{"id":12465,"date":"2022-05-13T12:03:48","date_gmt":"2022-05-13T09:03:48","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=12465"},"modified":"2022-06-07T02:14:43","modified_gmt":"2022-06-06T23:14:43","slug":"metodyka-obrobky-ta-synhronizacziyi-sygnaliv-u-programno-obumovlenyh-radiosystemah-z-ofdm","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=12465","title":{"rendered":"\u041c\u0435\u0442\u043e\u0434\u0438\u043a\u0430 \u043e\u0431\u0440\u043e\u0431\u043a\u0438 \u0442\u0430 \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u0457 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u0443 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u043e\u0431\u0443\u043c\u043e\u0432\u043b\u0435\u043d\u0438\u0445 \u0440\u0430\u0434\u0456\u043e\u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0445 \u0437 ofdm"},"content":{"rendered":"

<\/p>\n

\u041c\u0415\u0422\u041e\u0414\u0418\u041a\u0410 \u041e\u0411\u0420\u041e\u0411\u041a\u0418 \u0422\u0410 \u0421\u0418\u041d\u0425\u0420\u041e\u041d\u0406\u0417\u0410\u0426\u0406\u0407 \u0421\u0418\u0413\u041d\u0410\u041b\u0406\u0412 \u0423 \u041f\u0420\u041e\u0413\u0420\u0410\u041c\u041d\u041e-\u041e\u0411\u0423\u041c\u041e\u0412\u041b\u0415\u041d\u0418\u0425 \u0420\u0410\u0414\u0406\u041e\u0421\u0418\u0421\u0422\u0415\u041c\u0410\u0425 \u0417 OFDM<\/p>\n

SIGNAL PROCESSING AND SYNCHRONIZATION TECHNIQUE IN SOFTWARE-DEFINED RADIO SYSTEMS WITH OFDM<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438:\u00a012<\/strong>3<\/strong>-13<\/strong>2<\/strong>. \u041d\u043e\u043c\u0435\u0440: \u21162, 2022 (307)\u00a0\u00a0 \"\"<\/a> <\/strong>
\n\u00a0\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0411\u041e\u0419\u041a\u041e \u042e. \u041c.
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0003-0603-7827<\/a>
\ne-mail: boiko_julius@ukr.net<\/a>
\n\u041f\u042f\u0422\u0406\u041d \u0406. \u0421.
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0444\u0430\u0445\u043e\u0432\u0438\u0439 \u043a\u043e\u043b\u0435\u0434\u0436 \u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443 “\u041b\u044c\u0432\u0456\u0432\u0441\u044c\u043a\u0430 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u043a\u0430”
\nhttps:\/\/orcid.org\/0000-0003-1898-6755<\/a>
\ne-mail: ilkhmel@ukr.net<\/a>
\n\u041f\u0410\u0420\u0425\u041e\u041c\u0415\u0419 I. \u0420.
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0430\u0432\u0456\u0430\u0446\u0456\u0439\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0002-9510-7657<\/a>
\ne-mail: i_parhomey@ukr.net<\/a>
\nBOIKO JULIY M.
\nKhmelnytskyi National University
\nPYATIN ILYA S.
\nKhmelnytskyi Polytechnic, Professional College by Lviv Polytechnic National University
\nPARKHOMEY IGOR R.
