Universal Decentralized Detection in a Bandwidth-Constrained Sensor Network

Consider the problem of decentralized detection with a distributed sensor network where the communication channels between sensors and the fusion center are bandwidth constrained. Previous approaches to this problem typically rely on quantization of either the sensor observations or the local likelihood ratios, with quantization levels optimally designed using the knowledge of noise distribution. In this paper, we assume that each sensor is restricted to send a 1-bit message to the fusion center and that the sensor noises are additive, zero mean, and spatially independent but otherwise unknown and with possibly different distributions across sensors. We construct a universal decentralized detector using a recently proposed isotropic decentralized estimation scheme [10], [11] that requires only the knowledge of either the noise range or its second-order moment. We show that the error probability of this detector decays exponentially at a rate that is lower bounded either in terms of the noise range for bounded noise or the signal-to-noise ratio for noise with unbounded range.