<p>This paper introduces the Adaptive Hamiltonian-Based Least Mean Squares (AHLMS) algorithm, a high-performance framework that synergistically integrates optimal control theory with adaptive signal processing. By formulating the filter weight optimization problem through the mathematical rigor of Pontryagin’s maximum principle, AHLMS utilizes a receding horizon control strategy to overcome the inherent myopia and lag errors characteristic of standard gradient descent methods. Comprehensive Monte Carlo simulations, averaged over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$L=300$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mo>=</mo> <mn>300</mn> </mrow> </math></EquationSource> </InlineEquation> trials, demonstrate that AHLMS achieves elite-tier performance across diverse stationary and non-stationary environments. In stationary system identification, AHLMS reaches the noise floor approximately <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$62\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>62</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> faster than the Normalized LMS (NLMS) industry benchmark while maintaining a significantly lower Mean Square Deviation (MSD). In demanding non-stationary scenarios involving abrupt plant jumps, the algorithm demonstrates remarkable tracking resilience, recovering nearly <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$2.8\times $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.8</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> faster than NLMS. Further validation in QPSK adaptive channel equalization shows that AHLMS bridges the performance–complexity gap, delivering RLS-tier acquisition speeds and a matching steady-state error floor without the prohibitive <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\mathcal {O}(M^2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <msup> <mi>M</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> computational overhead. These results establish AHLMS as a superior “Elite” alternative for modern, high-speed, hardware-constrained communication systems.</p>

Adaptive Hamiltonian-based LMS for non-stationary systems: a receding horizon optimal control approach

期刊论文
发表日期：

2026年6月3日

查看全文

Thamer M. Jamel,
Hamsa D. Majeed

摘要

This paper introduces the Adaptive Hamiltonian-Based Least Mean Squares (AHLMS) algorithm, a high-performance framework that synergistically integrates optimal control theory with adaptive signal processing. By formulating the filter weight optimization problem through the mathematical rigor of Pontryagin’s maximum principle, AHLMS utilizes a receding horizon control strategy to overcome the inherent myopia and lag errors characteristic of standard gradient descent methods. Comprehensive Monte Carlo simulations, averaged over $L=300$ $L = 300$ trials, demonstrate that AHLMS achieves elite-tier performance across diverse stationary and non-stationary environments. In stationary system identification, AHLMS reaches the noise floor approximately $62\%$ $62 %$ faster than the Normalized LMS (NLMS) industry benchmark while maintaining a significantly lower Mean Square Deviation (MSD). In demanding non-stationary scenarios involving abrupt plant jumps, the algorithm demonstrates remarkable tracking resilience, recovering nearly $2.8\times $ $2.8 \times$ faster than NLMS. Further validation in QPSK adaptive channel equalization shows that AHLMS bridges the performance–complexity gap, delivering RLS-tier acquisition speeds and a matching steady-state error floor without the prohibitive $\mathcal {O}(M^2)$ $O (M^{2})$ computational overhead. These results establish AHLMS as a superior “Elite” alternative for modern, high-speed, hardware-constrained communication systems.