for any number of sensors K. Numerical results based on the simulation of the performance of our schemes with different number of sensors are presented. The performance of the optimal nonlinearities and quantizers is shown to outperform that of nonlinearities or quantizers obtained by ignoring the dependence in sensor observations and to improve as the number of sensors increases.