Detecting the number of 2-D harmonics in multiplicative and additive noise using enhanced matrix

This paper proposes a method for detecting the number of two-dimensional (2-D) harmonics in multiplicative and additive noise. We define an enhanced matrix using the generalized covariances of 2-D harmonics in multiplicative and additive noise and derive an inherent relation between the number of 2-D harmonics and the eigenvalues of the enhanced matrix. The number of 2-D harmonics in multiplicative and additive noise could be detected based on this special relation. The proposed method avoids the peaks searching and does not need any assumptions about the distribution and color of the multiplicative and additive noise. The computation complexity of the proposed method is analyzed. Simulations demonstrate the effectiveness of the proposed method.

[1]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[2]  Reda R. Gharieb,et al.  Estimating two-dimensional frequencies by a cumulant-based FBLP method , 1999, IEEE Trans. Signal Process..

[3]  Yingbo Hua.  Estimating two-dimensional frequencies by matrix enhancement and matrix pencil , 1992, IEEE Trans. Signal Process..

[4]  Georgios B. Giannakis,et al.  Harmonics in multiplicative and additive noise: parameter estimation using cyclic statistics , 1995, IEEE Trans. Signal Process..

[5]  Lihua Fu,et al.  Harmonic retrieval in complex noises based on wavelet transform , 2008, Digit. Signal Process..

[6]  D. Hampicke,et al.  Joint estimation of DoD, time-delay, and DoA for high-resolution channel sounding , 2000, VTC2000-Spring. 2000 IEEE 51st Vehicular Technology Conference Proceedings (Cat. No.00CH37026).

[7]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[8]  Qi Cheng.  Detection of 2-D cisoids using MODE least square error functions , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[9]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[10]  Philippe Forster,et al.  Harmonic retrieval in the presence of non-circular Gaussian multiplicative noise: performance bounds , 2005, Signal Process..

[11]  Etienne Barnard,et al.  Two-dimensional superresolution radar imaging using the MUSIC algorithm , 1994 .

[12]  Ananthram Swami.  Multiplicative noise models: parameter estimation using cumulants , 1990 .

[13]  P. Vainikainen,et al.  Detection of number of two-dimensional cisoids for array processing algorithms , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[14]  Xianda Zhang.  Two-dimensional harmonic retrieval and its time-domain analysis technique , 1991, IEEE Trans. Inf. Theory.

[15]  Stéphanie Rouquette-Léveil,et al.  Estimation of frequencies and damping factors by two-dimensional ESPRIT type methods , 2001, IEEE Trans. Signal Process..

[16]  Hongwei Li,et al.  Estimation of the number of harmonics in multiplicative and additive noise , 2007, Signal Process..

[17]  Georgios B. Giannakis,et al.  2-D harmonic retrieval using higher-order statistics , 1995, Multidimens. Syst. Signal Process..

[18]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.