Analysis of the LMS and NLMS algorithms using the misalignment norm
Paulo A. C. Lopes
Abstract
Abstract This work describes the convergence of the misalignment square norm (MSN) of the NLMS and LMS algorithms. It is shown that the MSN decrease is almost proportional to the mean square error (MSE). This allows obtaining simple expressions for the steady-state MSE. Also, it allows limiting the amount of time that the MSE takes large values and a curve that limits the MSE of LMS at any given time, independent of the input and background noise signals’ properties. Finally, it is also shown that many complications in the analysis of the LMS and NLMS algorithms can come from variations in the input vector square norm. The proposed analysis becomes very simple for long filters or constant power signals.
Topics & Concepts
Least mean squares filterNorm (philosophy)Mean squared errorAlgorithmMathematicsConvergence (economics)Square (algebra)LimitingAdaptive filterApplied mathematicsConstant (computer programming)Simple (philosophy)Computer scienceControl theory (sociology)StatisticsArtificial intelligencePolitical scienceGeometryControl (management)EconomicsLawPhilosophyEconomic growthProgramming languageMechanical engineeringEpistemologyEngineeringAdvanced Adaptive Filtering TechniquesBlind Source Separation TechniquesControl Systems and Identification