On diversity schemes in decentralized estimation

This paper is concerned with the decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements to a fusion center, using the analog amplify and forwarding technique. A distributed version of the diversity scheme where sensors decide what to transmit based only on their local information is also considered. We derive asymptotic expressions for the expected distortion of these schemes as the number of sensors becomes large. We also study the optimal power allocation problem for minimizing the expected distortion subject to average power constraints