A zero-attracting mixed norm LMS for sparse acoustic room system estimation

Recently, many adaptive filtering proposals that discuss the sparsity of the system have been appeared. These proposals are, mainly, based on the least-mean-square (LMS) algorithm. In this paper we propose two algorithms that exploit the sparsity of the system and based on the mixed norm LMS (MN-LMS) algorithm. The first algorithm is proposed by adding l₁-norm penalty to the cost function of the MN-LMS algorithms. This term enables us to attract the near-to-zero filter coefficients into zero very fast. However, when the system is highly non sparse, the algorithm almost fails. Because of that, we propose another algorithm that uses an approximation of thel₀-norm penalty term in the cost function of the MN-LMS algorithm. This provides high performance even if the system is highly non sparse system. The performances of the proposed algorithms are compared to those of the LMS and MN-LMS algorithms in an acoustic sparse system identification setting. The proposed algorithms provide significant performances compared to the others.