V. V. Makarenkov1, S. Yu. Sysuev2, V. S. Uss3, A. A. Shatalov4, V. A. Shatalova5, N. A. Kupriyanov6
1 A.F. Mozhaisky Military Space Academy (Saint Petersburg, Russia)
2, 4 Mikhailovskaya Military Artillery Academy (Saint Petersburg, Russia)
3 PJSC Scientific and Production Association Almaz named after Academician A.A. Raspletin (Territorial separate division Lianozovsky Electromechanical Plant) Scientific and Production Center (Saint Petersburg, Russia)
5 Bonch-Bruevich Saint Petersburg State University of Telecommunications (Saint Petersburg, Russia)
6 Krasnodar Higher Military Aviation School of Pilots (Krasnodar, Russia)

1 makar8722@mail.ru, 2 gonta-gv@yandex.ru, 6 sektor-ussr@rambler.ru

The article discusses the features of building digital filtering algorithms for conformal digital phased array antennas (DPAA) with signal processing based on ring phased array antennas (PAA), which are the main elements of cylindrical, conical and spherical PAA. The process of creating conformal DPAA is complicated by the need to additionally equip it with a number of signal processing functions. The fulfillment of the latter condition involves the development of adaptive algorithms that work in conditions of parametric and nonparametric uncertainty against the background of various kinds of interference, as well as appropriate software that allows performing digital signal processing (DSP) in real time. This part of the paper focuses on information processing algorithms based on the use of orthogonalization and biorthogonalization procedures for random processes. The use of these procedures proves to be most effective in cases where rapid adaptation with variable parameters is required, and the eigenvalues of the input signal vary greatly.

The goal of the article is to synthesize algorithms for information processing in ring-shaped DPAA based on the use of orthogonalization and biorthogonalization procedures for random processes.

An algorithm for processing information in a ring-shaped DPAA under conditions of parametric a priori uncertainty of the statistical characteristics of signals and interference has been presented. In this algorithm, information processing in relation to annular DPAA is implemented based on the use of a correspondence between a non-equidistant and an equivalent equidistant antenna array. An algorithm for processing information in a ring-shaped DPAA based on the use of a Nollen preprocessor circuit implementing the principal component method has been shown. Using the Nollen preprocessor circuit makes it possible to generate estimates of the power of spatially correlated interference in order to resolve them without using additional equipment. Synthesis of an information processing algorithm in a ring-shaped DPAA based on the use of a multidimensional biorthogonalizer filter has been carried out. The multidimensional biorthogonalizer filter is based on two sequentially connected multidimensional orthogonalizer filters, the first of which performs spatiotemporal orthogonalization of spatial channel voltages, and the second converts the signals at the outputs of the first filter into white noise.

A variant of the implementation of an information processing algorithm in a ring-shaped DPAA based on the use of a Nollen preprocessor circuit in the form of a U-matrix converter circuit has been presented. A variant of constructing an information processing algorithm in a ring-shaped DPAA based on the use of a multidimensional biorthogonalizer filter in the form of a set of sequentially connected multidimensional orthogonalizer filters with infinite and finite impulse response has been shown. The features of information processing in the developed algorithms have been considered using the example of an equidistant ring DPAA with the number of emitters equal to 12.

