Random Euler Complex-Valued Nonlinear Filters
This work addresses computational efficiency for researchers and engineers in signal processing, though it appears incremental as it builds on existing filter methods.
The authors tackled the high computational cost of neural networks and kernel adaptive filters in nonlinear signal processing by proposing two random Euler filters with simple, fixed structures, achieving effective performance in complex-valued nonlinear system identification and channel equalization.
Over the last decade, both the neural network and kernel adaptive filter have successfully been used for nonlinear signal processing. However, they suffer from high computational cost caused by their complex/growing network structures. In this paper, we propose two random Euler filters for complex-valued nonlinear filtering problem, i.e., linear random Euler complex-valued filter (LRECF) and its widely-linear version (WLRECF), which possess a simple and fixed network structure. The transient and steady-state performances are studied in a non-stationary environment. The analytical minimum mean square error (MSE) and optimum step-size are derived. Finally, numerical simulations on complex-valued nonlinear system identification and nonlinear channel equalization are presented to show the effectiveness of the proposed methods.