Sliding-window RLS low-cost implementation of proportionate affine projection algorithms

Yury Zakharov, V. Nascimento

Research output: Contribution to journalArticlepeer-review


This paper addresses adaptive filtering for sparse identification. Proportionate affine projection algorithms (PAPAs) are known to be efficient techniques for this purpose. We show that the PAPA performance may improve with an increase in the projection order M (for example, such as M = 512 ), which, however, also results in an increased complexity; the complexity is in general O(M2N) or at least O(M N) operations per sample, where N is the filter length. We show that PAPAs are equivalent to specific sliding-window recursive least squares (SRLS) adaptive algorithms with time-varying and tap-varying diagonal loading (SRLS-VDLs). We then propose an approximation to the SRLS-VDLs based on dichotomous coordinate descent (DCD) iterations with a complexity of O(NuN), which does not depend on M; it depends on the number of DCD iterations Nu, which as we show can be significantly smaller than M, thus allowing a low-complexity implementation of PAPA adaptive filters.
Original languageEnglish
Pages (from-to)1815-1824
Number of pages10
JournalIEEE Transactions On Audio Speech And Language Processing
Issue number12
Publication statusPublished - 27 Aug 2014

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