Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms

PENG Yi; ZHANG Pengfei; WANG Xiaoyong; GAO Junqi; LI Changlong; ZHANG Zhiyuan; SUN Tianxiang

doi:10.11999/JEIT250562

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PENG Yi, ZHANG Pengfei, WANG Xiaoyong, GAO Junqi, LI Changlong, ZHANG Zhiyuan, SUN Tianxiang. Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250562

Citation:

PENG Yi, ZHANG Pengfei, WANG Xiaoyong, GAO Junqi, LI Changlong, ZHANG Zhiyuan, SUN Tianxiang. Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250562

Citation:

PENG Yi, ZHANG Pengfei, WANG Xiaoyong, GAO Junqi, LI Changlong, ZHANG Zhiyuan, SUN Tianxiang. Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT250562

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Research on Inverse QR Decomposition Optimization for Sparse Adaptive System Identification Algorithms

doi: 10.11999/JEIT250562 cstr: 32379.14.JEIT250562

PENG Yi^{1, 2, 3},
ZHANG Pengfei^{1, 2, 3
,
,},
WANG Xiaoyong⁴,
GAO Junqi^{1, 2, 3},
LI Changlong^{1, 2, 3},
ZHANG Zhiyuan^{1, 2, 3},
SUN Tianxiang^{1, 2, 3}

1.
Harbin Engineering University, National Key Laboratory of Underwater Acoustic Technology, Harbin 150001, China
2.
Key Laboratory of Marine Information Acquisition and Security, Ministry of Industry and Information Technology, Harbin Engineering University, Ministry of Industry and Information Technology, Harbin 150001, China
3.
Harbin Engineering University, School of Underwater Acoustic Engineering, Harbin 150001, China
4.
Huangdao District Political Consultative Conference Service Guarantee Center, Qingdao 266555, China

Funds: The Key Laboratory Fund Project on Radio Wave Environment Characteristics and Modeling Technology (JCKY2024210C61424030202)

Received Date: 2025-06-18
Accepted Date: 2026-04-08
Rev Recd Date: 2026-03-12

Available Online: 2026-04-25

Abstract

Abstract

Objective Traditional sparse-regularized Recursive Least Squares (RLS) algorithms, namely L1/L0-norm Recursive Least Squares (L1/L0-RLS), have theoretical advantages in sparse parameter-space estimation and are widely used in system identification and channel equalization. However, under limited numerical precision, iterative covariance matrix computation may cause rounding errors to accumulate. This can lead to divergence and instability in the least-squares solution. Methods To address this problem, an improved algorithm based on the Inverse QR Decomposition (IQRD) framework is proposed. The framework suppresses rounding-error accumulation in traditional regularized RLS algorithms. It also removes the back-substitution step for weight coefficients required in conventional QR decomposition. These features improve numerical robustness and system identification efficiency in finite-precision environments. Specifically, L1-IQRD-RLS and L0-IQRD-RLS algorithms are constructed under an L1/L0-constrained IQRD architecture. A general recursive expression for the weight coefficients is derived. An automatic parameter selection mechanism is also incorporated into the algorithm framework to solve the dynamic optimization problem of the sparse regularization parameter. Results and Discussions Monte Carlo simulations are conducted to evaluate the sparse constraints and robustness of the proposed algorithms. The results show that L1-IQRD-RLS and L0-IQRD-RLS maintain long-term numerical stability in an 11-decimal-place fixed-point computing environment. Compared with traditional algorithms, the proposed algorithms show clear advantages in system sparsity representation, parameter estimation variance, and covariance matrix condition number. Measured-data verification further confirms that the improved algorithms maintain numerical stability under limited-precision conditions and are more robust than traditional methods. The measured-data results also show that the regularized RLS algorithms optimized by the IQRD framework have advantages in system sparsity representation, parameter estimation, and numerical stability. Their iterative convergence success rate is higher than that of traditional methods. Conclusions This paper addresses sparse system identification in adaptive filtering. Traditional sparse-regularized RLS algorithms still face numerical stability problems under limited numerical precision. To solve this problem, an IQRD framework is constructed to reduce the numerical ill-conditioning caused by accumulated rounding errors in sparse-regularized RLS algorithms. The proposed method improves numerical robustness in low-precision environments. In addition, an automatic parameter selection mechanism is incorporated into the algorithm framework. This reduces repeated parameter tuning and supports stable performance optimization under sparse constraints. In practical electromagnetic signal processing, system identification and beamforming are limited by the finite precision of hardware implementation and often exhibit inherent system sparsity. The proposed algorithm provides a targeted solution. Its finite-word-length robustness suppresses numerical divergence during adaptive weight updates and supports stable implementation on fixed-point processors. The sparse constraints also match the physical characteristics of sparse systems and improve estimation accuracy. This study provides a practical algorithm for high-performance and high-stability sparse-constrained systems on precision-limited hardware platforms.
- Recursive least squares,
- Sparse optimization,
- Inverse QR decomposition,
- System identification

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References(31)

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