Kernel Normalised Least Mean Squares with Delayed Model Adaptation

Kernel adaptive filters (KAFs) are non-linear filters which can adapt temporally and have the additional benefit of being computationally efficient through use of the “kernel trick”. In a number of real-world applications, such as channel equalisation, the non-linear mapping provides significant improvements over conventional linear techniques such as the least mean squares (LMS) and recursive least squares (RLS) algorithms. Prior works have focused mainly on the theory and accuracy of KAFs, with little research on their implementations. This article proposes several variants of algorithms based on the kernel normalised least mean squares (KNLMS) algorithm which utilise a delayed model update to minimise dependencies. Subsequently, this work proposes corresponding hardware architectures which utilise this delayed model update to achieve high sample rates and low latency while also providing high modelling accuracy. The resultant delayed KNLMS (DKNLMS) algorithms can achieve clock rates up to 12× higher than the standard KNLMS algorithm, with minimal impact on accuracy and stability. A system implementation achieves 250 GOps/s and a throughput of 187.4 MHz on an Ultra96 board with 1.8× higher throughput than previous state of the art.