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2. Ponomarev A. V. [Two-dimensional signal processing in discrete Fourier bases]. Intelligent systems in production. 2019, vol. 17, no.1, pp.71-77 (in Russ.). 3. Dudgeon D.E. Multidimensional Digital Signal Processing Prentice Hall, 1995. — 406 p. 4. Prehtt U. Cifrovaya obrabotka izobrazhenij. V 2-h knigah. Perevod s angl. [Digital image processing]. Moscow, World., 1982, 790 p.(in Russ.) 5. Ponomarev V.A., Ponomareva O.V., Ponomarev A.V. [Measurement of time spectra of discrete signals at finite intervals]’ Vestnik IzhGTU imeni M.T.Kalashnikova, 2016, vol/19, nj 2, pp.80-83 (in Russ.). 6. Ponomareva O.V. Razvitie teorii i razrabotka metodov i algoritmov cifrovoj obrabotki informacionnyh signalov v parametricheskih bazisah Fur'e [Development of the theory and development of methods and algorithms for digital processing of information signals in parametric Fourier bases]: Dissertation of the doctor of technical sciences]: Izhevsk, 2016, 357 p. (in Russ.). 7. Ponomareva O.V., Ponomarev A.V. [Spatial interpolation of two-dimensional discrete signals using fast Fourier transforms]. Intelligent systems in production. 2019, vol. 17, no.1, pp.88-94 (in Russ.). 8. Ponomarev V.A., Ponomareva O.V. [Trends in the development of discrete indirect measurements of the parameters of electrical signals]. Metrology, 2017, no.1, pp.20-32 (in Russ.). 9. Ponomareva O.V., Ponomarev A.V. [Fast Horizontal Sliding Frequency Span Processing Method]. Intelligent systems in production. 2019, vol. 17, no.2, pp.81-87 (in Russ.). 10. Ponomareva O.V. [Measurement of the spectra of complex signals at finite intervals by the method of aperiodic discrete Fourier transform]. Intellectual systems in production, 2014, no. (23) pp..100-107.2014 (in Russ.). 11. Ponomarev V.A, Ponomareva O.V., Ponomareva N.V. [The method of fast calculation of the discrete Hilbert transform in the frequency domain]. Modern information and electronic technologies, 2014, no.15, pp. 183-184 (in Russ.). 12. Ponomareva O.V., Ponomarev A.V., Ponomareva N.V. [Hierarchical morphological and informational description of the systems of functional diagnostics of objects]. Modern information and electronic technologies, 2013, no.14, pp..121-124 (in Russ.). 13. Ponomareva O.V. [Probability Theoretical Characteristics of Random Discrete Mformation Signals and the Axioms of Their Measurement]. Intelligent systems in production. 2019, vol. 17, no.2, pp.73-80 (in Russ.). 14. Ponomareva N.V. [Problems of computer spectral signal processing in musical acoustics] Intellectual systems in production, 2018, vol. 16, no.1, pp. 26-33 (in Russ.). 15. Ponomareva N.V., Ponomareva O.V., Hvorenkov V.V. [Determination of anharmonic discrete signal envelope based on the Hilbert transform in the frequency domain]. Intelligent systems in production, 2018, vol.16, no.1, pp.33-40 (in Russ.). 16. Ponomareva N.V, Ponomareva V.YU. [Localization of spectral peaks by the parametric discrete Fourier transform method]. Intellectual systems in production, 2016, no. 2 (29), pp.15-18 (in Russ.). 17. Ponomareva N.V. [Pre-processing of discrete signals in spectral analysis in the computer mathematics system MATLAB]. Intellectual systems in production, 2016, no. 4 (31). pp. 32-34 (in Russ.). 18. Ponomarev V.A., Ponomareva O.V. [Generalization of the discrete Fourier transform for interpolation in the time domain]. Izvestiya vuzov. Radioehlektronika, 1983, vol. XXVI, no. 9, pp. 67 - 68 (in Russ.). 19. Ponomareva O.V., Alekseev V.A., Ponomarev A.V. [Fast algorithm for measuring the spectrum of real signals by the aperiodic discrete Fourier transform method]. Vestnik IzhGTU imeni M.T.Kalashnikova, 2015, no. 2 (62), pp..106-109 (in Russ.). 20. Ponomareva O.V. [Invariance of the Fourier sliding energy spectrum of discrete signals in the basic system of parametric exponential functions]. Vestnik IzhGTU imeni M.T.Kalashnikova, 2015, no. 2 (62), pp.102-106 (in Russ.). 21. Gonzalez R.C., Woods R.E. Digital Image Processing, 4th Ed. Published by Pearson. 2018.–1168 pages.
