Distributed Detection in Sensor Networks: Joint Optimization via Hoeffding's Inequality

This paper addresses the optimization of wireless sensor networks for distributed detection applications. In general, the jointly optimum solution for the local sensor decision rules and the fusion rule is very difficult to obtain and does not scale well with the number of sensors. In this paper, the joint optimization of the local sensor decision rules and the fusion rule is facilitated by using an upper bound on the global probability of detection error. The bound is derived using Hoeffding's inequality and allows for non-identically distributed sensor observations, multi-bit sensor output, as well as noisy communication channels between the sensors and the fusion center. By considering the problem of detecting a known signal in the presence of Gaussian noise, numerical results reveal dependencies of the obtained solutions on the prior probabilities, the total number of sensors, and the local observation SNR.