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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\u00d7 higher than the standard KNLMS algorithm, with minimal impact on accuracy and stability. A system implementation achieves 250\u00a0GOps\/s and a throughput of 187.4\u00a0MHz on an Ultra96 board with 1.8\u00d7 higher throughput than previous state of the art.<\/jats:p>","DOI":"10.1145\/3376924","type":"journal-article","created":{"date-parts":[[2020,4,4]],"date-time":"2020-04-04T01:33:28Z","timestamp":1585964008000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Kernel Normalised Least Mean Squares with Delayed Model Adaptation"],"prefix":"10.1145","volume":"13","author":[{"given":"Nicholas J.","family":"Fraser","sequence":"first","affiliation":[{"name":"University of Sydney, Sydney, NSW, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3923-3499","authenticated-orcid":false,"given":"Philip H. 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