Universal decentralized estimation in a bandwidth constrained sensor network

We consider universal decentralized estimation of a noise-corrupted signal by a bandwidth constrained sensor network with a fusion center (FC). We show that in a homogeneous sensing environment and under a bandwidth constraint of 1-bit per sample per node, there exist universal decentralized estimation schemes (DES) with a mean squared error (MSE) decreasing at the rate 1/K, where K is the total number of sensors. We extend such 1-bit decentralized estimators to the case of a inhomogeneous sensing environment, and propose quantization and transmission power control strategies for local sensors in order to minimize the total consumed sensor energy while ensuring a given MSE performance. We also design a DES for the joint estimation of a vector source based on its noisy and linearly distorted observations, and show that to achieve a MSE within a factor of 2 away from the best linear unbiased estimator (BLUE), the local message length has a nice form of being the channel capacity of "a virtual AWGN channel" from "nature" to each local sensor.