-mail:grachev.m.v@rsreu.ruYu.N. Parshin e, -mail:parshin.y.n@rsreu.ru The Ryazan State Radio Engineering University named after V.F. Utkin (RSREU), Russia, Ryazan
A model of mutual influence between the receiving system's channels is based on changing the distance scale between the elements of a certain reference antenna system for which the matrix of mutual impedances can be calculated analytically is used in this paper. An antenna system in the form of thin vibrators is used as a reference antenna system. The multichannel receiving system considered in the work consists of an antenna system, a matching circuit, a unit of low-noise amplifiers, and a weight signal processing unit. The signal source is located in the far field. There are external antenna noise and amplifiers' inner noises in a multichannel receiving system. The matching circuit solves the problem of transmitting the maximum signal power from the antenna system to the low noise amplifier. The analysis of the mutual influence between the channels on signal-to-noise ratio in the multichannel receiving system is carried out. An increase in the number of channels at a fixed aperture value leads to an increase in the degree of mutual influence between the channels. The receiving system's channels mutual influence leads to correlation of antenna noise and a decrease in the efficiency of signal processing. With a strong degree of receiving systems channels mutual influence the output signal-to-noise ratio is practically independent of the number of channels and is equal to the signal-to-noise ratio at the output of a single-channel receiving system. It is also noted that the choice of the optimal weight vector allows increasing the stability of the multichannel receiving system to an increase in the degree of mutual influence of the channels. The influence of the antenna system size aperture on the output signal-to-noise ratio is considered. Increasing the size of the aperture leads to a decrease in the degree of mutual influence and to increase in the efficiency of signal receiving. However with a large number of receiving channels there is a mismatch between the elements of the antenna system and the low-noise-amplifiers. The analysis showed the need to take into account the mutual influence between the channels when choosing the processing weight vector and the spatial structure of the system. Increasing in the degree of receiving systems channels mutual influence leads to a decrease in the signal-to-noise ratio at the output of the multichannel receiving system. Taking into account signal distortions and noise correlation caused by mutual influence during signal weighting allows increasing the value of the output signal-to-noise ratio.
2. Hannula J., Lehtovuori A., Luomaniemi R., Saarinen T.O., and Viikari V. Beneficial interaction of coupling and mismatch in a two-antenna system // Proceedings of the 3th European Conference on Antennas and Propagation. - 2019. - Vol. EuCAP. - Pp. 1-4. 3. Korogodin I.V., Dneprov V.V. Impact of antenna mutual coupling on WiFi positioning and angle of arrival estimation // Proceedings of Moscow Workshop on Electronic and Networking Technologies (MWENT). - 2018. Pp. 1-6. 4. Parshin Yu.N., Grachev M.V. Efficiency of the angular coordinate estimation under the action of spatially correlated interferences and mutual influence of spatial channels // 2019 Radiation and Scattering of Electromagnetic Waves, RSEMW. - 2019. Pp. 1-4. 5. Parshin Yu.N., Grachev M.V. Target detection using optimal load matching and interference nulling // Proceedings of the 19th Inter-national Radar Symposium. - 2018. DGON. - Pp.1-7. 6. Efficiency analysis of signal spatial processing for nonlinear receiver path with different architecture by scaling method [Text] / Parshin Yu.N., Kolesnikov S.V., Grachev M.V. // 27th International Crimean Conference "Microwave engineering and telecommunication technologies" (CriMiCo'2017). Sevastopol, September 10-16, 2017: materials of the conf. in 8 volumes - Moscow; Minsk; Sevastopol, 2017. - Vol. 3. - Pp. 722-728. 7. Markov G.T., D.M. Sazonov. Antenny: uchebnik (Antennas: study book). M.: Jenergija, 1975. 