Two-Dimensional Frequency Estimation of Harmonics in Multiplicative and Additive Noise

The harmonic retrieval in noise is a classical signal processing problem, and it has been applied in a wide range of signal processing areas. This paper addresses the problem of two-dimensional (2-D) harmonic frequency estimation in the presence of zero-mean multiplicative and additive noise, and proposes an algorithm to estimate the frequencies of two-dimensional harmonics in zero-mean multiplicative and additive noise based on the singular value decomposition of data matrix and the rotational invariance of subspace. It is difficult for the traditional methods to directly estimate frequency of two-dimensional harmonics or failure of estimation in zero-mean multiplicative and addition noise. The observed harmonic signals are first changed by squaring the sample data. Then, a data matrix is constructed using the characteristics of this changed model. The inherent relation between the frequencies of harmonics in zero-mean multiplicative and addition noise and the data matrix is derived, which can be used to estimate the frequencies of two-dimensional harmonics in zero-mean multiplicative and addition noise. Meanwhile, the estimated frequencies are automatically paired. The effectiveness of the proposed algorithm is verified by some numerical experiments.