# Wireless Power Transfer for Distributed Estimation in Sensor Networks

## TL;DR

This paper proposes algorithms for optimizing power allocation in wireless sensor networks with energy harvesting, aiming to improve estimation accuracy and power efficiency at the fusion center.

## Contribution

It introduces iterative algorithms for joint optimization of amplification, beamforming, and filtering in energy-harvesting sensor networks, addressing non-convex power allocation problems.

## Key findings

- Algorithms converge to local optima
- Effective joint optimization improves estimation accuracy
- Framework applicable to arbitrary sensor and antenna configurations

## 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.