528 p. 8. Warnick K.F., Jensen M.A., Optimal noise matching for mutually coupled arrays // IEEE Transactions on Antennas and Propagation. – 2007. – Vol. 55. – No 6. – Pp. 1726-1731. 9. Warnick K.F., Jeffs B.D. Gain and aperture efficiency for a reflector antenna with an array feed // IEEE Antennas and Wireless Propagation Letters. – 2006. – Vol. 5. – Pp. 499-502. 10. Warnick K.F., Belostotski L., Russer P. Minimizing the noise penalty due to mutual coupling for a receiving array // IEEE Transactions on Antennas and Propagation. – 2009. – Vol. 57. – No 6. – Pp. 1634-1644. 11. Monzingo R. A., Miller T. W. Introduction to adaptive array. John Wiley & Sons, New York, 2004. 543 p. 12. Parshin Yu.N., Grachev M.V. Comparative Analysis of Algorithms for Searching the Load Impedances Optimal Value of Multi-Channel Radio System with Mutual Influence // Vestnik Rjazanskogo gosudarstvennogo radiotehnicheskogo universiteta. – 2020. – No. 73. – Pp. 10-18.
The article proposes a new mathematical apparatus for modeling the processes of bringing discrete messages through communication channels with decisive feedback, based on the theory of generating probability functions of a random variable. The substantiation of the validity of the use of this device for modeling a wide range of processes of information exchange of discrete messages and confirmation of the reliability of mathematical models obtained with its help is given. At the same time, it is shown that the developed method of studying the probabilistic-temporal characteristics of delivering multi-packet messages using generating probability functions does not contradict the results obtained in the traditional way, however, it can significantly reduce computational costs and automate the process of obtaining the result. 2. Tikhonov, V.I. Markov processes / V.I. Tikhonov, M. A. Mironov. - M.: "Soviet radio", 1977. - 488 p. with il. 3. Potapov, S. E. Automated synthesis of finite absorbing Markov chain that describes the bringing of multi-packet messages in connection "point to point" transmission systems and the study of its efficiency [Text] / S. E. Potapov, V. A. Tsymbal, V. E. Toskin, V. V. Chapter, O. I. Sorokin, M. A. Lygin, A. A. Berezhnoy, N. In. Hooks // Radio engineering and telecommunication systems : nauch.–tekhn. jour. – Murom, 2016. – Vol. 4. (24). – P. 59-65. – ISSN 2221-2574. 4. Sklar, B. Digital communications. Theoretical foundations and practical application. Ed. 2-E. : Trans. from English - M.: Publishing House "Williams", 2003. - 1104 p. : ill. - Par. tit. ISBN 5-8459-0497-8 (rus.). 5. Bostandzhiyan V.A. Manual on statistical distributions. - Chernogolovka. Editorial and Publishing Department of IPHV RAS, 2013. 1060 p. 6. Wentzel E.S. Probability theory / E.S. Wentzel. - M.: Nauka, 2003– - 564 p. 7. Potapov, S. E. Mathematical model of message delivery over a radio channel with a high probability of bit errors [Text] / S.E. Potapov, A.A. Potapova, V.E. Toiskin // International Conference "Digital Signal Processing and its application" (DSPA-2019); Reports ; / Russian Scientific and Technical Society. radio engineering, electron. and communications named after A.S. Popov. - M. : LLC "BRIS-M" - Issue XXI-1, Vol. 1. - pp. 237-240. 8. Tsimbal V. A. Information exchange in data transmission networks. Markov's approach: a monograph / V.A. Tsymbal. - M.: University Book, 2014. - 144 p. 9. Nuts S. E. Method of analysis of the temporal characteristics of the absorbing inhomogeneous finite Markov chain with a variable duration of the transitions / S. E. Nuts // Theory and technology of radio communications. - 2014. - No. 3. - P. 49-57. 10. Potapov, S. E. a Study of the process of transmission of information through virtual routes in radio communications systems with moving objects [Text] / Theory and equipment telecommunications : nauch.–tekhn. jour. – Voronezh, JSC "Concern "Sozvezdie", 2019. – Vol. 3. – P. 11-23. – ISSN 1995-7009. 11. Potapov, S. E. Relational-operator method of mathematical modeling of the transmission of multi-packet messages along virtual routes of the radio communication network // High-tech technologies in space research of the Earth. 2019. vol. 11. No. 6. pp. 61 -73. doi: 10.24411 /2409-5419-2018-10296.
