Block-Sparsity-Induced Adaptive Filter for Multi-Clustering System Identification
Block-Sparsity-Induced Adaptive Filter for Multi-Clustering System Identification
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用于多聚类系统识别的块稀疏性自适应滤波器
DOI：
10.1109/tsp.2015.2453133
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发表时间：
2015-10-15
影响因子：
5.4
通讯作者：
Gu, Yuantao
中科院分区：
文献类型：
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作者：
Jiang, Shuyang;Gu, Yuantao
为了提高基于最小均方（LMS）的自适应滤波识别块稀疏系统的性能，提出了一种新的自适应算法，称为块稀疏LMS（BS-LMS）。该算法的基础是将块稀疏性惩罚插入到传统 LMS 算法的成本函数中，块稀疏性惩罚是具有相同组分区大小的自适应抽头权重的混合 l2, 0 范数。为了描述块稀疏系统响应，我们首先提出了马尔可夫高斯模型，该模型可以使用给定参数生成一种任意平均稀疏度和任意平均块长度的系统响应。然后，我们针对白高斯输入数据提出了具有适当组划分大小的 BS-LMS 的稳态失调和瞬态收敛行为的理论表达式。基于上述结果，我们从理论上证明，在相同的小失调水平下，BS-LMS 比 l0-LMS 具有更好的收敛行为。最后，数值实验验证了所有理论分析与大范围参数的模拟结果非常吻合。
In order to improve the performance of least mean square (LMS)-based adaptive filtering for identifying block-sparse systems, a new adaptive algorithm called block-sparse LMS (BS-LMS) is proposed in this paper. The basis of the proposed algorithm is to insert a penalty of block-sparsity, which is a mixed l2, 0 norm of adaptive tap-weights with equal group partition sizes, into the cost function of traditional LMS algorithm. To describe a block-sparse system response, we first propose a Markov-Gaussian model, which can generate a kind of system responses of arbitrary average sparsity and arbitrary average block length using given parameters. Then we present theoretical expressions of the steady-state misadjustment and transient convergence behavior of BS-LMS with an appropriate group partition size for white Gaussian input data. Based on the above results, we theoretically demonstrate that BS-LMS has much better convergence behavior than l0-LMS with the same small level of misadjustment. Finally, numerical experiments verify that all of the theoretical analysis agrees well with simulation results in a large range of parameters.