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, Heilongjiang, 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, Heilongjiang, China
3.
Harbin Engineering University, School of Underwater Acoustic Engineering, Harbin 150001, Heilongjiang, China
4.
Huangdao District Political Consultative Conference Service Guarantee Center, Qingdao 266555, Shandong, China

Funds: Fundation: 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 The traditional sparse regularization recursive least squares algorithm, L1/L0 Norm Recursive Least Squares (L1/L0-RLS), demonstrates theoretical superiority in sparse parameter space estimation and has become a significant method in system identification and channel equalization. However, under limited numerical precision conditions, its covariance matrix iterative computation process can lead to successive accumulation of rounding errors, inducing divergence and instability in the least squares solution. Methods To address this issue, this paper proposes an improved algorithm based on the Inverse QR Decomposition (IQRD) framework. This framework not only effectively suppresses the accumulation of rounding errors in traditional regularized RLS algorithms, but also eliminates the calculation step of weight coefficient replacement in traditional QR decomposition, thereby significantly improving the numerical robustness and system identification efficiency of the algorithm in finite precision environments. Specifically, this article first systematically constructs the L1-IQRD-RLS and L0-IQRD-RLS algorithms under the L1/L0 constrained inverse QR decomposition architecture. Through theoretical derivation, a universal recursive expression for weight coefficients is obtained, and an innovative automatic parameter selection mechanism is introduced into the algorithm framework to solve the dynamic optimization problem of sparse regularization parameters. Results and Discussions To verify the effectiveness of the proposed algorithm in sparse constraints and robustness, Monte Carlo simulation experiments were used to quantitatively evaluate the algorithm performance. The results showed that L1-IQRD-RLS and L0-IQRD-RLS can maintain long-term numerical stability in an 11 decimal fixed-point computing environment. Compared with traditional algorithms, they exhibit significant performance advantages in key indicators such as system sparse representation, parameter estimation variance, and covariance matrix condition number. Further verification of actual test data confirms that the improved algorithm can maintain numerical stability even in environments with limited accuracy, significantly improving its robustness compared to traditional methods. The application effect of measured data shows that the regularized RLS algorithm improved by the inverse QR framework exhibits significant advantages in key indicators such as system sparsity representation, parameter estimation, and numerical stability. Its iterative convergence success rate is significantly improved compared to traditional methods. Conclusions This paper focuses on the issue of sparse system identification in the field of adaptive filtering. Currently, traditional sparse-regularized recursive least squares (RLS) algorithms still face challenges in numerical stability under limited numerical precision. To address this problem, this study proposes constructing an inverse QR decomposition framework to overcome the numerical ill-conditioning caused by successive rounding errors in sparse-regularized RLS algorithms. This approach significantly enhances the algorithm's numerical robustness in low-precision environments. Additionally, it innovatively introduces an automatic parameter selection mechanism into the algorithm framework, effectively eliminating the need for repeated parameter tuning and ensuring stable performance optimization through sparse constraints.In practical electromagnetic signal processing, tasks such as system identification and beamforming are constrained by the finite precision of hardware implementation and often face the inherent sparsity characteristics of the system itself. This paper's algorithm provides targeted solutions: its enhanced finite word-length robustness effectively suppresses numerical divergence in adaptive weight updates, ensuring stable implementation on fixed-point processors; meanwhile, the introduced sparse constraints naturally align with the physical structure of sparse arrays, improving the accuracy of algorithm estimation results. This research offers a practical algorithmic approach for achieving high-performance, 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(32)

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