2. Perov A.I. Statistical theory of radio engineering systems. Textbook. manual for universities .- M .: radio engineering, 2003, 400 p 3. Shirman Ya.D. Resolution and compression of signals. "Sov. Radio "1974, 360 p. 4. Radio engineering systems: Textbook. manual for universities in the specialty "Radio Engineering" / YP, Grishin, VP Ipatov, YM Kazarinov and others; edited by Yu.M. Kazarinov. - M .: Higher school, 1990.-496 p. 5. Slyusar V.I., Smolyar V.T. Frequency division multiplexing of communication channels based on super-Rayleigh signal resolution. Radio electronics. Izv. v.u.z., 2003, No. 7, pp. 30-39. 6.V.A. Pahotin, V.M. Aniskevich. Frequency division multiplexing of communication channels based on non-orthogonal signals. Digital Signal Processing and Its Application: Collection of Reports of the 16th International Conference and Exhibition. - Moscow, 2014. - Issue. XVI - pp. 296-300. 7.V.A. Pahotin and V.I. Strokov, A.N. Aleshchenko. Non-orthogonal signals in frequency division multiplex communication systems. "Radar. Navigation. Communication ": collection of reports of the 20th international scientific and technical conference. - Voronezh, NPF Sakvoye, 2014. - p. 354. 8. Dvorkovich V.P., Dvorkovich A.V. Window functions for harmonic analysis of signals, Moscow: Technosphere, 2014. - 112 p. ISBN 978-5-94836-378-8 9. Makarov S.B., Tsikin I.A. Transmission of discrete messages over radio channels with limited bandwidth. - M .: Radio and communication, 1988. -304 p .: ISBN 5-256-00067-5. 10. Simonov R.V., Pakhotin V.A., Petrov S.V., Molostova S.V. Resolution of ultrasonic signals by the method of maximum likelihood. On Sat. Radioelectronic devices and systems for infocommunication technologies “REDS-2021". Moscow, 2021. pp 41-45
V.N. Yakimov, Russia, Ryazan, e-mail: yvnr@hotmail.com A.V. Mashkov, e-mail: mavstu@list.ru Samara State Technical University, Russia, Samara Keywords:
The use of binary-sign stochastic quantization made it possible to carry out analytical calculation of integral operations in the transition from the analog form of modified periodograms to their calculation in discrete form. As a result, the calculation of the PSD estimate was reduced to processing discrete values of functions which are the result of the integral cosine and sine Fourier transforms for window functions. A set of such functions can be generated analytically depending on the used window functions and the requirements for spectral analysis. The main operations of processing these functions are addition and subtraction operations. The need to perform multiplication operations is practically eliminated, which increases the efficiency of spectral analysis. The study of metrological properties of computational algorithms was carried out using numerical experiments. In this case, test sets of models of complex signals were used. The procedure of binary-sign stochastic quantization for models of complex numerical code signals was carried out on the basis of discrete-event simulation modeling. The test strategy for numerical experiments was aimed at the ability to detect weak components in complex signals. The results of the numerical experiment showed that the developed approach allows performing spectral analysis at a sufficiently low signal-to-noise ratio.
