Distortion-Rate Analysis for Distributed Estimation with Wireless Sensor Networks†

We deal with centralized and distributed rate-constrained estimation of random signal vectors using a network of wireless sensors communicating with a fusion center. Specifically, we determine lower and upper bounds for the Distortion-Rate (D-R) function. The lower bound is obtained by considering centralized estimation with a single-sensor setup, for which we determine the D-R function in closed-form, and specify an estimator that achieves it. Furthermore, we derive a novel alternating scheme that numerically determines an achievable upper bound of the D-R function for general distributed estimation using multiple sensors. Numerical examples confirm that the algorithm performs well and yields D-R upper bounds which are tight.