The work objective is speeding the covariance matrix converter of the adaptive antenna array interference by reducing the number of operations performed. A problem of developing an aprior information inversion algorithm relying on the Hermitian nature of the reversible matrix is considered. The proposed algorithm is based on a bordering method in contrast to the well-known algorithms based on method of Gaussian-Jordan elimination. Because of complexity and a large operation num-ber, Gaussian-Jordan method does not allow realizing the real time signal processing in computing systems of the adaptive antenna arrays that are widely used in communication, radiolo-cation, and radio navigation systems. The proposed algorithm extends a well-known bordering method by taking into account Hermitian nature of the covariance interference matrix, and allows developing an algorithm based on the recursive rela-tions. An obtained gain in amount of calculation is no less than 25% comparing to the method of Gaussian-Jordan elimination. The calculation amount decrease and a more simple form of relations used for the matrix inversion algorithm elaboration allow developing a more simple design of the adaptive antenna array processor for the matrix inversion.
adaptive antenna array, adaptive array computing system, covariance interference matrix inversion, bordering method, Hermitian nature of covariance matrix, calculation amount decrease, device for matrix inversion.
Введение. На современном этапе развития радиоэлектронных систем (РЭС) в области связи, радиолокации и радионавигации отмечается значительное усложнение электромагнитной обстановки. Это связано с высокой пространствен-ной плотностью размещения РЭС и ограничениями используемых частотных диапазонов. Так, по данным [1], число базовых станций формата 3G/4G только одного российского оператора «МегаФон» к концу 2013 года составляло по-рядка 43,5 тыс.
1. “Megafon” - lider po chislu bazovikh stantsiy v Rossii [“Megafon” is a leader in base station number in Russia]: Available at: http://1234g.ru/novosti/110-megafon-lider-po-kolichestvu-bazovykh-stantsij-v-rossii; (accessed: 29.01.2015) (in Russian)
2. Ratynskiy, M.V. Adaptatsiya i sverkhrazreshenie v antennykh reshetkakh. [Adaptation and superresolution in an-tenna arrays.] Moscow: Radio i svyaz’, 2003 (in Russian).
3. Gabriel’yan, D.D., Zvezdina, M.Yu., Shokov, A.V., Ogayan, P.S. Potentially Achievable Characteristics Analysis for Superresolution Techniques. Journal of Electrical and Control Engineering. JECE, 2013, vol. 3, no. 4, pp.17-20.
4. Jonson, D.H., Miner, G.E. Comparison of superresolution algorithm for radio direction finding. IEEE Trans. Aero-space and Electron. Syst., 1986, vol. 22, no. 4, pp. 432-441.
5. Bartenev, V. Kvazioptimal’nye adaptivnye algoritmy obnaruzheniya signalov. [Quasioptimal adaptive algorithms of signal detection.] Sovremennaya radioelektronika, 2011, no. 2, pp. 70-73 (in Russian).
6. Volkov, S.S. Analiticheskoe reshenie kontaktnoy zadachi o vnedrenii sfericheskogo indentora v myagkiy uprugiy sloy. [Analytical solution to contact problem on spherical indenter penetration into soft elastic layer.] Vestnik of DSTU, 2012, no. 7(68), pp. 5-10 (in Russian).
7. Zolotykh, S.А., Stukopin, V.А. Ob opisanii predel’nogo spectra lentochnykh tyeplitsevykh matrits. [On formulation of limitary spectrum of banded Toeplitz matrices.] Vestnik of DSTU, 2012, no. 8 (69), pp. 5-11 (in Russian).
8. Gabriel’yan, D.D., Zvezdina, M.Yu., Bezuglov, E.D., Zvezdina, Yu.A., Sil’nitsky, S.A. Spatial Polarization Signal Processing in Circular Polarization Antenna. PIERS Draft Proc. Moscow, Russia, August 18-21, 2009. The Electromagnetics Academy, Cambridge, MA, 2009, pp. 1259-1262.
9. Vakhnenko, I.V., Gabriel’yan, D.D., Zvezdina, M.Yu. Nakhozhdenie vesovykh koeffitsientov v kombinirovannom metode prostranstvennoy selektsii signalov. [Finding weight coefficients for combined method of spatial signal selection.] State registration certificate for PC program no. 2009613223, 19.06.09.
10. Soleymani, F. A Rapid Numerical Algorithm to Compute Matrix Inversion. Int. Journal of Mathematics and Sci-ences, vol. 2012: Available at: http://www.hindawi.com/journals/ijmms/2012/134653.
11. Li, W., Li, Z. A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix. Applied Mathematics and Computation, 2010, vol. 215, no. 9, pp. 3433-3442.
12. Kohno, K., Inouye, Y., Kawamoto, M. A Matrix Pseudo-Inversion Lemma for Positive Semidefinite Hermitian Matrices and Its Application to Adaptive Blind Deconvolution of MIMO Systems. IEEE Trans. On Circuits and Systems J., 2008, no. 2, pp. 424-435.
13. Sohana, J., Imtiaz, A. Operation Properties of Adjoint Matrix of Hermitian Block Matrices. Int. Journal of Basic & Applied Sciences, 2010, vol.10, no. 2, pp.58-65: Available at: http://www.ijens.org/ 108102-6767%20IJBAS-IJENS.pdf
14. Zhongyun, L., Jing, L., Yulin, Z. On the Eigenstructure of Hermitian Toeplitz Matrices with Prescribed Eigenpairs. The 8th Int. Symp. On Operations and Its Applicat. (ISORA’09). Zhangjijie, China, Sept. 20-23, 2009, pp. 298-305.
15. Zvezdina, М.Yu., Zvezdina, Yu.A., Zabelkin, S.N., Podzorov, А.V., Samodelov, А.N. Primenenie metoda okay-mleniya dlya resheniya zadachi diffraktsii na krugovom metallicheskom tsilindre s pokrytiem. [Bordering method for diffrac-tion problem on coated circular metallic cylinder.] Electromagnetic Waves and Electronic Systems, 2011, vol. 16, no. 5, pp. 15-17 (in Russian).
16. Zvezdina, М.Yu. Poluchenie analiticheskogo resheniya zadachi diffraktsii na krugovom metallicheskom tsilindre s pokrytiem na osnove metoda okaymleniya. [Obtaining analytic solution for diffraction on coated circular metallic cylinder with bordering method.] Proc. Int.Sci.-Tech.Conf. “IREMV-2011”. Taganrog-Divnomorskoe, Russia, 2011, June 27 - July 1. Taganrog: Izd-vo TTI YuFU, 2011, pp. 227-230 (in Russian).
17. Sobolevskiy, P.I., Likhoded, N.A., Kos’yanchuk, V.V., Yakush, V.P. Ustroystvo dlya obrascheniya matrits. [Ma-trix inversion device.] Patent USSR, RU 1819020. G06F17/16, 1995 (in Russian).
18. Gabriel’yan, D.D., Novikov, A.N., Shatskiy, V.V., Shatskiy, N.V. Adaptivnaya antennaya reshetka. [Adaptive an-tenna array.] Patent RF, RU 2466482. Class H 01 Q 3 / 26, H 01 Q 21 / 00, 2012 (in Russian).
19. Gantmaher, F.-R. Teoriya matrits. [Matrix theory.] Moscow: Nauka, 1988, 552 p. (in Russian).
20. Fast Matrix Multiplication and Inversion: Available at: http://www.lehigh.edu/~gi02/m242/08linstras.pdf; (ac-cessed: 25.01.15)