\nNational Aviation University
\n\u00a0DOI:<\/strong>\u00a0https:\/\/www.doi.org\/10.31891\/2307-5732-2022-307-2-123-132<\/a><\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0412 \u0441\u0442\u0430\u0442\u0442\u0456 \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u0441\u0443\u0447\u0430\u0441\u043d\u0456 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0456\u0457 \u0440\u043e\u0437\u0432\u0438\u0442\u043a\u0443 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0457 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u043e\u0431\u0443\u043c\u043e\u0432\u043b\u0435\u043d\u043e\u0433\u043e \u0440\u0430\u0434\u0456\u043e (\u041f\u041e\u0420). \u0417\u0430\u043f\u0440\u043e\u043f\u043e\u043d\u043e\u0432\u0430\u043d\u043e \u0444\u0443\u043d\u043a\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0443 \u0441\u0445\u0435\u043c\u0443 \u0440\u0430\u0434\u0456\u043e\u0441\u0442\u0430\u043d\u0446\u0456\u0457 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e-\u043e\u0431\u0443\u043c\u043e\u0432\u043b\u0435\u043d\u043e\u0433\u043e \u0440\u0430\u0434\u0456\u043e \u0437 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f\u043c \u043c\u0435\u0442\u043e\u0434\u0443 \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0456 \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0457 \u0437 \u043c\u043e\u0434\u0443\u043b\u044f\u0446\u0456\u0454\u044e \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0456 \u043c\u0443\u043b\u044c\u0442\u0438\u043f\u043b\u0435\u043a\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u0437 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u043c \u0447\u0430\u0441\u0442\u043e\u0442\u043d\u0438\u043c \u0440\u043e\u0437\u0434\u0456\u043b\u0435\u043d\u043d\u044f\u043c \u043a\u0430\u043d\u0430\u043b\u0456\u0432 (OFDM). \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u0443\u043c\u043e\u0432\u0438 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0435\u043d\u043d\u044f \u0441\u0438\u043c\u0432\u043e\u043b\u044c\u043d\u043e\u0457 \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u0457 OFDM-\u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432. \u0412\u0438\u0437\u043d\u0430\u0447\u0435\u043d\u043e, \u0449\u043e \u0437\u0440\u0438\u0432 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u0456 OFDM-\u0441\u0438\u043c\u0432\u043e\u043b\u0456\u0432 \u0441\u0443\u043f\u0440\u043e\u0432\u043e\u0434\u0436\u0443\u044e\u0442\u044c \u0442\u0430\u043a\u0456 \u044f\u0432\u0438\u0449\u0430 \u044f\u043a \u0432\u0438\u043d\u0438\u043a\u043d\u0435\u043d\u043d\u044f \u043c\u0456\u0436\u0441\u0438\u043c\u0432\u043e\u043b\u044c\u043d\u0438\u0445 \u0437\u0430\u0432\u0430\u0434 \u0442\u0430 \u044f\u0432\u0438\u0449\u0435 \u043c\u0456\u0436\u043a\u0430\u043d\u0430\u043b\u044c\u043d\u0438\u0445 \u0437\u0430\u0432\u0430\u0434. \u041c\u0435\u0442\u043e\u0434\u043e\u043c \u043a\u043e\u043d\u0441\u0442\u0435\u043b\u044f\u0446\u0456\u0439\u043d\u0438\u0445 \u0434\u0456\u0430\u0433\u0440\u0430\u043c \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043e \u0432\u043f\u043b\u0438\u0432 \u043f\u043e\u043c\u0438\u043b\u043e\u043a \u0432\u0438\u043a\u043b\u0438\u043a\u0430\u043d\u0438\u0445 \u0437\u0430\u0432\u0430\u0434\u0430\u043c\u0438 \u043d\u0430 \u044f\u043a\u0456\u0441\u0442\u044c \u043e\u0431\u0440\u043e\u0431\u043a\u0438 \u0431\u0430\u0433\u0430\u0442\u043e\u043f\u043e\u0437\u0438\u0446\u0456\u0439\u043d\u0438\u0445 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432. \u041e\u0446\u0456\u043d\u0435\u043d\u043e \u0432\u043f\u043b\u0438\u0432 \u0437\u0430\u0432\u0430\u0434 \u0432 \u043a\u0430\u043d\u0430\u043b\u0456 \u0437 OFDM \u043d\u0430 \u0444\u0430\u0437\u0443 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u043f\u0440\u0438 \u0457\u0445 \u043e\u0431\u0440\u043e\u0431\u0446\u0456. \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0456 \u043c\u043e\u0434\u0435\u043b\u0456 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u0437 OFDM \u0437\u0430 \u043d\u0430\u044f\u0432\u043d\u043e\u0441\u0442\u0456 \u0437\u0430\u0432\u0430\u0434\u043e\u0432\u0438\u0445 \u0432\u043f\u043b\u0438\u0432\u0456\u0432.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> OFDM, \u0437\u0430\u0432\u0430\u0434\u043e\u0441\u0442\u0456\u0439\u043a\u0456\u0441\u0442\u044c, \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u044f, \u043c\u043e\u0434\u0443\u043b\u044f\u0446\u0456\u044f, SDR.<\/p>\n

\u00a0<\/strong> \u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The article describes modern concepts for the development of Software-defined Radio (SDR) technology. A functional diagram of a software-defined radio station using the method of transmitting information with modulation based on Orthogonal Frequency Division Multiplexing (OFDM) is proposed. The conditions for ensuring symbol synchronization of OFDM signals are investigated. It is determined that the disruption of the orthogonality of OFDM symbols is accompanied by such phenomena as the occurrence of inter-symbol interference and inter-channel interference. The method of constellation diagrams was used to study the effect of errors caused by interference on the quality of processing of multiposition signals. The effect of interference in a channel from OFDM on the phase of signals during their processing is estimated. Mathematical models of signals with OFDM in the presence of interference effects are obtained. Two types of errors are considered, which are caused by carrier distortion. In particular, the occurrence of phase noise is possible, the cause of which is associated with the instability of the generating equipment of the carrier signals both on the transmitting and on the receiving side. Another factor is carrier offset due to Doppler frequency. The proposed SDR receiver structure is based on the digital IF architecture. This architecture has more flexibility than traditional RF architectures and is not sensitive to DC offset, LO leakage, etc. Moreover, since the I\/Q up\/down conversion is done digitally in the IF stage, the negative effects caused by I\/Q imbalance will be minimized. The SDR consists of a small piece of hardware at the RF input, i.e., an antenna and a high-rate ADC capable of capturing and digitizing broadband radio signals. To increase the communication range in SDR, we use amplifiers in front of two DAC\/ADC stages. The receiver has a low-noise amplifier to reduce the quantization noise of the transducer and increase the Signal-to-noise Ratio (SNR). The data is then processed on specialized computational units within the embedded system, enabling important demodulation, synchronization, and decoding techniques to be implemented.
