Title :
Large System Spectral Analysis of Covariance Matrix Estimation
Author :
Li, Husheng ; Poor, H. Vincent
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of Tennessee, Knoxville, TN
fDate :
3/1/2009 12:00:00 AM
Abstract :
Eigendecomposition of estimated covariance matrices is a basic signal processing technique arising in a number of applications, including direction-of-arrival estimation, power allocation in multiple-input/multiple-output (MIMO) transmission systems, and adaptive multiuser detection. This paper uses the theory of non-crossing partitions to develop explicit asymptotic expressions for the moments of the eigenvalues of estimated covariance matrices, in the large system asymptote as the vector dimension and the dimension of signal space both increase without bound, while their ratio remains finite and nonzero. The asymptotic eigenvalue distribution is also obtained from these eigenvalue moments and the Stieltjes transform, and is extended to first-order approximation in the large sample-size limit. Numerical simulations are used to demonstrate that these asymptotic results provide good approximations for finite systems of moderate size.
Keywords :
MIMO systems; covariance matrices; direction-of-arrival estimation; eigenvalues and eigenfunctions; estimation theory; multiuser detection; signal processing; spectral analysis; transforms; vectors; MIMO system; Stieltjes transform; adaptive multiuser detection; asymptotic eigenvalue distribution; asymptotic expressions; covariance matrix estimation; direction-of-arrival estimation; eigendecomposition; eigenvalue moments; estimated covariance matrices; large system asymptote; large system spectral analysis; multiple-input/multiple-output transmission systems; non-crossing partitions; power allocation; signal processing technique; vector dimension; Covariance matrix; Direction of arrival estimation; Eigenvalues and eigenfunctions; MIMO; Multiple signal classification; Multiuser detection; Principal component analysis; Signal processing; Spectral analysis; Transmitters; Covariance matrix; free cumulants; non-crossing partition; spectrum analysis;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.2011440