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.
翻译：这项工作对循环复杂彩色高斯输入的普通最小正平方(NLMS)算法(NLMS)的平均值分析提出了一种新颖的方法。 分析的基础是对以美元( ⁇ bf u ⁇ bf D ⁇ 1 ⁇ 2( ⁇ bf u ⁇ bf D ⁇ 2 ⁇ 2 ⁇ bf D ⁇ 2 ⁇ 2}} ⁇ 1美元为异端矢量的随机变数的累积分布函数(CDF)的封闭式表达式( CDF)的推断。 具体来说, 研究了NLMS算法的短暂性、 稳态和 跟踪平均值的行为 。
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