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Compound time-frequency domain method for estimating parameters of uniform-sampling polynomial-phase signals on the entire identifiable region

机译:用于估计整个可识别区域上均匀采样多项式相位信号参数的复合时频域方法

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摘要

Parameter estimation of polynomial-phase signals (PPSs) observed in additive white Gaussian noise (AWGN) is addressed. Most of the existing estimators cannot work on a fully identifiable region. Using the algebraic number theory, McKilliam et al. proposed a least squares unwrapping (LSU) estimator, which can operate on the entire identifiable region. However, its computational load may be large, especially when the number of samples is large. In this study, the authors first extend the amplitude-weighted phase-based estimator (AWPE) for sinusoidal and chirp signals to PPSs and derive a time domain maximum likelihood estimator. The performance is analysed and compared with the Cramér-Rao lower bound (CRLB). Then, the authors propose an iterative compound time-frequency domain parameter estimation method, which includes a coarse estimation step and a fine estimation step conducted by the discrete polynomial phase transform and AWPE estimator, respectively. Monte-Carlo simulations show that the proposed method can work on the entire identifiable region and that it outperforms the existing state-of-the-art estimators. Its computational complexity is considerably lower than that of the LSU estimator, while its threshold signal-to-noise ratio is a few decibels higher than that of the LSU estimator.
机译:解决了在加性高斯白噪声(AWGN)中观察到的多项式相位信号(PPS)的参数估计问题。大多数现有的估算器无法在完全可识别的区域内工作。使用代数数论,McKilliam等。提出了一种最小二乘展开(LSU)估计器,该估计器可以在整个可识别区域上运行。但是,其计算量可能很大,尤其是在样本数量很大时。在这项研究中,作者首先将正弦和线性调频信号的基于振幅加权的基于相位的估计器(AWPE)扩展到PPS,并推导出时域最大似然估计器。对性能进行了分析并与Cramér-Rao下限(CRLB)进行了比较。然后,作者提出了一种迭代复合时频域参数估计方法,该方法包括由离散多项式相位变换和AWPE估计器分别进行的粗略估计步骤和精细估计步骤。蒙特卡洛模拟显示,该方法可以在整个可识别区域内工作,并且优于现有的最新估算器。它的计算复杂度明显低于LSU估计器,而其阈值信噪比却比LSU估计器高几分贝。

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