Geometric Algebra Adaptive Filter Based on Multi-Dimensional Complex-Valued Random Fourier Features
Zihao Zhang, Peng Cai, Minglin Shen, Gangyi Huang, Shiyuan Wang · 2022
The complex-valued random Fourier geometric algebra mapping (CRFGAM) method can solve the over-coupling issue of the real and imaginary parts for complex-valued signals. In order to improve the accuracy of nonlinear mapping in the CRFGAM method, this paper proposes a multi-dimensional complex-valued random Fourier geometric algebraic mapping (MDCRFGAM) method by expanding the CRFGAM to a multi-dimension mapping space. Therefore, a multi-dimensional complex-valued random Fourier geometric algebra least mean square (MDCRFGALMS) algorithm is proposed based on the MDCRFGAM method. Simulations on nonlinear channel equalization are conducted to validate the performance superiorities of the proposed algorithm from the aspect of filtering accuracy.