稀疏信道估计的重新加权l1-norm惩罚LMS及其分析
Reweighted l1-norm Penalized LMS for Sparse Channel Estimation and Its Analysis
摘要：
提出并研究了一种新的稀疏信道估计算法-加权l1范数惩罚最小均方（LMS）算法。由于标准LMS算法不考虑关于信道脉冲响应（CIR）的稀疏性信息，因此LMS算法的稀疏性感知修改旨在通过向标准LMS代价函数引入惩罚项来优于标准LMS，该惩罚项迫使解是稀疏的。我们的重新加权l1-范数惩罚LMS算法引入了另外的CIR系数估计的重新加权，以促进稀疏的解决方案，甚至更多和近似l0-伪范数更接近。我们提供了深入的定量分析的加权l1范数惩罚LMS算法。该算法的超额均方误差（MSE）的表达式也推导出这表明，在适当的条件下，加权l1-范数惩罚LMS算法优于标准LMS，这是预期的。然而，我们的定量分析也回答了这个问题，什么是最大的稀疏度水平在信道中的加权l1范数惩罚LMS算法优于标准LMS。仿真结果表明，更好的性能的加权l1范数惩罚LMS算法相比，其他现有的LMS型算法。
英文摘要：
A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l1-norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l0-pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l1-norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l1-norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l1-norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l1-norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.
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