Adaptive sparsity tradeoff for ℓ1-constraint NLMS algorithm

Embedding the norm in gradient-based adaptive filtering is a popular solution for sparse plant estimation. Even though the foundations are well understood, the selection of the sparsity hyper-parameter still remains today matter of study. Supported on the modal analysis of the adaptive algorithm near steady state, this paper shows that the optimal sparsity tradeoff depends on filter length, plant sparsity and signal-to-noise ratio. In a practical implementation, these terms are obtained with an unsupervised mechanism tracking the filter weights. Simulation results prove the robustness and superiority of the novel adaptive-tradeoff sparsity-aware method.