  This work presents a novel approach to the mean-square analysis of the
normalized least mean squares (NLMS) algorithm for circular complex colored
Gaussian inputs. The analysis is based on the derivation of a closed-form
expression for the Cumulative Distribution Function (CDF) of random variables
of the form $(||{\bf u}||_{{\bf D}_1}^2)(||{\bf u}||_{{\bf D}_2}^2)^{-1}$ where
${\bf u}$ is an isotropic vector and ${\bf D}_1$ and ${\bf D}_2$ are diagonal
matrices and using that to derive some moments of these variables. These
moments in turn completely characterize the mean-square behavior of the NLMS
algorithm in explicit closed-form expressions. Specifically, the transient,
steady-state, and tracking mean-square behavior of the NLMS algorithm is
studied.
