Performance Analysis of the Decentralized Eigendecomposition and ESPRIT Algorithm

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 me...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2016-05, Vol.64 (9), p.2375-2386
Main Authors: Suleiman, Wassim, Pesavento, Marius, Zoubir, Abdelhak M.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
averaging consensus
Covariance matrices
decentralized DOA estimation
Decentralized eigendecomposition
Direction-of-arrival estimation
ESPRIT
Estimating techniques
Estimation
Mean square errors
Performance analysis
power method
Protocols
Signal processing algorithms
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2016.2523448