Random Fourier features based nonlinear recurrent kernel normalized LMS algorithm with multiple feedbacks.

The performance of kernel adaptive filtering algorithms (KAFs) with nonlinear recurrent structures surpasses traditional KAFs, attributed to the nonlinear contribution of feedback. Nevertheless, the existing nonlinear recurrent KAFs primarily focus on a single feedback output, potentially limiting their latent filtering capabilities. In this paper, we introduce a novel alternative, named nonlinear recurrent kernel normalized least-mean-square with multiple feedbacks (NR-KNLMS-MF), which leverages the information from multiple feedback outputs. Additionally, to tackle the computational complexity challenges associated with KAFs, we integrate random Fourier features (RFF) into NR-KNLMS-MF, resulting in an efficient variant called as RFF-NR-KNLMS-MF. Furthermore, we conduct a theoretical analysis of the mean-square convergence for RFF-NR-KNLMS-MF. Simulation results on time-series predictions demonstrate the superiority of our proposed algorithms over other competing alternatives, validating their effectiveness.