V.V. Makarenkov1, N.A. Kupriyanov2, V.D. Liferenko3, I.S. Lutsko4, S.V. Vasiliev5

1,3–5 Military Space Academy named after A.F. Mozhaisky (Saint-Petersburg, Russia)

2 Krasnodar Higher Military Aviation School of Pilots named after A.K. Serov (Krasnodar, Russia)

The functioning of modern information systems is carried out in difficult conditions for observing objects. One of these conditions is the solution of the problem of detection and tracking of multiple targets against the background of various sources of interference. Adaptive beamforming of a phased antenna array is used to eliminate the negative impact of interfering factors on the operation of radar facilities. The solution of this problem in practice is complicated by the random nature of the impact of several sources of interference at once with unknown motion trajectories and relatively low compared to digital antenna arrays, the phase shifters have a bit depth, which does not allow the formation of deep zeros in the radiation pattern. Therefore, a number of requirements are imposed on the algorithm for adaptive construction of the phased antenna array radiation pattern under conditions of a limited time resource. Chief among these requirements is the requirement for the rate of convergence of the algorithm with its limited computational complexity. Based on this, the study of issues of improving the performance of adaptation algorithms in modern radar systems to changing conditions of the situation is an urgent task. This article discusses the issue of increasing the rate of convergence of the adaptation algorithm using the eigenvalues of the correlation matrix of interference and noise sources. Matrix eigenvalues are calculated based on the discrete Karhunen-Loeve decomposition. The solution of the adaptation problem is complicated by the operation of the algorithm on a classified sample without preliminary training.

Development of an adaptive algorithm for the formation of a phased antenna array beamforming using the discrete Karhunen-Loeve decomposition on a classified sample without preliminary training under the influence of several interference sources.

It is shown that the solution of the problem of adjusting the weighting coefficients of the phased antenna array radiation pattern using the discrete Karhunen-Loeve expansion creates favorable conditions for the initial stage of the considered adaptive algorithm in difficult noise conditions. The gain in convergence rate is explained by the fact that at the initial stage of the algorithm eigenvalues are selected in ascending order. As a result, the gap between the expected and calculated value of the interference and noise matrix is significantly reduced.

Solving the problem of adjusting the weight coefficients of the phased antenna array radiation pattern using the discrete Karhunen-Loeve expansion allows increasing 2 times the speed of the algorithm with virtually no increase in its computational complexity. This effect indicates the expediency of applying the considered computational procedure the conditions of a limited time resource and restrictions on the number of arithmetic operations performed by the algorithm.

Makarenkov V.V., Kupriyanov N.A., Liferenko V.D., Lutsko I.S., Vasiliev S.V. Adaptive beamforming algorithm for a phased antenna array using the discrete Karhunen-Loev decomposition. Electromagnetic waves and electronic systems. 2023. V. 28. № 4. P. 48−56. DOI: https://doi.org/10.18127/j15604128-202304-05 (in Russian)

1. Makarenkov V.V., Podyachev V.V., Lutsko I.S. Adaptive algorithm for adjusting the weight coefficients of a phased array antenna by the least squares criterion using the cell matrix inversion lemma. Electromagnetic waves and electronic systems. 2022. V. 27. № 6. P. 13–20. DOI 10.18127/j5604128-202206-02. (in Russian)
2. Vorobyov D.N., Kupriyanov N.A. Onufriy A.Yu. Algorithmic implementation of trajectory data comparison by a long-range detection radar station. Radio electronics issues. Series: Television Technology. 2020. № 4. P. 81–88. (in Russian)
3. Makarenkov V.V., Moroz A.V., Sakhno I.V., Semenov A.A., Dvorov A.V. Methodology for the formation of DN and calculation of the signal-to-noise ratio at the output of the synthesized antenna array of an ultrasonic location stand under interference conditions. Bulletin of the Metrologist. 2021. № 3. P. 28–33. (in Russian)
4. Makarenkov V.V., Shatalov A.A., Shatalova V.A., Yastrebkov A.B. Adaptive algorithm for recognizing signals received from slowly and rapidly fluctuating targets against the background of interference in multi-band multi-position radar with headlights. Bulletin of Aerospace Defense. 2021. № 4(32). P. 56–65. (in Russian)
5. Kupriyanov N.A., Kurakin S.Z., Stepenko A.S. The concept of synthesis of the interference channel of a radar system with a phased antenna array. Materials of the II National Scientific Conference. "Science of the XXI century: technology, management, security". Kurgan: Kurgan State University. 2022. P. 227–232. (in Russian)
6. Slyusar V.I. SMART antennas went into series. Electronics: Science, technology, business. 2004. № 2(52). P. 62–65. (in Russian)
7. Handbook of radar / Ed. by M.I. Skolnik. In 2 books. Book 1. M.: Technosphere. 2014. 672 p. (in Russian)
8. Dzhigan V.I. Adaptive signal filtering: theory and algorithms. M.: Technosphere. 2013. 528 p. (in Russian)
9. Perunov Yu.M. Foreign radio-electronic means. In 4 books. Book 1: Radar. M.: Radio engineering. 2010. 336 p. (in Russian)
10. Balukhto A.N. Artificial intelligence in space technology. Condition. Prospects of application. Monograph. M.: Radio engineering. 2021. 440 p. (in Russian)