Parameter Tracking via Optimal Distributed Beamforming in an Analog Sensor Network

TL;DR

This paper develops an optimal distributed beamforming strategy for sensor networks tracking a dynamic parameter, minimizing estimation error through power control under various constraints, and demonstrates significant improvements over equal power schemes.

Contribution

It introduces a method to optimize sensor transmission gains and phases for dynamic parameter tracking, providing closed-form and SDP-based solutions for different power constraints.

Findings

Optimized power control reduces mean squared error significantly.

Closed-form solutions are available for global power constraints.

SDP relaxation effectively finds solutions under individual power constraints.

Abstract

We consider the problem of optimal distributed beamforming in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses a Kalman filter to track the parameter using the observations from the sensors, and we show how to find the optimal gain and phase of the sensor transmissions under both global and individual power constraints in order to minimize the mean squared error (MSE) of the parameter estimate. For the case of a global power constraint, a closed-form solution can be obtained. A numerical optimization is required for individual power constraints, but the problem can be relaxed to a semidefinite programming problem (SDP), and we show how the optimal solution can be constructed from the solution to the SDP. Simulation results show that compared with equal power transmission, the use of optimized power control can significantly reduce the MSE.