Tight Performance Bounds for Distributed Detection

Evaluating the performance measures of distributed detection in sensor networks is important for design procedures aiming at optimal configurations. Direct computation of the global error probabilities is a difficult problem and feasible only in some special cases. In this paper, we present an approach that provides closed-form upper bounds on the detection error probabilities in the parallel fusion network which are both computationally simple and numerically tight. The bounds are derived by combining a probability inequality formulated by Hoeffding with a multiplicative form factor which is due to Talagrand. We demonstrate that the bounds apply to sensor networks of varying size, an arbitrary number of local quantization levels, and non-identical sensors.