非高斯有色噪声中谐波恢复的累积量投影方法

本文研究非高斯有色噪声中的谐波恢复问题。首先建立了复数线性非高斯过程的高阶累积量投影定理。应用该定理，由含噪谐波信号的四阶累积量求得非高斯有色噪声的自相关，然后通过求解一个广义特征值问题对矢量空间进行预白化，最后结合噪声子空间方法ＭＵＳＩＣ恢复谐波信号参数。本文方法克服了以往的困难，成功地解决了对称分布非高斯噪声背景下和谐波信号中存在二次相位耦合时的谐波恢复问题。仿真实验验证了本文结论。

Cumulant Projection Method For Harmonic Retrieval in Colored Non-Gaussian Noise

The problem of concern here is the harmonic retrieval in colored non Gaussian noise. The cumulant projection theorem of the complex linear non Gaussian process was established. Based on this theorem, the noise covariance estimates are obtained using the elaborately defined fourth order cumulant of the complex noisy signal. Then a generalized eigenvalue problem is solved to prewhiten the vector space, finally noise subspace method such as MUSIC is employed to retrieve the harmonics. This method succeeds in harmonic retrieval in colored non Gaussian noise, especially when the noise is symmetrically distributed or there exist quadratic phase coupled cosinusoids. Simulation examples are presented to support the result of this paper.