高斯白噪声中单频复正弦信号频率估计

Frequency estimation of single complex sinusoid in white Gaussian noise

本文提出了一种在加性复高斯白噪声中对单频复正弦信号频率的估计方法。该方法是基于利用自相关系数对Kay的方法的扩展。它从自相关系数的相位差的最佳线性组合中提取频率值。相对于Kay的方法,自相关系数中相位差信息的信噪比提高了。新的估计方法的方差具有更低的输入信噪比阈值,而保持了Kay的方法的无偏性和频率估计范围。我们给出了新方法的均方误差分析及其数值结果。该方差分析适用于中等以上的信噪比或大样本长度的情况。给出了估计其估计方差输入信噪比阈值的近似公式,该公式得出的阈值与样本长度大于24的模拟结果相当接近。

A method for estimating the frequency of a complex sinusoid in additive complex white Gaussian noise is proposed. This method is basically to extend Kay抯 method on using autocorrelations. It retrieves the frequency from the optimal linear combination of the differenced phase of autocorrelations. It is shown that the signal-to-noise ratio (SNR) in the phase information is improved in comparison with the Kay抯 approach. The new estimator gives threshold than Kay抯 method while retaining the unbiased property and estimation range. Mean square error analysis and numerical evaluation are carried out. The variance analysis is shown valid fir medium to high SNRs or for large data length. An approximation formula for the estimation of variance threshold is derived and shown quite close to simulation for data length larger than 24.