Analyzing Step-Size Approximation for Fixed-Point Implementation of LMS and BLMS Algorithms

Mohd. Tasleem Khan*, Oscar Gustafsson

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this work, we analyze the step-size approximation for fixed-point least-mean-square (LMS) and block LMS (BLMS) algorithms. Our primary focus is on investigating how step size approximation impacts the convergence rate and steady-state mean square error (MSE) across varying block sizes and filter lengths. We consider three different FP quantized LMS and BLMS algorithms. The results demonstrate that the algorithm with two quantizers in single precision behaves approximately the same as one quantizer under quantized weights, regardless of block size and filter lengths. Subsequently, we explore the approximation effects of nearest power-of-two and their combinations with different design parameters on the convergence performance. Simulation results for within the context of a system identification problem under these approximations reveal intriguing insights. For instance, a single quantizer algorithm without quantized error is more robust than its counterpart under these approximations. Additionally, both single quantizer algorithms with combined power-of-two approximations matches the behavior of the actual step-size.

Original languageEnglish
Title of host publication2023 IEEE Nordic Circuits and Systems Conference (NorCAS)
ISBN (Electronic)9798350337570
Publication statusPublished - 6 Nov 2023
Event9th IEEE Nordic Circuits and Systems Conference 2023 - Aalborg, Denmark
Duration: 31 Oct 20231 Nov 2023


Conference9th IEEE Nordic Circuits and Systems Conference 2023
Abbreviated titleNorCAS 2023

ASJC Scopus subject areas

  • Hardware and Architecture
  • Biomedical Engineering
  • Electrical and Electronic Engineering


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