NLMS is More Robust to Input-Correlation Than LMS: A Proof
Anum Ali, Muhammad Moinuddin, Tareq Y. Al-Naffouri
Abstract
In this work, we comparatively analyze the least mean squares (LMS) algorithm and the normalized least mean squares (NLMS) algorithm. We use the input moment matrices for comparison as the mean-square behavior of both algorithms is determined by the input moment matrices. First, we derive the closed-form expressions of the input moment matrices of the NLMS. Second, we do a numerical and theoretical comparison of the input moment matrices of the LMS and the NLMS. The analysis shows why the performance of the NLMS is less sensitive to the changes in eigenvalue-spread (of the input-correlation matrix) than the LMS.
Topics & Concepts
Least mean squares filterMoment (physics)Eigenvalues and eigenvectorsMathematicsRecursive least squares filterMatrix (chemical analysis)Applied mathematicsSquare (algebra)Second moment of areaAlgorithmControl theory (sociology)Adaptive filterComputer scienceArtificial intelligencePhysicsMaterials scienceClassical mechanicsComposite materialQuantum mechanicsGeometryControl (management)Advanced Adaptive Filtering TechniquesBlind Source Separation TechniquesSpeech and Audio Processing