\nKeywords:<\/strong> OFDM, noise immunity, synchronization, modulation, SDR.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
  1. \u0411\u043e\u0439\u043a\u043e \u042e. \u041c. \u041e\u0446\u0456\u043d\u043a\u0430 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0456 \u043a\u0430\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043a\u043e\u0434\u0443\u0432\u0430\u043d\u043d\u044f \u0443 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u044f\u0445 \u0437 OFDM [\u0422\u0435\u043a\u0441\u0442] \/ \u042e. \u041c. \u0411\u043e\u0439\u043a\u043e, \u0414. \u0412. \u041d\u043e\u0432\u0456\u043a\u043e\u0432 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 2021. \u2013 \u2116 5. \u2013 \u0421. 150-159.<\/li>\n
  2. \u0411\u043e\u0439\u043a\u043e \u042e. \u041c. \u0422\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u043d\u0456 \u0430\u0441\u043f\u0435\u043a\u0442\u0438 \u043f\u0456\u0434\u0432\u0438\u0449\u0435\u043d\u043d\u044f \u0437\u0430\u0432\u0430\u0434\u043e\u0441\u0442\u0456\u0439\u043a\u043e\u0441\u0442\u0456 \u0439 \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0456 \u043e\u0431\u0440\u043e\u0431\u043a\u0438 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u0432 \u0440\u0430\u0434\u0456\u043e\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0445 \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u044f\u0445 \u0442\u0430 \u0437\u0430\u0441\u043e\u0431\u0430\u0445 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0437\u0430 \u043d\u0430\u044f\u0432\u043d\u043e\u0441\u0442\u0456 \u0437\u0430\u0432\u0430\u0434: \u043c\u043e\u043d\u043e\u0433\u0440\u0430\u0444\u0456\u044f \/ \u042e. \u041c. \u0411\u043e\u0439\u043a\u043e, \u0412. \u0410. \u0414\u0440\u0443\u0436\u0438\u043d\u0456\u043d, \u0421. \u0412. \u0422\u043e\u043b\u044e\u043f\u0430. – \u041a\u0438\u0457\u0432: \u041b\u043e\u0433\u043e\u0441, 2018. – 227 \u0441.<\/li>\n
  3. Shengli Z. OFDM Basics. OFDM for Underwater Acoustic Communications \/ Z. Shengli, W. Zhaohui. \u2013 USA: Wiley Telecom, 2014. – P.23-38.<\/li>\n
  4. Prasad R. OFDM for Wireless Communications Systems \/ R. Prasad. \u2013 London: Artech House, Inc., 2004, P. 292.<\/li>\n
  5. \u041a\u043e\u0437\u043b\u043e\u0432\u0441\u044c\u043a\u0438\u0439 \u0412. \u0412. \u0421\u0438\u043d\u0442\u0435\u0437 \u0441\u043a\u043b\u0430\u0434\u043d\u043e\u0433\u043e \u0440\u043e\u0437\u0456\u043c\u043a\u043d\u0443\u0442\u043e\u0433\u043e \u0437\u0432\u2019\u044f\u0437\u043a\u0443 \u0432 \u0441\u0438\u0441\u0442\u0435\u043c\u0456 \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u0457 \u043f\u0440\u0438 \u0443\u043c\u043e\u0432\u0456 \u043c\u0456\u043d\u0456\u043c\u0456\u0437\u0430\u0446\u0456\u0457 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0457 \u0444\u0430\u0437\u043e\u0432\u043e\u0457 \u043f\u043e\u043c\u0438\u043b\u043a\u0438 \u0432 \u0445\u043e\u0434\u0456 \u0441\u0442\u0435\u0436\u0435\u043d\u043d\u044f \u0437\u0430 \u043d\u0435\u0441\u0443\u0447\u043e\u044e \u0447\u0430\u0441\u0442\u043e\u0442\u043e\u044e \/ \u0412. \u0412. \u041a\u043e\u0437\u043b\u043e\u0432\u0441\u044c\u043a\u0438\u0439, \u041e. \u041b. \u0422\u0443\u0440\u043e\u0432\u0441\u044c\u043a\u0438\u0439 \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u2013 2020. \u2013 \u0421. 162 -168.<\/li>\n
