Estimation in Phase-Shift and Forward Wireless Sensor Networks

TL;DR

This paper investigates phase-shift transmission in wireless sensor networks, proposing algorithms for optimal phase factor design, analyzing asymptotic performance, and addressing sensor selection to improve parameter estimation.

Contribution

It introduces two novel algorithms for phase factor optimization, provides asymptotic analysis, and explores sensor selection strategies in phase-shift wireless sensor networks.

Findings

Algorithms achieve near-optimal performance

Asymptotic analysis for large sensor/antenna networks

Sensor selection improves estimation accuracy

Abstract

We consider a network of single-antenna sensors that observe an unknown deterministic parameter. Each sensor applies a phase shift to the observation and the sensors simultaneously transmit the result to a multi-antenna fusion center (FC). Based on its knowledge of the wireless channel to the sensors, the FC calculates values for the phase factors that minimize the variance of the parameter estimate, and feeds this information back to the sensors. The use of a phase-shift-only transmission scheme provides a simplified analog implementation at the sensor, and also leads to a simpler algorithm design and performance analysis. We propose two algorithms for this problem, a numerical solution based on a relaxed semidefinite programming problem, and a closed-form solution based on the analytic constant modulus algorithm. Both approaches are shown to provide performance close to the theoretical bound. We derive asymptotic performance analyses for cases involving large numbers of sensors or large numbers of FC antennas, and we also study the impact of phase errors at the sensor transmitters. Finally, we consider the sensor selection problem, in which only a subset of the sensors is chosen to send their observations to the FC.