2. Marple, Jr.S.L. Digital spectral analysis with applications: Second edition. Dover Publications Inc, 2019. 432 p. 3. Papadopoulos H.C., Wornell G.W., Oppenheim A.V. Sequential signal encoding from noisy measurements using quantizers with dynamic bias control // IEEE Transactions on information theory, 2001, vol.47, no. 3, pp. 978–1002. DOI: 10.1109/18.915654. 4. Bilinsky I.Ya., Mikelson A.K. Stokhasticheskaya tsifrovaya obrabotka nepreryvnykh signalov (Stochastic digital processing of continuous signals). Riga: Zinatne, 1983. 292 p. 5. Mirskii G.Ya. Harakteristiki stohasticheskoj vzaimosvjazi i ih izmerenija (Characteristics of stochastic interconnections and their measurement). Moscow: Energoizdat. 1982. 320 p. (in Russian). 6. Max J. Methodes et techniques de traitement du signal et applications aux mesures physiques. Tome 1: Principes generaux et methodes classiques. Masson. Paris, 1996. 354 p. 7. Yakimov V.N., Mashkov A.V. Algoritm vychisleniya otsenki spektral'noy plotnosti moshchnosti na osnove obrabotki znakovykh signalov s ispol'zovaniyem vremennykh vesovykh funktsiy (Algorithm to compute estimate of a power spectral density based on sign signal processing using time-weighting functions) // Tsifrovaya obrabotka signalov (Digital Signal Processing). 2016, no. 4, pp. 3–8 (in Russian). 8. Yakimov V.N., Mashkov A.V., Gorbachev O.V. Tsifrovoy garmonicheskiy analiz na osnove metoda usredneniya Fur'ye-preobrazovaniya psevdoansamblya segmentov znakovogo signala (Digital harmonic analysis based on the method of averaging the Fourier transform of segments pseudo-ensemble of sign-function signal) // Tsifrovaya obrabotka signalov (Digital Signal Processing). 2016, no. 2, pp. 31–34 (in Russian). 9. Yakimov V.N. Tsifrovoy kompleksnyy statisticheskiy analiz na osnove znakovogo predstavleniya sluchaynykh protsessov (Digital complex statistical analysis based on the sign-function representation of random processes) // Izvestija samarskogo nauchnogo centra Rossijskoj akademii nauk (Izvestia of Samara scientific center of the Russian academy of sciences). 2016, vol. 18, no. 4(7), pp. 1346–1353 (in Russian). 10. Fichtenholz G.M. Kurs differentsialnogo i integralnogo ischisleniya (Course of differential and integral calculus). Moscow: Fizmatlit. 2003. Vol. 1. 680 p. (in Russian). 11. Harris F.J. On the use of windows for harmonic analysis with the discrete Fourier transform // Proceedings of the IEEE, 1978. vol. 66, no. 1, pp. 51-83. DOI: 10.1109/PROC.1978.10837 12. Prabhu, K.M.M. Window functions and their applications in signal processing. CRC Press, Taylor and Francis Group, 2014. 382 p. 13. Dvorkovich V.P., Dvorkovich A.V. Okonnye funkcii dlya garmonicheskogo analiza signalov (Windows functions for harmonic analysis of signals). Moscow: Tekhnosfera. 2016. 208 p. (in Russian). 14. Dvorkovich V.P., Dvorkovich A.V. Okonnye funkcii dlya garmonicheskogo analiza signalov (Windows functions for harmonic analysis of signals). Ed. 2nd. Moscow: Tekhnosfera Publ., 2016, 208 p. (in Russian). 15. Yakimov V.N., Gorbachev O.V. Firmware of the amplitude spectrum evaluating system for multicomponent processes // Instruments and Experimental Techniques, 2013, vol. 56, no. 5, pp. 540–545. 16. Yakimov V.N., Zaberzhinskij B.E., Mashkov A.V. Bukanova Yu.V. Multi-threaded Approach to Software High-speed Algorithms for Spectral Analysis of Multi-component Signals // Proceedings of IEEE XXI International Conference on Complex Systems: Control and Modeling Problems (CSCMP), 2019. pp. 698-701.
