Abstract
The chapter shows original methods of logical and mathematical background of adaptive spatial signal processing with not exactly known parameters. The elements of axiomatic and some analogues as well as elements of the theory of generalized linear systems are introduced. It is shown that the problem of development of effective algorithms of adaptive spatial signal processing with not exactly known parameters is reduced to construction of some operators for the Banach space. Next, the methods for these operators construction are proposed and it is shown that the minimax approach can be used. The last part of the chapter is devoted to construction of optimization tasks with different restrictions such as quadratic restriction (conditional inequality), mixed restriction, and generalized mixed restriction.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kostrynin, A.I.: Introduction to algebra. Foundations of algebra. Nauka, M. (1994) (in Russian)
Zuravlev, A.K., Lukoshkin, A.P., Poddubnyj, S.S.: Processing of signals in adaptive antenna arrays. LGU, L. (1983) (in Russian)
Kolmogorov, A.N., Fomin, S.V.: Elements of function theory and functional analysis. Nauka, M. (1989) (in Russian)
Tichonov, A.N., et al.: Regularization algorithms and a priori information. Nauka, M. (1983) (in Russian)
Tichonov, A.N., Leonov, A.S., Jagola, A.G.: Nonlinear recurrent tasks. Nauka, M. (1995) (in Russian)
Tichonov, A.N., Arsenin, V.J.: Methods for solution of incorrect tasks. Nauka, M. (1986) (in Russian)
Parlet, B.: The symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs (1980)
Bertsekas, D.: Constrained Optimization and Lagrange Multiplier Methods. Academic, N.Y. (1982)
Pshenichny, B.N.: Convex analysis and extreme tasks. Nauka, M. (1980) (in Russian)
Vasiljev, F.P.: Methods solution of extreme tasks. Nauka, M. (1981) (in Russian)
Guntmacher, F.R.: Theory of matrices. Nauka, M. (1988) (in Russian)
Kallianpur, G.: Stochastic filtering theory. Springer, Berlin (2010)
Mathew, G., Reddy, V.U.: A quasi-newton adaptive algorithm for generalized symmetric eigenvalue problem. IEEE Trans. Signal Processing. 44(10), 2413–2421 (1996)
Obeng, G., Ackland, I.: Applied nonlinear analysis. Academic Press, London (1986)
Van Trees, H.: Detection, estimation and modulation theory (Part 1). John Wiley and Sons, N.J. (2001)
Traub, J.: A general theory of optimal algorithms. Academic Press, London (1980)
Traub, J.: Information, uncertainty, complexness. Academic Press, London (1986)
Wilkinson, J.H.: The algebraic eigenvalue problem. Clarendon Press, Oxford (1965)
Abramov, J.I.: Variance methods in theory of operator bundles. Spectral optimization. LGU, L. (1983) (in Russian)
Marchuk, L.A.: Method for synthesis of robust algorithms of aaa control. Izvestia Wuzov. Radioelectronika 39(9), 61–66 (1996) (in Russian)
Marchuk, L.A., Efimov, A.A., Titarenko, L.A.: Application of interval estimates for parameters of useful signal for synthesis of robust algorithms of adaptive spatial filtration. In: Proceedings of International Conference “Theory and Technique of Transmission, Receiving and Processing of Information”, pp. 26–27. KTURE (1996) (in Russian)
Marchuk, L.A., Giniatulin, N.F., Kolinko, A.V.: Analysis of algorithms for minimizing power of output signal in adaptive antenna arrays. Radiotechnika i Elektronika 42(6), 1–6 (1997) (in Russian)
Marchuk, L.A., Kondratjeva, N.L., Efimov, A.A.: Method for synthesis of robust algorithms adaptation of antenna arrays. In: Proceedings of UNDIRT, vol. (3) (1996) (in Russian)
Marchuk, L.A., Fattachov, V.V.: Peculiarities of control aaa algorithm synthesized along criterion of minimum power of output signal. Izvestia Wuzov. Radioelectronika 36(5), 74–79 (1993)
Titarenko, L.A.: Peculiarities of adaptive spatial-temporal signal processing with prrf. Radiotechnika (123), 191–195 (2001) (in Russian)
Losev, J.I., et al.: Adaptive compensation of interferences in channels of communication. Radio i Swjaz, M. (1988) (in Russian)
Minut, M.: Mathematical programming. McGraw Hill, N.Y. (1989)
Parodi, M.: Localization of characteristic numbers of matrices and its application. Academic, N.Y. (1959)
Huber, P.J.: Robust Statistics. John Wiley and Sons, New York (1981)
Bellman, R.: Introduction to matrix analysis. McGraw Hill, N.Y. (1970)
Horn, R., Johnson, T.: Topics in matrix analysis. Cambridge University Press, Cambridge (1994)
Monzigmo, R.A., Miller, T.W.: Adaptive antenna arrays. Introduction into theory. Skitech Publishers, N.Y. (2004)
Pillai, S.U.: Array Signal Processing. Springer, N.Y. (1989)
Komarovich, V.F., Marchuk, L.A.: To theory of adaptive spatial signal processing with unclear known parameters. In: Proceedings of International Conference “Theory and Technique of Transmission, Receiving and Processing of Information”, vol. 2(26), pp. 36–37. KTURE (1996) (in Russian)
Tihonov, V.I., Harisov, V.N.: Statistical analysis and synthesis radiotechnical systems and devices. Radio i Swjaz, M. (1991) (in Russian)
Efimenko, V.S., Harisov, V.N.: Adaptive spatial-temporal filtration for multichannel receiving. Radiotehnika i Elektronika 32(9), 1889–1893 (1987)
Wojevodin, V.V., Kuznecov, J.A.: Matrices and calculations. Nauka, M. (1984) (in Russian)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Titarenko, L., Barkalov, A. (2013). Background of ASSP with Not Exactly Known Parameters. In: Methods of Signal Processing for Adaptive Antenna Arrays. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32132-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-32132-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32131-3
Online ISBN: 978-3-642-32132-0
eBook Packages: EngineeringEngineering (R0)