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Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

机译:循环平稳白高斯和非高斯输入的LMS和NLMS算法的随机分析

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This paper studies the stochastic behavior of the LMS and NLMS algorithms in a system identification framework for a cyclostationary white input without assuming a Gaussian distribution for the input. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation behavior of the adaptive weights as a function of the input cyclostationarity. Analytical models are first derived for the LMS and NLMS algorithms for cyclostationary white inputs. These models show the dependence of the two algorithms upon the kurtosis of the input. Significant differences are found between the behaviors of the two algorithms when the analysis is applied to non-Gaussian cases. Monte Carlo simulations provide strong support for the theory.
机译:本文在不假定输入为高斯分布的情况下,在系统识别框架中研究了LMS和NLMS算法在随机平稳白色输入系统中的随机行为。输入的循环平稳信号由具有周期性时变功率的白色随机过程建模。系统参数根据随机游走而变化。根据输入循环平稳性,得出自适应权重的均值和均方差行为的数学模型。首先推导用于循环平稳白输入的LMS和NLMS算法的分析模型。这些模型显示了两种算法对输入峰度的依赖性。当将分析应用于非高斯情况时,发现两种算法的行为之间存在显着差异。蒙特卡洛模拟为该理论提供了有力的支持。

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