The purpose of this work is to estimation the probability density function of the complex envelope of the QAM signal. The histogram method and the maximum likelihood method for estimate the probability density function of the coefficients of the complex envelope of the QAM signal are used. The results of numerical simulation are presented. It is shown that in the case of using the histogram method, a significant sample size is required, which is unacceptable when analyzing signals received from channels with fast changing characteristics. Therefore, the authors considered the application of the maximum likelihood method. An analytical expression is derived of the probability density function of the complex envelope for the case of signals with QAM-4 and QAM-16. The results obtained can application in the problems of estimating the SNR of information signals with QAM modulation.
2. Jammalamadaka S.R., SenGupta A. Topics in Circular Statistics. – Singapore: World Scientific Publishing Co., 2001. 3. Smal M.S. Non-test methods for HF channel state estimation in adaptive radio links. Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, 2018. 4. Patyukov V.G., Patyukov E.V., Silantiev A.A. Measurement of the attitude a signal/noise on the basis of phase fluctuations of a signal // Journal of radio electronics. – 2013. – No 4. – P. 1. 5. Xiong F. Digital Modulation Techniques, Second Edition. – Boston: Artech House, Inc, 2006. 6. Tikhonov V.I. Statistical Radio Engineering. Sovetskoe radio, Moscow, 1966. 7. Sirota A.A. Methods and algorithms of data analysis and its modeling in MATLAB. – Saint-Petersburg, BHV-Peterburg, 2016. 8. Iglin S.P. Probability theory and mathematical statistics based on MATLAB. Har'kov, NTU «HPI», 2006. 9. Fukunaga K. Introduction to statistical pattern recognition. New York, Academic. Press, 1972.
Moreover, in cases where the SNR is large enough, most of the known methods, both test and blind, do not allow obtaining a "good" estimate with a small size of analyzed data. An increase in the size of the analyzed sample will lead to a decrease in the efficiency when timely deciding on the select of the optimal state of the communication system. A problem of this kind arises in channels with fast changing propagation conditions, as well as in the functioning of an adaptive data transmission system in a difficult signal-interference environment. The article proposes method of estimation the signal-to-noise ratio using data signals of short duration. This problem is reduced to solving the inverse problem or the problem of inverse modeling, moreover the noise component dispersion value is estimated. The proposed method makes it possible to quickly estimate the variance of the noise component, on the basis of which current estimates of the bit error rate and signal-to-noise ratio can be obtained. 2. Smal M.S. Non-test methods for HF channel state estimation in adaptive radio links. Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, 2018. 3. MIL-STD-188-190. Methods for communications systems measurements. – United States Department of Defense Interface Standard, 1990. 4. Patyukov V.G., Patyukov E.V., Silantiev A.A. Measurement of the attitude a signal/noise on the basis of phase fluctuations of a signal // Journal of radio electronics. – 2013. – No 4. – P. 1. 5. Beaulieu N.C., Toms A.S., Pauluzzi D.R. Comparison of four SNR estimators for QPSK modulations // IEEE Commun. Lett. – 2000. – V. 4 ¹ 2. – P. 43–45. 6. Rice M.A. Wicker S.B. Sequential Scheme for Adaptive Error Control over Slowly Varying Channels // IEEE Trans. Commun. – 1994. – P. 1533-1643. 7. Cui T., Tellambura C. Power Delay Profile and Noise Variance Estimation for OFDM // IEEE Commun. Lett. – 2006. – V. 10. ¹. 1. – P. 25-27. 8. Tikhonov V.I. Statistical Radio Engineering. Sovetskoe radio, Moscow, 1966. 9. Fink L.M. Theory of discrete message transmission. Sovetskoe radio, Moscow, 1970.
