maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2022-1-6-19mais-1604Research ArticleAlgorithmsАлгоритм углового сверхразрешения с использованием разложения Холецкого и его реализация на основе технологии параллельных вычисленийThe Algorithm of Angular Superresolution Using the Cholesky Decomposition and its Implementation Based on Parallel Computing Technologyhttps://orcid.org/0000-0002-3210-1485МищенкоСергей ЕвгеньевичMishchenkoSergey E.mihome@yandex.ruhttps://orcid.org/0000-0002-6365-7734ШацкийНиколай ВитальевичShatskiyNikolay V.hteiz@mail.ruФГУП “Ростовский научно-исследовательский институт радиосвязи”РоссияRostov-on-Don Institute of RadiocommunicationsRussian FederationРадиотехнический институт имени академика А. Л. МинцаРоссияAcademician A. L. Mints Radiotechnical InstitutRussian Federation202217032022291619Copyright © Мищенко С.Е., Шацкий Н.В., 20222022Мищенко С.Е., Шацкий Н.В.Mishchenko S.E., Shatskiy N.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1604

Предложен алгоритм углового сверхразрешения на основе разложения Холецкого, представляющий собой модификацию алгоритма Кейпона. Показано, что предложенный алгоритм позволяет отказаться от обращения ковариационной матрицы входных сигналов. Проведено сравнение предложенного алгоритма с алгоритмом Кейпона по числу операций. Установлено, что предложенный алгоритм при большой размерности задачи обеспечивает некоторый выигрыш как при реализации на однопоточном, так и на многопоточном вычислителе. Получены численные оценки быстродействия предложенного и исходного алгоритма с использованием технологии параллельных вычислений CUDA NVIDIA. Установлено, что предложенный алгоритм обеспечивает экономию вычислительных ресурсов GPU и способен решать задачу построения пространственного спектра при увеличении размерности ковариационной матрицы входных сигналов почти в два раза.

An algorithm of angular superresolution based on the Cholesky decomposition, which is a modification of the Capon algorithm, is proposed. It is shown that the proposed algorithm makes it possible to abandon the inversion of the covariance matrix of input signals. The proposed algorithm is compared with the Capon algorithm by the number of operations. It is established that the proposed algorithm, with a large dimension of the problem, provides some gain both when implemented on a single-threaded and multithreaded computer. Numerical estimates of the performance of the proposed and original algorithm using parallel computing technology CUDA NVidia are obtained. It is established that the proposed algorithm saves GPU computing resources and is able to solve the problem of constructing a spatial spectrum with an increase in the dimension of the covariance matrix of input signals by almost two times.

