Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

TL;DR

This paper analyzes the performance of decentralized eigendecomposition and ESPRIT algorithms, deriving analytical expressions for their estimation errors and showing their limitations and effectiveness through simulations.

Contribution

It provides the first analytical performance analysis of the decentralized power method and introduces a fully decentralized ESPRIT algorithm with derived MSE expressions.

Findings

Decentralized power method is not asymptotically consistent unless over infinite iterations.

Analytical MSE expressions for decentralized DOA estimation are derived.

Simulations confirm the theoretical performance analysis.

Abstract

In this paper, we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol. An analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error (MSE) of subspace-based estimators is presented. We show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations. Moreover, we introduce the decentralized ESPRIT algorithm which yields fully decentralized direction-of-arrival (DOA) estimates. Based on the performance analysis of the decentralized power method, we derive an analytical expression of the MSE of DOA estimators using the decentralized ESPRIT algorithm. The validity of our asymptotic results is demonstrated by simulations.