1. Indenbom M.V. Antennye reshetki podvizhnykh obzornykh RLS: teoriya, raschet, konstruktsii. M.: Radiotekhnika. 2015. (in Russian)
2. Indenbom M.V., Kurochkin N.Yu. Kol'tsevye antennye reshetki s maksimal'nym koeffitsientom usileniya i mnogolepestkovoj diagrammoj napravlennosti. Antenny. 2018. № 8. S. 31–37. (in Russian)
3. Makarenkov V.V., Shatalov A.A., Shatalova V.A., Yastrebkov A.B. Adaptivnyj algoritm raspoznavaniya signalov, prinimaemykh ot medlenno i bystro fluktuiruyushchikh tselej na fone pomekh v mnogodiapazonnykh mnogopozitsionnykh RLS s FAR. Vestnik vozdushno-kosmicheskoj oborony. 2021. № 4 (32). S. 56–65. (in Russian)
4. Grigor'ev L.N. Tsifrovoe formirovanie diagrammy napravlennosti v fazirovannykh antennykh reshetkakh. M.: Radiotekhnika. 2010. (in Russian)
5. Bachevskij A.S., Konovalov D.Yu., Labets V.V., Shatalov A.A., Shatalova V.A. Adaptivnyj algoritm raspoznavaniya signalov, prinimaemykh ot bystro fluktuiruyushchikh tselej i tselej s doplerovskim rasseyaniem pri nalichii pomekh. Trudy Voenno-kosmicheskoj akademii imeni A.F. Mozhajskogo. 2017. № 656. S. 25–34. (in Russian)
6. Vinokurov A.D., Kupriyanov N.A., Makarenkov V.V., Ul'yanov G.N., Shatalov A.A., Shatalova V.A. Osobennosti sozdaniya i primeneniya algoritmov mnogomernoj adaptivnoj fil'tratsii vo vremennoj i chastotnoj oblastyakh. Chast' 1. Fil'tratsiya. Naukoemkie tekhnologii. 2024. T. 25. № 3. S. 5–19. (in Russian)
7. Vinokurov A.D., Kupriyanov N.A., Makarenkov V.V., Ul'yanov G.N., Shatalov A.A., Shatalova V.A., Yastrebkov A.B. Osobennosti sozdaniya i primeneniya algoritmov mnogomernoj adaptivnoj fil'tratsii vo vremennoj i chastotnoj oblastyakh. Chast' 3. Ekstrapolyatsiya. Naukoemkie tekhnologii. 2024. T. 25. № 4. S. 12–27.
8. Kruglov V.M. Sluchajnye protsessy. V 2-kh chastyakh. Chast' 2. Osnovy stokhasticheskogo analiza. M.: Izdatel'stvo Yurajt. 2024. (in Russian)
9. Makarenkov V.V., Kupriyanov N.A., Liferenko V.D., Luts'ko I.S., Vasil'ev S.V. Adaptivnyj algoritm formirovaniya diagrammy napravlennosti fazirovannoj antennoj reshetki s ispol'zovaniem diskretnogo razlozheniya Karunena-Loeva. Elektromagnitnye volny i elektronnye sistemy. 2023. T. 28. № 4. S. 48–56. (in Russian)
10. Haykin S. Adaptive filter theory. 5th Ed. Ontario: Communications Research Laboratory. 2014.
11. Bishop M.C. Pattern recognition and machine learning. New York: Springer. 2006.
12. Butorin E.L., Vinokurov A.D., Kupriyanov N.A., Ul'yanov G.N., Shatalov A.A., Shatalova V.A., Chebotar' K.I. Osobennosti sozdaniya i primeneniya algoritmov mnogomernoj adaptivnoj fil'tratsii vo vremennoj i chastotnoj oblastyakh. Chast' 2. Interpolyatsiya. Naukoemkie tekhnologii. 2024. T. 25. № 3. S. 20–33. (in Russian)
13. Shatalova V.A., Labets V.V. Adaptivnyj algoritm otsenivaniya ranga sluchajnykh protsessov i ego primenenie k resheniyu zadachi razresheniya-obnaruzheniya mnogikh tselej. Trudy RTI im. akademika A.L. Mintsa. 2010. Vyp. 2 (46). S. 85–96. (in Russian)
14. Kivalov A.N., Shatalova V.A. Sravnitel'nyj analiz rezul'tatov vychislenij v pozitsionnoj sisteme schisleniya i sisteme ostatochnykh klassov. Izvestiya Tul'skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. 2022. Vyp. 12. S. 235–244. (in Russian)
15. Makarenkov V.V., Stepenko A.S., Kakaev I.V., Kupriyanov N.A. Adaptivnyj algoritm podstrojki vesovykh koeffitsientov fazirovannoj antennoj reshetki s ispol'zovaniem induktivnogo metoda konformnogo prognozirovaniya. Sb. trudov nauchno-tekhnich. konf. Sankt-Peterburgskogo NTO RES im. A.S. Popova, posvyashchennoj Dnyu radio. 2025. № 1 (80). S. 29–31. (in Russian)