  6. Berkman L. Designing a system to synchronize the input signal in a telecommunication network under the condition for reducing a transitional component of the phase error \/ L. Berkman, O. Tkachenko, O. Turovsky, V. Fokin, V. Strelnikov \/\/\u0412\u043e\u0441\u0442\u043e\u0447\u043d\u043e-\u0415\u0432\u0440\u043e\u043f\u0435\u0439\u0441\u043a\u0438\u0439 \u0436\u0443\u0440\u043d\u0430\u043b \u043f\u0435\u0440\u0435\u0434\u043e\u0432\u044b\u0445 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0438\u0439. \u2013 2021. \u2013 \u0422. 1. \u2013 \u2116. 9-109. \u2013 \u0421. 66-76.<\/li>\n
  7. Boiko J. M. Investigation of signals distortion during interpolation in SDR transmitters with QPSK modulation \/ J. M. Boiko, I. S. Pyatin, O. I. \u0415r\u043emenko, I. R. Parkhomey \/\/ \u0410\u0434\u0430\u043f\u0442\u0438\u0432\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f. \u2013 2019. \u2013 \u2116 1\u2019 (34). \u2013 \u0421. 5-15.<\/li>\n
  8. \u0428\u043a\u0443\u0440\u0443\u043f\u0456\u0439 C. C. \u0410\u043d\u0430\u043b\u0456\u0437 \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u0457 \u0435\u0442\u0430\u043b\u043e\u043d\u043d\u0438\u0445 \u0447\u0430\u0441\u0442\u043e\u0442\u043d\u043e-\u0447\u0430\u0441\u043e\u0432\u0438\u0445 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u0432\u0456\u0439\u0441\u044c\u043a\u043e\u0432\u0438\u043c \u043a\u043e\u0440\u0438\u0441\u0442\u0443\u0432\u0430\u0447\u0430\u043c \/ C.C. \u0428\u043a\u0443\u0440\u0443\u043f\u0456\u0439, \u0412.\u041c. \u041f\u0438\u043b\u0438\u043f\u0435\u043d\u043a, \u041e.\u041e. \u041a\u043b\u0456\u043c\u0456\u0448\u0435\u043d, \u041c.\u0406. \u041a\u043e\u0436\u0443\u0448\u043a\u043e, \u0406.\u041e. \u0410\u0442\u0430\u043c\u0430\u043d\u0435\u043d\u043a\u043e \/\/\u041d\u0430\u0443\u043a\u0430 \u0456 \u0442\u0435\u0445\u043d\u0456\u043a\u0430 \u041f\u043e\u0432\u0456\u0442\u0440\u044f\u043d\u0438\u0445 \u0421\u0438\u043b \u0417\u0431\u0440\u043e\u0439\u043d\u0438\u0445 \u0421\u0438\u043b \u0423\u043a\u0440\u0430\u0457\u043d\u0438. \u2013 2021. \u2013 \u2116. 4 (45). \u2013 \u0421. 116-123.<\/li>\n
  9. \u041f\u044f\u0442\u0456\u043d \u0406. \u0421. \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u044f \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0438 \u043f\u043e\u0447\u0430\u0442\u043a\u043e\u0432\u043e\u0433\u043e \u0434\u043e\u0441\u0442\u0443\u043f\u0443 \u0434\u043e \u043c\u0435\u0440\u0435\u0436\u0456 \u0437\u0432\u2019\u044f\u0437\u043a\u0443 \u043f\u2019\u044f\u0442\u043e\u0433\u043e \u043f\u043e\u043a\u043e\u043b\u0456\u043d\u043d\u044f \/ \u0406. \u0421. \u041f\u044f\u0442\u0456\u043d, \u0414. \u0410. \u041c\u0430\u043a\u0430\u0440\u0438\u0448\u043a\u0456\u043d, \u0412. \u0412. \u041c\u0456\u0448\u0430\u043d, \u041c. \u0421. \u0428\u043f\u0456\u0440\u0443\u043a \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 2021. \u2013 \u2116 5. \u2013 \u0421. 141-149.<\/li>\n
