Linear coherent distributed estimation with cluster-based sensor networks

The authors consider distributed estimation using sensor network with coherent multiple access channel model and LMMSE fusion rule. The sensors in the network are divided into a number of clusters. Sensors within the same cluster are allowed to collaborate through an amplification matrix to form a message this then transmitted. They formulate the problem of choosing the amplification matrices as an optimal power allocation problem under a total power constraint. The solution gives the optimal amplification matrices as scaled outer products of the observation gain and the channel gain vectors. The authors show that collaboration improves performance and, in simulations, demonstrate that the amount of improvement is closely related to the amount of collaboration.