论文标题

在存在彩色噪声的情况下,增强的RMT估计器的信号数估计值

Enhanced RMT estimator for signal number estimation in the presence of colored noise

论文作者

Yi, Huiyue, Zhang, Wuxiong, Xu, Hui

论文摘要

基于子空间的技术被广泛用于各种科学领域,并且需要对信号子空间维度进行准确的估计。基于随机矩阵理论的模型顺序估计的经典RMT估计器假设噪声是白色高斯,并且在有彩色噪声的情况下表现不佳,并具有未知的协方差矩阵。在存在彩色噪声的情况下,多元回归(MV-R)算法将源检测模拟为多元回归问题,并从残差误差的协方差矩阵中渗透模型顺序。但是,MV-R算法要求噪声足够弱于信号。为了解决这些问题,本文提出了一种新的信号数估计算法,该算法是在存在彩色噪声的情况下,基于对信息理论标准的行为的分析。首先,第一个标准被定义为当前特征值和下一个特征值的比率,并且相对于过度建模和模型底层分析了其属性。此外,第二个标准被设计为当前值的比率和第一个标准的下一个值,并且相对于过度建模和模型底盘分析了其属性。然后,通过分析这两个标准获得的信号数估计值,MV-R估计器和RMT估计值,提出了一种新型增强的RMT估计量来进行信号估计,以顺序确定被测试的特征值是由信号或噪声引起的。最后,提出了仿真结果,以说明所提出的增强的RMT估计器的估计性能比现有方法更好。

The subspace-based techniques are widely utilized in various scientific fields, and they need accurate estimation of the signal subspace dimension. The classic RMT estimator for model order estimation based on random matrix theory assumes that the noise is white Gaussian, and performs poorly in the presence of colored noise with unknown covariance matrix. In the presence of colored noise, the multivariate regression (MV-R) algorithm models the source detection as a multivariate regression problem and infers the model order from the covariance matrix of the residual error. However, the MV-R algorithm requires that the noise is sufficiently weaker than the signal. In order to deal with these problems, this paper proposes a novel signal number estimation algorithm in the presence of colored noise based on the analysis of the behavior of information theoretic criteria. Firstly, a first criterion is defined as the ratio of the current eigenvalue and the mean of the next ones, and its properties is analyzed with respect to the over-modeling and under-modeling. Moreover, a second criterion is designed as the ratio of the current value and the next value of the first criterion, and its properties is analyzed with respect to the over-modeling and under-modeling. Then, a novel enhanced RMT estimator is proposed for signal number estimation by analyzing the detection properties among the signal number estimates obtained by these two criteria, the MV-R estimator and the RMT estimator to sequentially determine whether the eigenvalue being tested is arising from a signal or from noise. Finally, simulation results are presented to illustrate that the proposed enhanced RMT estimator has better estimation performance than the existing methods.

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