L2-Stability Analysis of the SM-NLMS Algorithm
Rajab Shabaani
TL;DR
This paper proves that the SM-NLMS algorithm is stable in the L2 sense, ensuring it does not diverge regardless of parameter choices, supported by numerical simulations.
Contribution
The paper provides the first L2-stability analysis of the SM-NLMS algorithm, demonstrating its robustness and non-divergence under any parameter settings.
Findings
SM-NLMS algorithm is L2-stable
The algorithm never diverges regardless of parameter selection
Numerical simulations confirm the theoretical analysis
Abstract
In this letter, we analyze, two properties, the local and the global robustness of the set-membership normalized least mean square (SM-NLMS) algorithm. We will show that the SM-NLMS algorithm has l2-stability. Indeed, the SM-NLMS algorithm never diverges; no matter how the parameters of the SM-NLMS algorithm has been selected. Ultimately, the numerical simulations corroborate the validity of our analysis.
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Taxonomy
TopicsAdvanced Adaptive Filtering Techniques · Control Systems and Identification · Blind Source Separation Techniques