A Reduced Gaussian Kernel Least-Mean-Square Algorithm for Nonlinear Adaptive Signal Processing

作者：Liu, Yuqi; Sun, Chao^*; Jiang, Shouda

来源：Circuits, Systems, and Signal Processing, 2019, 38(1): 371-394.

DOI：10.1007/s00034-018-0862-0

• Kernel adaptive filters
• KLMS algorithm
• Gaussian kernel
• Taylor expansion
• Nonlinear channel equalization

The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems. However, the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity. This paper introduces a reduced Gaussian kernel that is a finite-order Taylor expansion of a decomposed Gaussian kernel. The corresponding reduced Gaussian kernel least-mean-square (RGKLMS) algorithm is derived. The proposed algorithm avoids the sustained growth of the weighted network in a nonstationary environment via an implicit feature map. To verify the performance of the proposed algorithm, extensive simulations are conducted based on scenarios involving time-series prediction and nonlinear channel equalization, thereby proving that the RGKLMS algorithm is a universal approximator under suitable conditions. The simulation results also demonstrate that the RGKLMS algorithm can exhibit a comparable steady-state mean-square-error performance with a much lower computational complexity compared with other algorithms.

• 出版日期2019-1
• 单位哈尔滨工业大学