Description: Min-Norm is a one of eigenstructure methods and it provides good resolution in the case of high and low signal-to- noise ratios. In the article, the problem of direction of arrival estimation of radiation sources by Min-Norm method is considered. Such problem is a part of the problem of estimation of communication channel for the communication systems with MIMO and MIMO-OFDM. The possibility of reduction of computational load of the Min-Norm method is investigated. Caley-Hamilton theorem is used in the paper. Modification of the Min-Norm method based on the power basis of the correlation matrix of input sequence is suggested. The main difference of proposed modification as compared to known fast Min-Norm is calculation of noise power without the knowledge of eigenvalues of correlation matrix or with calculation the least noise eigenvalue. Therefore the limita-tion of initial approach related with requirement of a priori knowledge of threshold between noise subspace and signal-subspace eigenvalues is reduced. Furthermore, the estimation of the number of sources is introduced using the method without eigendecomposition. Several variants of computation of the noise variance are considered. The application of proposed ap-proach is preferable for the case when the number of sources is lower than then the antenna elements. The simulation results are presented, where the performance of Min- norm method when using different bases is compared. They confirm the saving of effi-ciency of spectral analysis by Min-Norm method. It is of interest to use the considered results for realization of combined estima-tion of angular coordinates of radiation sources (i.e. so called joint estimation strategy). Furthermore, the very interesting appli-cation of power basis is a spatial separation of sources for the communication systems with MIMO (MIMO-OFDM). The so-called surrogate data technology can be used in order to improve the estimate of correlation matrix. Furthermore, for the case when minimum value of correlation matrix will be estimated the remaining noise subspace eigenvalues can be forecasted. It is also of interest to consider application of another base to reduce the computational load of Min-Norm method.
Keywords: Power basis, Caley-Hamilton theorem, Min-norm method, eigenvectors, eigenvalues
1. Gershman, A.B. and Sidiropoulos, N.D. (2005), Space-time processing for MIMO communications, John Wiley&Sons, 390 p.
2. Marple, S.L., Jr. (1987), Digital spectral analysis with applications, Prentice Hall, New Jersey, 512 p.
3. Ermolaev, V.T. and Flaksman, A.G. (2011), Theoretical foundations for signal processing in wireless communication Systems, Nizhny Novgorod, 344 p.
4. Moreno, J.H. and Lang, T. (1991), Matrix computations on systolic-type arrays, Springer science, New York, 297 p.
5. Ermolaev, V.T. and Gershman, A.B. (1994), Fast algorithm for minimum-norm direction-of-arrival estimation, IEEE Trans.on SP, Vol .42, No. 9, pp. 2389-2394.
6. Mallat, S. (1999), A wavelet tour of signal processing, Academic Press, Boston, 637 p.
7. Fenn, A.J. (2008), Adaptive Antennas and Phased Arrays for Radar and Communications, Artech House, Boston, 393 p.
8. Vasylyshyn, V.І. (2014), “Predvaritalnaya obrabotka signalov s ispolzovaniem metoda SSA v zadachach spectralnogo analiza” [Signal preprocessing with using the SSA method in spectral analysis problems], Applied Radio Electronics: Sci. Journ, Vol. 13, No. 1, pp. 43-50.
9. Vasylyshyn, V.I. (2015), Adaptive variant of the surrogate data technology for enhancing the effectiveness of signal spectral analysis using eigenstructure methods, Radioelectronics and Communications Systems, Vol. 58, No. 3, pp. 116-126.
10. Hande, P. and Tong, L. (2001), Signal Parameter Estimation via the Cayley–Hamilton Constraint, IEEE Signal Proc-essing Letters, Vol. 8, No. 4, pp. 110-113.
11. Xin, J., Zheng, N. and Sano, A. (2007), Simple and efficient nonparametric method for estimating the number of signals without eigendecomposition, IEEE Trans. on SP, Vol. 55, No. 4, pp. 1405-1420.
12. Golub, G.H. and Van Loan, C.F. (2013), Matrix computations: fourth ed., The Johns Hopkins University Press, Balti-more, 780 p.