# Optimized Transmission for Parameter Estimation in Wireless Sensor Networks

## TL;DR

This paper introduces a cyclic optimization method for tuning sensor gains and phase-shifts in wireless sensor networks to improve parameter estimation accuracy, applicable in centralized and decentralized settings.

## Contribution

It proposes a low-cost, iterative design framework for optimizing sensor configurations, handling complex scenarios including sensor selection and discrete phase-shifts.

## Key findings

- Outperforms existing methods in computational efficiency
- Effective in large-scale sensor networks
- Applicable to both centralized and decentralized estimation

## Abstract

A central problem in analog wireless sensor networks is to design the gain or phase-shifts of the sensor nodes (i.e. the relaying configuration) in order to achieve an accurate estimation of some parameter of interest at a fusion center, or more generally, at each node by employing a distributed parameter estimation scheme. In this paper, by using an over-parametrization of the original design problem, we devise a cyclic optimization approach that can handle tuning both gains and phase-shifts of the sensor nodes, even in intricate scenarios involving sensor selection or discrete phase-shifts. Each iteration of the proposed design framework consists of a combination of the Gram-Schmidt process and power method-like iterations, and as a result, enjoys a low computational cost. Along with formulating the design problem for a fusion center, we further present a consensus-based framework for decentralized estimation of deterministic parameters in a distributed network, which results in a similar sensor gain design problem. The numerical results confirm the computational advantage of the suggested approach in comparison with the state-of-the-art methods---an advantage that becomes more pronounced when the sensor network grows large.