  10. \u0411\u043e\u0439\u043a\u043e \u042e. Transmission of control information in 5G broadband telecommunication systems \/ \u042e. \u0411\u043e\u0439\u043a\u043e, \u0406. \u041f\u2019\u044f\u0442\u0456\u043d, \u041b. \u041a\u0430\u0440\u043f\u043e\u0432\u0430, I. \u041f\u0430\u0440\u0445\u043e\u043c\u0435\u0439 \/\/ \u0410\u0434\u0430\u043f\u0442\u0438\u0432\u043d\u0456 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0447\u043d\u043e\u0433\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u0456\u043d\u043d\u044f. \u2013 2021. \u2013 \u0422. 1. \u2013 \u2116. 38. \u2013 \u0421. 82-95.<\/li>\n
  11. Korde M. Synchronization Aspects in 5G \/ M. Korde \/\/ 2020 International Conference on Communication and Signal Processing (ICCSP), 2020, pp. 0474-0478.<\/li>\n
  12. Zhurakovskyi B. Coding for information systems security and viability \/ B. Zhurakovskyi, S. Toliupa, S. Otrokh, V. Kuzminykh, H. Dudarieva, V. Zhurakovskyi, \/\/I\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0439\u043d\u0456 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0457 \u0456 \u0431\u0435\u0437\u043f\u0435\u043a\u0430. \u2013 2020. \u2013 P. 71-84.<\/li>\n
  13. Zhurakovskyi B. Increasing the efficiency of information transmission in communication channels \/ B. Zhurakovskyi, J. Boiko, V. Druzhynin, I. Zeniv, \u041e. Eromenko \/\/Indonesian Journal of Electrical Engineering and Computer Science. \u2013 2020. \u2013 \u0422. 19. \u2013 \u2116. 3. \u2013 \u0421. 1306-1315.<\/li>\n
  14. \u0422\u0443\u0440\u043e\u0432\u0441\u044c\u043a\u0438\u0439 \u041e. \u041b. \u041e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u043e\u0446\u0435\u043d\u043a\u0435 \u043d\u0435\u0441\u0443\u0449\u0435\u0439 \u0447\u0430\u0441\u0442\u043e\u0442\u044b \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0441\u043f\u0443\u0442\u043d\u0438\u043a\u043e\u0432\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u043f\u0435\u0440\u0435\u0434\u0430\u0447\u0438 \u0434\u0430\u043d\u043d\u044b\u0445 \/ \u041e. \u041b. \u0422\u0443\u0440\u043e\u0432\u0441\u044c\u043a\u0438\u0439, \u0421. \u0412. \u041f\u0430\u043d\u0430\u0434\u0456\u0439, \u041d. \u041e. \u041b\u0456\u0449\u0438\u043d\u043e\u0432\u0441\u044c\u043a\u0430 \/\/\u0422\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439\u043d\u0456 \u0442\u0430 \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u0439\u043d\u0456 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0457. \u2013 2020. \u2013 \u2116. 1. \u2013 \u0421. 174-187.<\/li>\n
  15. Berkman Analyzing the code structures of multidimensional signals for a continuous information transmission channel \/ L. Berkman, O. Turovsky, L .Kyrpach, O. Varfolomeeva, V. Dmytrenko, O. Pokotylo \/\/ Eastern-European Journal of Enterprise Technologies. \u2013 2021 \u2013 \u0422. 5. \u2013 \u2116. 9. \u2013 \u0421. 70-81.<\/li>\n
  16. Narasimhamurthy A. OFDM Systems for Wireless Communications \/ <\/em> Narasimhamurthy, M. Banavar, C. Tepedelenliouglu. – USA: Morgan & Claypool, 2010. \u2013 P. 78.<\/li>\n
  17. \u041f\u044f\u0442\u0456\u043d \u0406. \u0421. \u0414\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u044f \u0441\u0438\u0441\u0442\u0435\u043c \u0437\u0432\u2019\u044f\u0437\u043a\u0443 \u0437 \u0441\u0438\u0433\u043d\u0430\u043b\u0430\u043c\u0438 F-OFDM \/ \u0406. \u0421. \u041f\u044f\u0442\u0456\u043d, \u0412. \u0404. \u0413\u0430\u0432\u0440\u043e\u043d\u0441\u044c\u043a\u0438\u0439, \u0412. \u0406. \u041b\u0443\u0436\u0430\u043d\u0441\u044c\u043a\u0438\u0439, \u0412. \u041e. \u041c\u0438\u0445\u0430\u043b\u044c\u0447\u0443\u043a \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 2021. \u2013 \u2116 5. \u2013 \u0421. 170-176.<\/li>\n
