Analysis on error surface and fast algorithms of multichannel quadratic Volterra adaptive filters
Analysis on error surface and fast algorithms of multichannel quadratic Volterra adaptive filters
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DOI：
10.1109/mwscas.2004.1354380
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发表时间：
2004-07
期刊：
影响因子：
--
通讯作者：
Jinhui Chao
中科院分区：
文献类型：
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作者：
Jinhui Chao
本文对多通道二次型沃尔泰拉自适应滤波器（ADF）进行了理论分析。结果表明，这些滤波器的自适应训练是一个病态的问题，或误差表面总是非常陡峭的一个特定的方向，但相对平坦的高斯输入的其余方向。这一结果推广了单通道或横向滤波器的情况下以前的报告。对于不相关的情况，本文还对高斯输入的相关矩阵的特征结构进行了完整的分析。对于高斯输入信号，示出了成本为O（N/sup 2/）次乘法的快速Newton-Raphson算法，其中N是滤波器输入中的线性项的数目，与NLMS算法相同的成本，而对于沃尔泰拉ADF，RLS算法每个样本成本为O（N/sup 5/）次乘法。仿真结果表明，该算法在非高斯输入情况下也能很好地工作。
This paper presents a theoretical analysis on multichannel quadratic Volterra adaptive filters (ADF). It is shown that adaptive training of these filters is an ill-conditioned problem, or the error surfaces are always extremely steep in one particular direction but relatively flat in the rest directions for Gaussian inputs. This result generalizes previous reports in the case of single channel or transversal filters. A complete analysis on eigen-structure of correlation matrix of the Gaussian inputs is also explicitly obtained for the uncorrelated case. A fast Newton-Raphson algorithm is shown for Gaussian input signals costing O(N/sup 2/) multiplications where N is the number of linear terms in the filter input, the same cost as the NLMS algorithm, while the RLS algorithm for Volterra ADF costs O(N/sup 5/) multiplications per sample. Simulations shown that this algorithm works well also in non-Gaussian input cases.