Sparsity-aware reuse of coefficients normalised least mean squares

Noise is an ubiquitous phenomenon that hampers adaptive filtering-based system identification procedures. Recently, the coefficient reuse strategy has been proposed to address the challenging case where the signal-to-noise ratio is low. In this Letter, a new derivation approach that incorporates both coefficient reusing (which reduces the oscillation magnitude of each adaptive coefficient) and norm-constrained adaptation (that penalises non-sparse solutions) is advanced. The proposed algorithm performs relaxed projections into hyperplanes of interest in order to obtain the desired robustness and high convergence rate in sparse scenarios with low computation burden and reduced number of adjustable parameters. The resulting method can be implemented in both normalised and non-normalised versions.