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.

中文翻译：

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$$\ell _1$$-用于稀疏信道估计的范数迭代维纳滤波器

递归最小二乘 (RLS) 算法是最具代表性的自适应滤波算法之一。$$\ell _1$$-norm 全递归 RLS 也已成功应用于各种与稀疏相关的领域。然而，在 $$\ell _1$$-norm 全递归 RLS 中计算自相关矩阵的逆会产生数值不稳定性，从而导致发散。此外，$$\ell _1$$-norm 的正则化系数计算往往需要实际的信道信息或依赖经验方法。迭代维纳滤波器 (IWF) 具有与 RLS 算法相似的性能，并且不需要自相关矩阵的逆。因此，IWF 可以用作数值稳定的 RLS。本文提出了使用 IWF 和 $$\ell_1$$-norm 进行稀疏信道估计的 $$\ell_1$$-norm IWF。本文提出的算法包括一个不需要实际信道信息的现实正则化系数计算。仿真表明，该算法的稀疏信道估计性能与使用真实信道信息的常规$$\ell_1$$-norm全递归RLS相似，并且在数值稳定性方面具有优越性。