Title: Wireless Power Transfer for Distributed Estimation in Sensor Networks,
Abstract: This paper studies power allocation for distributed estimation of an unknown
scalar random source in sensor networks with a multiple-antenna fusion center
(FC), where wireless sensors are equipped with radio-frequency based energy
harvesting technology. The sensors' observation is locally processed by using
an uncoded amplify-and-forward scheme. The processed signals are then sent to
the FC, and are coherently combined at the FC, at which the best linear
unbiased estimator (BLUE) is adopted for reliable estimation. We aim to solve
the following two power allocation problems: 1) minimizing distortion under
various power constraints; and 2) minimizing total transmit power under
distortion constraints, where the distortion is measured in terms of
mean-squared error of the BLUE. Two iterative algorithms are developed to solve
the non-convex problems, which converge at least to a local optimum. In
particular, the above algorithms are designed to jointly optimize the
amplification coefficients, energy beamforming, and receive filtering. For each
problem, a suboptimal design, a single-antenna FC scenario, and a common
harvester deployment for colocated sensors, are also studied. Using the
powerful semidefinite relaxation framework, our result is shown to be valid for
any number of sensors, each with different noise power, and for an arbitrarily
number of antennas at the FC.