A block proportionate arctangent LMS algorithm for cluster sparse system

The conventional least mean square (LMS) algorithm suffers from deteriorated convergence in cluster sparse systems under non-Gaussian noise, severely limiting its applicability to practical identification tasks. To address this limitation, in this paper, we proposed a block proportionate arctangent least mean square (BPALMS) algorithm that effectively exploits the cluster sparsity characteristic while maintaining robustness against non-Gaussian noise. A block ℓ1,0-norm constrained proportionate matrix is embedded into the iterative expression of the arctangent framework LMS (ATLMS) algorithm, where ℓ1-norm characterizes the sparsity within the block, and ℓ0-norm constrains the sparsity between blocks. During iterations, the norm value of the taps in each block is dynamically evaluated by its mixed ℓ1,0-norm metric, which automatically assigns larger step sizes to blocks containing more active taps. As a result, the BPALMS algorithm can fully utilize the cluster sparsity characteristic and accelerate the convergence rate. The steady-state performance and computational complexity of the BPALMS algorithm are derived and discussed. Experiments show that in non-Gaussian noise environment, the proposed BPALMS algorithm performs more effectively than the conventional adaptive filter algorithms in both one-cluster and multi-cluster systems.