Steady-State Performance Analysis of the Nearest Kronecker Product Decomposition Based LMS Adaptive Algorithm

• Published in: IEEE signal processing letters Vol. 32; pp. 1995 - 1999
• Main Authors: Li, Lei, Zheng, Yunfei, Guo, Zhongyuan, Qian, Guobing, Wang, Shiyuan
• Format: Journal Article
• Language: English
• Published: New York IEEE 2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive filter; Adaptive filters; Algorithms; Decomposition; Filtering algorithms; Finite impulse response filters; Impulse response; least mean square; Matrix decomposition; nearest Kronecker product; Performance analysis; Signal processing algorithms; Simulation; Steady state; System identification; Upper bounds; Vectors; Wiener filters
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2025.3565395

Inorder to address issues, such as convergence rate, stability, and computational complexity caused by the identification of long length impulse response systems, an effective nearest Kronecker product (NKP) decomposition strategy has been introduced and extended to various adaptive filters in recent years. However, the theoretical performance of the NKP decomposition-based adaptive filtering algorithms has not been thoroughly analyzed in these studies. In this letter, we focus on analyzing the steady-state performance of the NKP-based least mean square (NKP-LMS) algorithm and presents the theoretical upper bound of the step-size. Finally, simulation results confirm the precision of the theoretical assessment of the NKP-LMS algorithm and highlight its benefits in low-rank system identification.