O.D. Kuprikov1, V.V. Sokolov2, R.G. Teplukhin3, S.V. Vaskovskii4, S.S. Kerimov5

1–5 V.A. Trapeznikov Institute of Control Sciences of the RAS (Moscow, Russia)
1 kuprikovod@ipu.ru, 2 sok@ipu.ru, 3 tepluhin@ipu.ru, 4 vask@ipu.ru, 5 serverdevel@ipu.ru

Exploring the seas and oceans of our planet is still an important task. Modern underwater monitoring and exploration tools such as ROV and AUV can be equipped with advanced technologies in the field of machine vision, autonomous navigation, and group work, but to implement these functions, it is necessary to use wireless underwater communication systems between underwater devices. The most promising and researched is hydroacoustic communication, based on the principle of transmitting information through an acoustic carrier wave.

The main problem of the hydroacoustic communication channel lies in its special characteristics and their non-stationarity, which leads to the need to use special signal modulation methods in conjunction with adjusting the parameters of both information and carrier signals. Based on the investigated characteristics of the sonar signal, it is necessary to rationalize the choice of the type of modulation and investigate the most promising signal modulation methods that provide the best acoustic signal parameters.

In the article the characteristics of a hydroacoustic communication channel are investigated, followed by modeling the effect of the characteristics on the transmitted signal to determine acceptable conditions and boundaries of the stationary state of the information transmission medium. Based on the data obtained, the most suitable method of multi-position frequency modulation is selected and rationalized within the framework of the tasks set. A functional diagram of prototypes implementing fourth-order multi-position frequency modulation for a modulator and demodulator in Simulink environment is presented.

An overview of this method is presented with a functional diagram of a prototype receiver and transmitter of a hydroacoustic signal based on 4-FSK modulation, implemented in a Simulink environment taking into account the parameters of the environment. The results of the study can be used in the further design of a high-speed sonar modem for communication with underwater objects.

Kuprikov O.D., Sokolov V.V., Teplukhin R.G., Vaskovskii S.V., Kerimov S.S. Research of prospective frequency modulation methods for transmitting through hydroacoustic channel under instability conditions // Dynamics of complex systems. 2026. V. 20. № 4.
P. 48−62. DOI: 10.18127/j19997493-202604-04

