Statistical analysis of multichannel FxLMS algorithm for narrowband active noise control

Chen Gong, Ming Wu*, Jianfeng Guo, Jing Chen, Zeqiang Zhang, Yin Cao, Jun Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


This paper analyzes the statistical performance of a multichannel narrowband active noise control (NANC) system based on the filtered-x least mean square (FxLMS) algorithm. The difference equations for the mean and mean square transient convergence behavior of the multichannel NANC system are derived. Steady-state expressions for weight-errors and mean square errors are then developed in closed forms. Stability boundaries for the multichannel FxLMS algorithm in the mean and mean square sense are also derived. When considering the mean square convergence, the coupling between the cross secondary paths and different frequencies is considered skillfully by matrixing and vectorization operations. Extensive simulations verify the accuracy of the theoretical analysis. Our findings deepen the understanding of the transient and steady-state behaviors of the multichannel NANC system and provide guidance for algorithm design, facilitate its improvement, and assist in parameter selection.

Original languageEnglish
Article number108646
JournalSignal Processing
Publication statusPublished - Nov 2022
Externally publishedYes


  • FxLMS
  • Multichannel narrowband active noise control
  • Statistical analysis
  • Steady-state behavior
  • Transient convergence behavior


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