Abstract

In this paper, we determine the joint estimates variance minimum of the signal parameters, a mixture of narrowband and wideband signals and white Gaussian noise that are presented as a complex total signal. An expression is obtained for calculating the Fisher matrix elements to establish the lower Rao–Cramer boundary. The dependences of the standard deviations (RMS) of the estimates on the signal-to-noise ratio, sample length, and on the initial signal parameters, such as the central frequencies of the signal components and the width of the broadband component, are presented. A comparison with the minimal standard deviations obtained for a signal model that includes only the broadband component is performed. Analysis of the results allows assessing the requirements that may be imposed on the developed algorithms for joint estimation of the mixture parameters of the considered signals depending on the set values of the sampling frequency and the sample size.

中文翻译：

---

具有白噪声的窄带和宽带信号混合的参数联合估计的方差的下Rao-Cramer边界

摘要

在本文中，我们确定信号参数，窄带和宽带信号以及白高斯噪声的混合估计联合方差最小值，这些信号呈现为复杂的总信号。获得用于计算Fisher矩阵元素以建立下Rao-Cramer边界的表达式。给出了估计的标准偏差（RMS）对信噪比，样本长度以及初始信号参数（例如信号分量的中心频率和宽带分量的宽度）的依赖性。与仅包含宽带分量的信号模型获得的最小标准偏差进行比较。