Observation-Transformed Distributed Detection in Sensor Networks

Distributed detection (DD) plays a crucial role in sensor networks, where sensors gather data from a region of interest and report their observations to a fusion center (FC). The FC then makes a decision regarding a specific task, such as determining the presence or absence of a target. Given the constraints imposed by the transmission power, bandwidth, and noise impact in both sensing and data reporting channels, what should be reported from the sensors significantly affects the final detection accuracy. Existing methods include observation-untransformed DD (UDD), codewords-based DD (CDD), and quantized-but-uncoded DD (QDD). In this paper, we attempt to find the optimal sensor decision rule, i.e., the best transform for the observed data to be reported, by formulating the task as a functional optimization problem. To bypass the difficulty of theoretically solving the problem, we present two methods: an approximation function and a numerical solution for the Gaussian noise case. Our simulation results demonstrate that a variation of the hyperbolic tangent function can be an effective approximation of the optimal transform. This work could lead to further studies on the optimal design for distributed detection.