论文标题
基于噪声特征值的线性收缩估计，通过RMT估计量列出来枚举使用相对较少的样品
Source Enumeration via RMT Estimator Based on Linear Shrinkage Estimation of Noise Eigenvalues Using Relatively Few Samples
论文作者
论文摘要
估计噪声中嵌入的信号数量是阵列信号处理中的一个基本问题。基于随机矩阵理论（RMT）的经典RMT估计器倾向于低估信号的数量，因为它不考虑有限样本量的特征值之间的不可忽略的偏置项。此外，RMT估计器患噪声方差估计问题的不确定性。为了克服这些问题，我们首先通过利用噪声样品特征值的线性收缩（LS）估算值来得出更准确的表达来表达样品特征值和特征值之间的偏置项。然后，我们分析了特征值对RMT估计器的估计性能的影响，并得出了该偏置项产生的RMT估计量的不足估计概率的增加。基于这些结果，我们通过将偏置项纳入RMT估计器的决策标准中，提出了一个基于噪声特征值（称为LS-RMT估计器）的LS估计值的新型RMT估计器。当LS-RMT估计器将本特征值之间的该偏差项纳入RMT估计器的决策标准时，它可以检测到沉浸在此偏置项中的信号特征值。因此，LS-RMT估计量可以克服特征值偏置项产生的RMT估计量的较高估计概率，并且还避免了RMT估计器所遭受的噪声方差估计值的不确定性，因为噪声方差是在噪声估计的假设下是在噪声中估算的。最后，提出了广泛的仿真结果，以表明所提出的LS-RMT估计器的表现优于现有估计器。
Estimating the number of signals embedded in noise is a fundamental problem in array signal processing. The classic RMT estimator based on random matrix theory (RMT) tends to under-estimate the number of signals as it does not consider the non-negligible bias term among eigenvalues for finite sample size. Moreover, the RMT estimator suffers from uncertainty in noise variance estimation problem. In order to overcome these problems, we firstly derive a more accurate expression for the distribution of the sample eigenvalues and the bias term among eigenvalues by utilizing the linear shrinkage (LS) estimate of noise sample eigenvalues. Then, we analyze the effect of the bias term among eigenvalues on the estimation performance of the RMT estimator, and derive the increased under-estimation probability of the RMT estimator incurred by this bias term. Based on these results, we propose a novel RMT estimator based on LS estimate of noise eigenvalues (termed as LS-RMT estimator) by incorporating the bias term into the decision criterion of the RMT estimator. As the LS-RMT estimator incorporates this bias term among eigenvalues into the decision criterion of the RMT estimator, it can detect signal eigenvalues immersed in this bias term. Therefore, the LS-RMT estimator can overcome the higher under-estimation probability of the RMT estimator incurred by the bias term among eigenvalues, and also avoids the uncertainty in the noise variance estimation suffered by the RMT estimator as the noise variance is estimated under the assumption that the eigenvalue being tested is arising from noise. Finally, extensive simulation results are presented to show that the proposed LS-RMT estimator outperforms the existing estimators.
