A mixed norm constraint IPNLMS algorithm for sparse channel estimation

This paper presents a novel approach for structure extraction of the cluster sparse system identification. Different from adopting ℓ₁-norm constraint to regularize the sparsity in the improved proportionate normalized least mean square (IPNLMS) algorithm, we directly work with the block sparse structure via ℓ_{1 , 0}-norm constraint. In particular, we develop a cluster sparse IPNLMS by the block ℓ norm regularization, named IPNLMS-BL0 method. The cluster sparse constraint is regarded as an extended version for the sparse constraint term. On the other hand, the iterations of IPNLMS-BL0 are derived by the steepest descent strategy. Then, we provide the analysis of block size choices of the cluster sparse constraint, computational complexity, and steady-state error of the proposed method. Various simulations are designed to test the performance of the IPNLMS-BL0 algorithm and its counterparts to identify and track the unknown sparse systems. The results are provided and analyzed to confirm the effectiveness and superiority of the proposed IPNLMS-BL0 algorithm.