KLMS‐Net: Deep unrolling for kernel least mean square algorithm

Abstract The performance of the kernel least mean square (KLMS) algorithm heavily depends on the utilized kernel function and its associated parameters. To address this inherent limitation, this letter proposes a novel network framework based on the deep unrolling of KLMS (KLMS‐Net). KLMS‐Net transforms the iterative process of KLMS into the forward propagation of deep neural networks (DNNs), which learn the implicit feature mappings in a model‐driven manner, providing DNNs with explicit interpretability. Compared to standalone DNNs, KLMS‐Net compresses the size of the solution space of DNNs within the mathematical framework of KLMS. Through prediction experiments on nonlinear systems across various scenarios, KLMS‐Net exhibits significantly enhanced convergence speed and prediction accuracy, achieving improvements of approximately two orders of magnitude compared to the original KLMS and standalone DNNs. These findings highlight the substantial potential of KLMS‐Net in processing data with complex nonlinear structures and connect the fields of kernel adaptive filtering and deep learning.