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

Area of Science:

• Signal Processing
• Machine Learning

Background:

• Kernel adaptive filtering algorithms (KAFs) with nonlinear recurrent structures show enhanced performance over traditional KAFs due to nonlinear feedback.
• Existing nonlinear recurrent KAFs are limited by focusing on a single feedback output, potentially restricting their filtering capacity.

Purpose of the Study:

• To introduce a novel nonlinear recurrent kernel adaptive filtering algorithm utilizing multiple feedback outputs.
• To develop an efficient variant of this algorithm to address computational complexity.
• To theoretically analyze the convergence properties and empirically validate the proposed methods.

Main Methods:

• Development of the nonlinear recurrent kernel normalized least-mean-square with multiple feedbacks (NR-KNLMS-MF) algorithm.
• Integration of random Fourier features (RFF) to create an efficient version, RFF-NR-KNLMS-MF.
• Theoretical analysis of the mean-square convergence of RFF-NR-KNLMS-MF.
• Performance evaluation through simulations on time-series prediction tasks.

Main Results:

• The proposed NR-KNLMS-MF algorithm demonstrates superior performance by leveraging information from multiple feedback outputs.
• The RFF-NR-KNLMS-MF variant effectively reduces computational complexity while maintaining high performance.
• Simulation results confirm the effectiveness of both proposed algorithms compared to existing methods.

Conclusions:

• The novel NR-KNLMS-MF algorithm enhances filtering capabilities through multiple feedback utilization.
• The RFF-NR-KNLMS-MF offers an efficient and effective solution for complex signal processing tasks.
• The proposed algorithms represent a significant advancement in nonlinear recurrent kernel adaptive filtering.