1. Farxadov M.P., Shavrin S.S., Kuprikov O.D., Zhidomirov I.F., Vas`kovskij S.V. Issledovanie osobennostej peredovy`x modemov gidroakusticheskoj svyazi i sravnitel`ny`j analiz ix xarakteristik. Datchiki i sistemy`. 2025. № 6(284). S. 38–48. (In Russian).
2. Farxadov M.P., Kuprikov O.D., Vas`kovskij S.V. Issledovanie i analiz sostoyaniya i tendencij razvitiya modemov gidroakusticheskoj svyazi mirovy`x proizvoditelej. Trudy` 20-j Vserossijskoj shkoly`-konferencii molody`x ucheny`x «Upravlenie bol`shimi sistemami» (UBS2024, Novocherkassk). Novocherkassk: YuRGPU (NPI). 2024. T. 2. S. 33–39. (In Russian).
3. Farxadov M.P., Kuprikov O.D., Komanich D.V. Hydroacoustic signal characteristics researching for an underwater communication channel development. Proceedings of 2022 International Conference on Information, Control, and Communication Technologies (ICCT). Astraxan`: IEEE. 2022. S. 1–7.
4. Krasil`nikov V.A., Kry`lov. V.V. Vvedenie v fizicheskuyu akustiku: Uchebnoe posobie. M.: Izd-vo MGU. 1984. 400 s. (In Russian).
5. Kudryavcev V.I. Gidroakustika ry`boxozyajstvennaya. M.: Izd-vo VNIRO. 2018. 460 s. (In Russian).
6. Francois R.E., Garrison G.R. Sound absorption based on ocean measurements: Part II: Boric acid contribution and equation for total absorption. J. Acoust. Soc. Am. 1982. № 72(6). P. 1879–1890.
7. Walree P., Othens R., Jenserud T. The Watermark manual and user’s guide version 1.0. Norwegian Defence Research Establishment (FFI). 2016. 40 p.
8. Walree P., Othens R., Jenserud T. The Watermark Benchmark for Underwater Acoustic Modulation Schemes. IEEE Journal of Oceanic Engineering. October 2017. V. 42. № 4. P. 1007–1018.
9. Dushin S.V., Aleshin V.S., Shavrin S.S., Farxadov M.P., Kurov I.Yu. Ispol`zovanie srednego chastotnogo diapazona akusticheskix voln dlya peredachi informacii v poverxnostny`x vodax. Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vy`chislitel`naya texnika i informatika. 2021. № 54. S. 38–47. (In Russian).
10. Lozhkin K.Yu., Mironov V.A., Prozhetorko S.S. Pomexoustojchivost` priema OFDM-signala s fazovoj manipulyaciej podnesushhix na fone impul`snoj poligarmonicheskoj pomexi. Radiotexnika. 2018. № 11. S. 58–63. DOI: 10.18127/j00338486-201811-09 (In Russian).
11. Kuprikov O.D., Shavrin S.S. Analiz osobennostej ispol`zovaniya razlichny`x vidov modulyacii v gidroakusticheskom kanale. Telekommunikacii i informacionny`e texnologii: nauchny`j zhurnal. 2021. T. 8. № 2. S. 63–68. (In Russian).
12. Gel`gor A.L., Puz`ko D.A., Skorodumov Yu.M., Lukoyanov E.V., Panarin A.E., Pashkevich I.V. Primenenie OFDM-signalov dlya gidroakusticheskoj podvodnoj svyazi v usloviyax priema signala nizhe urovnya shumov. Radiotexnika. 2024. T. 88. № 3. S. 48–62. DOI: https://doi.org/10.18127/j00338486-202403-06 (In Russian).
13. Lajons R. Cifrovaya obrabotka signalov: Vtoroe izdanie. Per. s angl. M.: OOO «Binom-Press». 2006. 656 s. (In Russian).
14. Zhang Z., Zhang L., You M., Lei M. Bit error rate approximation of MIMO-OFDM systems with carrier frequency offset and channel estimation errors. EURASIP Journal on Wireless Communications and Networking. 2010. V. 2010. № 1(176083). P. 1–14.
15. Indiarto M., Siswono H. Analysis of equalizer performance against bit error rate in filter bank multicarrier system with AWGN and multipath channel. International Journal of Computer Applications. 2021. V. 183. № 15. P. 21–25.
16. Vinck A.J.H., Häring J. Coding and modulation for power-line communications. Power Line Commun. and Its Applicat. (ISPLC). 2000. P. 265–271.
17. Xiang Y., Milstein L.B. Power-Bandwidth Tradeoff for Ultra-Low Power MFSK and G-MFSK Systems. IEEE Access. 2023. V. 11. P. 3942–3954.
18. Salah M., Omer O.A., Mohammed U.S. Enhanced MFSK spectral efficiency based on super-resolution spectral estimation. 2018 International Conference on Innovative Trends in Computer Engineering (ITCE). IEEE. 2018. P. 209–213.
19. Fan X., Tan Z., Song P. Bit Error Rate analysis for FH/MFSK system with Follower Jamming. Mathematical Problems in Engineering. 2020. V. 2020. № 1. P. 1–8.
20. Electromagnetic compatibility and Radio spectrum Matters (ERM); Digital Mobile Radio (DMR) Systems. Part 1: DMR Air Interface (AI) protocol // ETSI TS 102 361-1 V1.4.5 (2007-12) URL: https://www.etsi.org/deliver/etsi_ts/102300_102399/10236101/01.04.05_60/ts_10236101v010405p.pdf (data obrashheniya: 07.05.2026).
21. Druzhinin Yu.O., Sokolov V.V., Abdulov A.V., Abramenkov A.N., Rozhnov A.V. Organizaciya monitoringa baziruyushhimisya na sudne soprovozhdeniya tochechny`x ob``ektov avtonomny`mi neobitaemy`mi apparatami. Dinamika slozhny`x sistem – 21 vek. 2026. T. 20. № 4. S. 37–47. DOI: 10.18127/j19997493-202604-03 (In Russian).