  18. \u0422\u0443\u0440\u043e\u0432\u0441\u044c\u043a\u0438\u0439 \u041e. \u041b. \u041e\u0446\u0456\u043d\u043a\u0430 \u043c\u043e\u0436\u043b\u0438\u0432\u043e\u0441\u0442\u0435\u0439 \u043f\u0456\u0434\u0432\u0438\u0449\u0435\u043d\u043d\u044f \u0435\u0444\u0435\u043a\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u0456 \u0440\u043e\u0431\u043e\u0442\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u0456\u0437\u0430\u0446\u0456\u0457 \u0440\u0430\u0434\u0456\u043e\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0441\u0442\u0440\u043e\u044e \u0432 \u0445\u043e\u0434\u0456 \u0441\u0442\u0435\u0436\u0435\u043d\u043d\u0456 \u0437\u0430 \u043d\u0435\u0441\u0443\u0447\u043e\u044e \u0447\u0430\u0441\u0442\u043e\u0442\u043e\u044e \/ \u041e. \u041b. \u0422\u0443\u0440\u043e\u0432\u0441\u044c\u043a\u0438\u0439 \/\/ \u0412\u0438\u043c\u0456\u0440\u044e\u0432\u0430\u043b\u044c\u043d\u0430 \u0442\u0430 \u043e\u0431\u0447\u0438\u0441\u043b\u044e\u0432\u0430\u043b\u044c\u043d\u0430 \u0442\u0435\u0445\u043d\u0456\u043a\u0430 \u0432 \u0442\u0435\u0445\u043d\u043e\u043b\u043e\u0433\u0456\u0447\u043d\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0430\u0445. \u2013 2020. – \u21161. \u2013 \u0421. 116 \u2013 122.<\/li>\n
  19. \u0411\u043e\u0439\u043a\u043e \u042e. \u041c. \u041e\u0446\u0456\u043d\u044e\u0432\u0430\u043d\u043d\u044f \u0432\u043f\u043b\u0438\u0432\u0443 \u0443\u043c\u043e\u0432 \u0456\u043d\u0442\u0435\u0440\u043f\u043e\u043b\u044f\u0446\u0456\u0457 \u0456 \u0434\u0435\u0446\u0438\u043c\u0430\u0446\u0456\u0457 \u0441\u0438\u0433\u043d\u0430\u043b\u0456\u0432 \u043d\u0430 \u0435\u043d\u0435\u0440\u0433\u0435\u0442\u0438\u043a\u0443 \u0437\u0430\u0441\u043e\u0431\u0456\u0432 \u0442\u0435\u043b\u0435\u043a\u043e\u043c\u0443\u043d\u0456\u043a\u0430\u0446\u0456\u0439 \u0437 \u0444\u0430\u0437\u043e\u0432\u043e\u044e \u043c\u0430\u043d\u0456\u043f\u0443\u043b\u044f\u0446\u0456\u0454\u044e \/ \u042e. \u041c. \u0411\u043e\u0439\u043a\u043e, \u0406. \u0421. \u041f\u044f\u0442\u0456\u043d \/\/ \u0412\u0447\u0435\u043d\u0456 \u0437\u0430\u043f\u0438\u0441\u043a\u0438 \u0422\u041d\u0423 \u0456\u043c\u0435\u043d\u0456 \u0412.\u0406. \u0412\u0435\u0440\u043d\u0430\u0434\u0441\u044c\u043a\u043e\u0433\u043e. \u0421\u0435\u0440\u0456\u044f: \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u2013 2019. \u2013 \u0422. 30 (69), \u0427. 1, \u2116 5. – C. 29-37.<\/li>\n
  20. \u041a\u0430\u0440\u043f\u043e\u0432\u0430 \u041b. \u0412. \u0412\u043f\u043b\u0438\u0432 \u0440\u043e\u0437\u043c\u0456\u0449\u0435\u043d\u043d\u044f \u043e\u0434\u043d\u0456\u0454\u0457 \u0442\u0430 \u043a\u0456\u043b\u044c\u043a\u043e\u0445 \u0430\u043d\u0442\u0435\u043d \u043d\u0430 \u043f\u0440\u043e\u043f\u0443\u0441\u043a\u043d\u0443 \u0437\u0434\u0430\u0442\u043d\u0456\u0441\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c \u0437\u0432’\u044f\u0437\u043a\u0443 C2C \/ \u041b. \u0412. \u041a\u0430\u0440\u043f\u043e\u0432\u0430, \u0410. \u041e. \u0411\u043e\u0439\u043a\u043e \/\/ \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443. \u2013 2021. – \u2116 6. \u2013 \u0421. 181 \u2013 185.<\/li>\n<\/ol>\n

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