This paper studies minimal-energy decentralized estimation in sensor networks under best-linear-unbiased-estimator fusion rule. While most of the existing related works require the knowledge of instantaneous noise variances for energy allocation, the proposed approach instead relies on an associated statistical model. The minimization of total energy is subject to certain performance constraint in terms of mean square error (MSE) averaged over the noise variance distribution. A closed-form formula for the overall MSE metric is derived, based on which the problem can be reformulated in the form of convex optimization and is shown to yield an analytic solution. The proposed method shares several attractive features of the existing designs via instantaneous noise variances; through simulations it is seen to significantly improve the energy efficiency against the uniform allocation scheme.

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This paper studies the energy-constrained MMSE decentralized estimation problem with the best-linear-unbiasedestimator fusion rule, under the assumptions that i) each sensor can only send a quantized version of its raw measurement to the fusion center (FC), and ii) exact knowledge of the sensor noise variance is unknown at the FC but only an associated statistical description is available. The problem setup relies on maximizing the reciprocal of the MSE averaged with respect to the prescribed noise variance distribution. While the considered design metric is shown to be highly nonlinear in the local sensor transmit energy (or bit loads), we leverage several analytic approximation relations to derive a associated tractable lower bound; through maximizing this bound a closed-form solution is then obtained. Our analytical results reveal that sensors with bad link quality are shut off to conserve energy, whereas the energy allocated to those active nodes is proportional to the individual channel gain. Simulation results are used to illustrate the performance of the proposed scheme.