Efficient Functional Link Adaptive Filters based on Nearest Kronecker Product Decomposition

Functional link adaptive filters (FLAFs) utilize expansion blocks to nonlinearly augment the input signal to a higher dimensional space, after which an adaptive weight algorithm is applied. These filters are useful for nonlinear system identification tasks, as they can update a large number of coefficients to effectively model the nonlinear system, even when the degree of nonlinearity is not comprehended in advance. However, in many cases, not all of the weights in the nonlinear and linear filter will significantly contribute to the identified model. This paper introduces a novel class of FLAFs based on the nearest Kronecker product (NKP) decomposition. Utilizing the inherent low-rank nature of weight vectors in many scenarios, our approach aims to improve convergence performance and tracking capabilities compared to traditional FLAFs. Additionally, we address noise mitigation challenges, particularly in nonlinear acoustic echo cancellation scenarios. By incorporating NKP decomposition, our proposed FLAFs offer promising solutions for enhancing adaptability and performance in nonlinear system identification, making them valuable tools in practical applications.