Numerous real-life systems exhibit complex nonlinear input-output relationships. Kernel adaptive filters, a popular class of nonlinear adaptive filters, can efficiently model these nonlinear input-output relationships. Their growing network structure, however, poses considerable challenges in terms of their hardware implementation, making them inefficient for real-time applications. Random Fourier features (RFF) facilitate the development of kernel adaptive filters with a fixed network structure. For the first time, this paper attempts to implement the RFF-based kernel least mean square (RFF-KLMS) algorithm on hardware. To this end, we propose several reformulations of the feature functions (FFs) that are computationally expensive in their native form so that they can be implemented in real-time VLSI. Specifically, we reformulate inner product evaluation, cosine, and exponential functions that appear in the implementation of FFs. With these reformulations, the proposed delayed RFF-KLMS (DRFF-KLMS) is then synthesized using 45-nm CMOS technology with 16-bit fixed-point representations. According to the synthesis results, pipelined DRFF-KLMS architectures require minimal hardware increase over the state-of-the-art conventional delayed LMS architecture while significantly improving estimation performance for the nonlinear model. Our results suggest that the cosine feature function-based DRFF-KLMS is appropriate for applications requiring high accuracy, whereas the exponential function-based DRFF-KLMS may be well suited for resource-constrained applications.
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Algorithm and Architecture Design of Random Fourier Features-Based Kernel Adaptive Filters