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 bandlimited. 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. We assume that each sensor is restricted to send a 1-bit message to the fusion center, and that sensor noise is additive, zero mean, 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 (Z.-Q. Luo, 2003) which 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 which is optimal for bounded range noise, and, for noise with unbounded range, is lower bounded in terms of the signal-to-noise ratio.