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

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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.

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Acknowledgements

This paper was supported by Agency for Defense Development (ADD) in S. Korea (UD190005DD).

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  1. Department of Electrical Engineering, Sejong University, Kunja, Kwangjin, 98, Seoul, 143-747, Korea

    Jun-seok Lim

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  1. Jun-seok Lim
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Correspondence to Jun-seok Lim.

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Lim, Js. \(\ell _1\)-Norm Iterative Wiener Filter for Sparse Channel Estimation. Circuits Syst Signal Process 39, 6386–6393 (2020). https://doi.org/10.1007/s00034-020-01467-x

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