Find in Library

In this paper, we consider a distributed estimation of a deterministic parameter vector in a bandwidth constrained wireless sensor network. Due to the stringent bandwidth limitation, each sensor compresses its observation to one message transmitted to the fusion center. We assume that the observation noise is uncorrelated across the sensors and focus on a homogeneous case in which all the sensors possess identical noise covariance matrix. Our aim is to design the compression matrix so that the estimation error attains a universal lower bound. When the noise covariance matrix is a scaled identity matrix, we provide a closed-form expression of the optimal compression matrix. Meanwhile, for a general noise covariance matrix, the optimal compression matrix can be attained explicitly as well, if the dimension of the parameter estimated is less than or equal to 4. Furthermore, as a byproduct, two hyperplane-based vector quantization problems can be solved completely and partly, respectively. Performance analysis and simulations demonstrate the merits of our constructed optimal compression matrices when compared with the existing compression strategy.