TY - JOUR
T1 - Large system spectral analysis of covariance matrix estimation
AU - Li, Husheng
AU - Poor, H. Vincent
N1 - Funding Information:
Manuscript received December 23, 2006; revised January 21, 2008. Current version published February 25, 2009. This work was supported by the National Science Foundation under Grants ANI-03-38807 and CNS-06-25637. H. Li is with the Department of Electrical Engineering and Computer Science, the University of Tennessee, Knoxville, TN 37996 USA (e-mail: [email protected]). H. V. Poor is with the School of Engineering and Applied Science, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). Communicated by L. Tong, Associate Editor for Detection and Estimation. Color versions of Figures 1–14 in this paper are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2008.2011440
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Covariance matrix
KW - Free cumulants
KW - Non-crossing partition
KW - Spectrum analysis
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U2 - 10.1109/TIT.2008.2011440
DO - 10.1109/TIT.2008.2011440
M3 - Article
AN - SCOPUS:62749096812
SN - 0018-9448
VL - 55
SP - 1395
EP - 1422
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 3
ER -