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Summary: IEEE SIGNAL PROCESSING LETTERS, VOL. 12, NO. 2, FEBRUARY 2005 85
Eigenanalysis of Autocorrelation Matrices in the
Presence of Noncentral and Signal-Dependent Noise
Wei Wang, Student Member, IEEE, and Tülay Adali, Senior Member, IEEE
Abstract--We present approximations for eigenvalues of auto-
correlation matrices in the presence of noncentral and signal-de-
pendent noise as a function of eigenvalues of noiseless input. We
derive error bounds for the approximations and discuss their prop-
erties. The results of the eigenanalysis are applied to the study of
first-order polarization mode dispersion for optical systems. The
simulation results demonstrate a good match between the approx-
imated and true eigenvalues.
Index Terms--Autocorrelation matrix, eigenanalysis, noncentral
and signal-dependent noise.
I. INTRODUCTION
THE input autocorrelation matrix plays an important role in
describing the properties of statistical filters, in particular
those that are based on second-order statistics. For example,
both the convergence and misadjustment characteristics of the
least-mean-squares adaptive filter can be explained through
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