цифровые антенные решеткиалгоритм сверхразрешения Кейпонаразложение Холецкогометод окаймленияпараллельные вычисленияdigital array antennasCapon super-resolution algorithmCholesky decompositionbordering methodparallel computingReferencesR. Klemm, Principles of Space-Time Adaptive Processing. London: IEE, 2002.R. Klemm, Principles of Space-Time Adaptive Processing. London: IEE, 2002.M. Parker, Radar Basics-Part 4: Space-time adaptive processing, 2011. [Online]. Available: https://www.eetimes.com/design/programmable-logic/4217308/Radar-Basics-Part-4-Space-time-adaptive-processing.M. Parker, Radar Basics-Part 4: Space-time adaptive processing, 2011. [Online]. Available: https://www.eetimes.com/design/programmable-logic/4217308/Radar-Basics-Part-4-Space-time-adaptive-processing.W. Bürger, Space-Time Adaptive Processing: Algorithms, 2006. [Online]. Available: http://ftp.rta.nato.int/public//PubFullText/RTO/EN/RTO-EN-SET-086///EN-SET-086-07.pdf.W. Bürger, Space-Time Adaptive Processing: Algorithms, 2006. [Online]. Available: http://ftp.rta.nato.int/public//PubFullText/RTO/EN/RTO-EN-SET-086///EN-SET-086-07.pdf.S. Nefedov, I. Kruchkov, M. Noniashvili, G. Lesnikov, and N. Soloviev, “A Review of the Signal Space-Time Adaptive Processing (STAP) Basic Techniques in Space-Based Radars with Synthetic Aperture)”, Vestnik MGTU im N.E. Baumana. Ser. ”Priborostroenie”, no. 8, pp. 251-258, 2012.S. Nefedov, I. Kruchkov, M. Noniashvili, G. Lesnikov, and N. Soloviev, “A Review of the Signal Space-Time Adaptive Processing (STAP) Basic Techniques in Space-Based Radars with Synthetic Aperture)”, Vestnik MGTU im N.E. Baumana. Ser. ”Priborostroenie”, no. 8, pp. 251-258, 2012.M. Ratynskij, Adaptation and Superresolution in Array Antennas. Moscow: Radio i svyaz, 2003.M. Ratynskij, Adaptation and Superresolution in Array Antennas. Moscow: Radio i svyaz, 2003.S. Tulenev, A. Savinkov, and V. Vereitin, “Application of CUDA Parallel Programming Technology to Increase the Speed Of Calculation of Superresolution Algorithms in Direction Finding”, Vestnik Voronezhskogo instituta MVD Rossii, no. 2, pp. 196-203, 2021.S. Tulenev, A. Savinkov, and V. Vereitin, “Application of CUDA Parallel Programming Technology to Increase the Speed Of Calculation of Superresolution Algorithms in Direction Finding”, Vestnik Voronezhskogo instituta MVD Rossii, no. 2, pp. 196-203, 2021.Developing a Linux Kernel Module using GPUDirect RDMA. [Online]. Available: https://docs.nvidia.com/cuda/gpudirect-rdma/index.html.Developing a Linux Kernel Module using GPUDirect RDMA. [Online]. Available: https://docs.nvidia.com/cuda/gpudirect-rdma/index.html.V. Voevodin, Numerical Methods of Algebra. Moscow: Nauka, 1966.V. Voevodin, Numerical Methods of Algebra. Moscow: Nauka, 1966.A. Novikov, D. Gabriel’yan, E. Novikova, and N. Shatskiy, Device to Covariance Matrix of Interference Sygnals Inversion, Rus. Patent 2 562 389, Sept. 2015.A. Novikov, D. Gabriel’yan, E. Novikova, and N. Shatskiy, Device to Covariance Matrix of Interference Sygnals Inversion, Rus. Patent 2 562 389, Sept. 2015.M. Zvezdina, O. Komova, N. Shatskiy, and A. Shokov, “Hermitian matrix inversion algorithm”, Vestnik Donskogo gosudarstvennogo universiteta, no. 2(81), pp. 78-84, 2015.M. Zvezdina, O. Komova, N. Shatskiy, and A. Shokov, “Hermitian matrix inversion algorithm”, Vestnik Donskogo gosudarstvennogo universiteta, no. 2(81), pp. 78-84, 2015.F. Gantmacher, The Theory of Matrices. New York: Chelsea Publishing Company, 1959.F. Gantmacher, The Theory of Matrices. New York: Chelsea Publishing Company, 1959.T. Shoup, A Practical Guide to Computer Methods for Engineers. New York: Prentice-Hall, Inc., Englewood Cliffs, 1979.T. Shoup, A Practical Guide to Computer Methods for Engineers. New York: Prentice-Hall, Inc., Englewood Cliffs, 1979.C. Lomont, “Fast Inverse Square Root”, vol. 32, 2003. [Online]. Available: http://www.lomont.org/papers/2003/InvSqrt.pdf.C. Lomont, “Fast Inverse Square Root”, vol. 32, 2003. [Online]. Available: http://www.lomont.org/papers/2003/InvSqrt.pdf.N. Shilov, D. Kondratyev, I. Anureev, E. Bodin, and A. Promsky, “Platform-independent Specification and Verification of the Standard Mathematical Square Root Function”, Modeling and Analysis of Information Systems, vol. 25, no. 6, pp. 637-666, 2018. doi: 10.18255/1818-1015-2018-6-637-666.N. Shilov, D. Kondratyev, I. Anureev, E. Bodin, and A. Promsky, “Platform-independent Specification and Verification of the Standard Mathematical Square Root Function”, Modeling and Analysis of Information Systems, vol. 25, no. 6, pp. 637-666, 2018. doi: 10.18255/1818-1015-2018-6-637-666.

The authors declare that there are no conflicts of interest present.