The Algorithm of Angular Superresolution Using the Cholesky Decomposition and its Implementation Based on Parallel Computing Technology
https://doi.org/10.18255/1818-1015-2022-1-6-19
Abstract
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.
Keywords
digital array antennas,
Capon super-resolution algorithm,
Cholesky decomposition,
bordering method,
parallel computing
MSC2020: 78A50, 78M50, 68W10
About the Authors
Sergey E. Mishchenko
Rostov-on-Don Institute of Radiocommunications
Russian Federation
Russian Federation
Nikolay V. Shatskiy
Academician A. L. Mints Radiotechnical Institut
Russian Federation
Russian Federation
References
1. R. Klemm, Principles of Space-Time Adaptive Processing. London: IEE, 2002.
2. 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.
3. 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.
4. 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.
5. M. Ratynskij, Adaptation and Superresolution in Array Antennas. Moscow: Radio i svyaz, 2003.
6. 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.
7. Developing a Linux Kernel Module using GPUDirect RDMA. [Online]. Available: https://docs.nvidia.com/cuda/gpudirect-rdma/index.html.
8. V. Voevodin, Numerical Methods of Algebra. Moscow: Nauka, 1966.
9. 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.
10. M. Zvezdina, O. Komova, N. Shatskiy, and A. Shokov, “Hermitian matrix inversion algorithm”, Vestnik Donskogo gosudarstvennogo universiteta, no. 2(81), pp. 78-84, 2015.
11. F. Gantmacher, The Theory of Matrices. New York: Chelsea Publishing Company, 1959.
12. T. Shoup, A Practical Guide to Computer Methods for Engineers. New York: Prentice-Hall, Inc., Englewood Cliffs, 1979.
13. C. Lomont, “Fast Inverse Square Root”, vol. 32, 2003. [Online]. Available: http://www.lomont.org/papers/2003/InvSqrt.pdf.
14. 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.
Review
For citations:
Mishchenko S.E., Shatskiy N.V. The Algorithm of Angular Superresolution Using the Cholesky Decomposition and its Implementation Based on Parallel Computing Technology. Modeling and Analysis of Information Systems. 2022;29(1):6-19. (In Russ.) https://doi.org/10.18255/1818-1015-2022-1-6-19
Views:
566
Email this article 