论文标题
与协方差不匹配的训练样本分析SNR损失分布
Analysis of the SNR loss distribution with covariance mismatched training samples
论文作者
论文摘要
我们分析了自适应滤波器输出的信号与噪声比（SNR）损耗的分布，该滤波器的样品训练，这些样品与未预见过滤器的样品相同的协方差矩阵。我们的目标是找到SNR损耗的分布的准确近似，该分布的形式与无不匹配的情况相似。我们依次考虑了两个协方差矩阵满足所谓的广义特征和它们是任意的情况的情况。在前一种情况下，这相当于在正常变量中近似中央二次形式，而后一种情况则需要在学生分布式变量中近似非中心二次形式。为了获得近似分布，提倡一种皮尔森类型的方法。一项数值研究表明，这种近似相当准确，使人们可以直接地评估协方差不匹配的影响。
We analyze the distribution of the signal to noise ratio (SNR) loss at the output of an adaptive filter which is trained with samples that do not share the same covariance matrix as the samples for which the filter is foreseen. Our objective is to find an accurate approximation of the distribution of the SNR loss which has a similar form as in the case of no mismatch. We successively consider the case where the two covariance matrices satisfy the so-called generalized eigenrelation and the case where they are arbitrary. In the former case, this amounts to approximate a central quadratic form in normal variables while the latter case entails approximating a non-central quadratic form in Student distributed variables. In order to obtain the approximate distribution, a Pearson type approach is advocated. A numerical study show that this approximation is rather accurate and enables one to assess, in a straightforward manner, the impact of covariance mismatch.
