Estimation of the frequencies of a complex sinusoidal noisy signal using fourth order statistics

The problem of estimating the frequencies of a complex sinusoidal signal corrupted by a correlated Gaussian noise is dealt with using the fourth order statistics. A definition of the complex fourth order statistics is introduced. A fourth order moments matrix, M4, and a fourth order cumulant matrix, C4, are defined. In the general case of a nonGaussian signal corrupted by a Gaussian noise, expressions of M4 and C4 in function of the second-order moment matrix of the noise and the fourth and second order moment matrices of the signal are given. With these expressions, the complex harmonic retrieval problem is solved and simulations are performed