The Haar measure and the generation of random unitary matrices

This paper derives the Haar measure over the set of unitary matrices. The Haar measure is essential when studying the statistical behavior of complex sample covariance matrices in terms of their eigenvalues and eigenvectors. The characterization is based on Murnaghan's parameterization of unita...

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Bibliographic Details
Published in2004 IEEE Sensor Array and Multichannel Signal Processing Workshop pp. 114 - 118
Main Authors Lundberg, M., Svensson, L.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2004
Subjects
Colored noise
Communication channels
Covariance matrix
Eigenvalues and eigenfunctions
MIMO
Performance evaluation
Signal Processing
Signal processing algorithms
Signalbehandling
Statistics
Symmetric matrices
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Summary:This paper derives the Haar measure over the set of unitary matrices. The Haar measure is essential when studying the statistical behavior of complex sample covariance matrices in terms of their eigenvalues and eigenvectors. The characterization is based on Murnaghan's parameterization of unitary matrices which can be seen as a generalization of the representation of orthogonal matrices using Givens rotations. In addition to deriving the Haar measure, an efficient method to obtain samples from it is also presented.
ISBN:9780780385450
0780385454
DOI:10.1109/SAM.2004.1502919