$$\ell _1$$-Norm Iterative Wiener Filter for Sparse Channel Estimation

Abstract

The recursive-least-squares (RLS) algorithm is one of the most representative adaptive filtering algorithms. $$\ell _1$$ -norm full-recursive RLS has also been successfully applied to various sparsity-related areas. However, computing the autocorrelation matrix inverse in the $$\ell _1$$ -norm full-recursive RLS generates numerical instability that results in divergence. In addition, the regularization coefficient calculation for $$\ell _1$$ -norm often requires actual channel information or relies on empirical methods. The iterative Wiener filter (IWF) has a similar performance to the RLS algorithm and does not require the inverse of the autocorrelation matrix. Therefore, IWF can be used as a numerically stable RLS. This paper proposes $$\ell _1$$ -norm IWF for sparse channel estimation using the IWF and $$\ell _1$$ -norm. The algorithm proposed in this paper includes a realistic regularization coefficient calculation that does not require actual channel information. The simulation shows that the sparse channel estimation performance of the proposed algorithm is similar to the conventional $$\ell _1$$ -norm full-recursive RLS using real channel information as well as being superior in terms of numerical stability.