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Low Complexity RLS Adaptive Filters

This paper presents two adaptive filters with a reduced arithmetic complexity which are based on the Recursive Least Squares (RLS) algorithms. The first one is the cascaded adaptive filter. The second one is the adaptive filter with the diagonalized correlation matrix of the input signal. The both filters have a reduced arithmetic complexity comparing to the direct implementation of the adaptive filter. The cost of the reduction is some degradation of the adaptive filter performance. The reduction is achieved only if the RLS algorithms with quadratic complexity are used. The computational procedures and the arithmetic complexities of the considered adaptive filters are the same, but the performance is different. This paper presents the RLS algorithms based on the Matrix Inversion Lemma (MIL). However, all the results and conclusions are valid for any RLS algorithms with quadratic complexity. The paper demonstrates the considered adaptive filter performance via simulation.