2. Assaf M., Ponomarev O. G. Sample Clock Offset Compensation in the Fifth-Generation New Radio Downlink.” Journal of Physics: Conference Series, vol. 1889, no. 2, 2021, p. 022091. 3. Chen S., Zhao J., The requirements, challenges, and technologies for 5G of terrestrial mobile communication, IEEE communications magazine, vol. 52, no. 5, May 2014, pp. 36 - 43. 4. Dahlman E., Parkvall S., Skold J. 5G NR: The next generation wireless access technology. Academic Press, 2018. – 466 p. 5. Kundu L., Xiong G., Cho J., Physical uplink control channel design for 5g new radio, in 2018 IEEE 5G World Forum (5GWF), Jul. 2018, pp. 233–238 6. Kim, Young-Hoon, et al. Performance Comparison of DTX Detection Schemes for 5G NR PUCCH. 2020 International Conference on Information and Communication Technology Convergence (ICTC), 2020. 7. Du Y., He W., Long H., An improved semi-blind detection algorithm for nr pucch, in 2019 IEEE 5th International Conference on Computer and Communications (ICCC), Dec. 2019, pp. 66–71. 8. ETSI TS 138 211 V15.2.0 (2018-07). Technical specification. 5G; NR; Physical channels and modulation (3GPP TS 38.211 version 15.2.0 Release 15). 9. ETSI TS 38.104. 5G; NR; Base Station (BS) radio transmission and reception (3GPP, TS 38.104 version 16.4.0 Release 16).
Two variants of the formation of the transmitted signal are considered. In the first variant, the number of values of the message element is 2, in the second variant, the number of values of the message element is 4. Each value of the message element corresponds to a simplex signal. The specific bandwidth costs for the first and second options are 1.18 and 1.09, respectively, peak factor 2 and 2.63. It is shown that the second option allows for significantly better noise immunity, but the peak factor of the transmitted signal increases. The possibility of forming and processing a high-frequency transmitted signal using a complex envelope is considered. At the same time, the main part of the algorithm of formation and processing is carried out in the low-frequency region. The transmitted signal is formed from a complex envelope using a quadrature modulator. When receiving, the complex envelope is formed using a quadrature demodulator and low-pass filters. When modulating with a minimum shift (a known transmission method), the specific cost of the band is 1.18, the peak factor is 1.41. The noise immunity is the same as in the first variant under consideration. The second option makes it possible to obtain significantly better noise immunity than with modulation with minimal shift, but the peak factor increases. 2. Vershinin V.A. Ispol'zovanie algoritma Viterbi pri peredache perekryvajushhimisja jelementarnymi signalami [Using the Viterbi algorithm when transmitting overlapping elementary signals]// Cifrovaja obrabotka signalov [Digital signal processing].– 2020.– ¹4. (in Russian)
When the signal passes through the structure of the interpolated adaptive filter, additional spectral components appear. To exclude additional spectral components, a low-order smoothing filter is used. Therefore, the use of an interpolated filter assumes the construction of a two-stage system, including an interpolated IIR adaptive filter and an FIR or IIR smoothing filter. It was shown that the use of a structure consisting of an adaptive interpolated and smoothing filter gives a significant advantage over classical structures in the direct modeling of narrowband filters. With a slight increase in the computational costs required to implement the smoothing filter and some increase in the data memory, it is possible to achieve a much more accurate convergence and to increase the convergence rate of adaptation algorithms. An additional advantage is an increase in filter stability for some parameters of the adaptation algorithms. The two-stage scheme makes it possible to construct stable adaptive filters based on classical algorithms with an improvement in the identification accuracy of an unknown system. In this work, the LMS and RLS algorithms were used without any special modifications, the changes made to the structure of the adaptive IIR filter are also minimal. 2. Proakis J.G., Digital Communication, 4th edn., McGraw Hill, New York, 2001 3. Widrow B., S.D. Stearns, Adaptive Signal Processing, Prentice Hall, Englewood Cliffs, 1985 4. Wood L.C., Treitel S., Seismic signal processing. Proc. IEEE 63, 1975, pp. 649–661 5. Shynk G J. J., Adaptive IIR filtering, IEEE ASSP Magazine, pp. 4-21, Apr. 1989. 6. Vityazev V.V. Mnogoskorostnaya obrabotka signalov (Multirate signal processing). M.: Gorjachaja linija–Telekom, 2017. – 336 p 7. Goriushkin R.S., Vityazev V.V., Analiz primeneniya adaptivnyh grebenchatyj BIH-fil'trov v zadache vydeleniya uzkopolosnogo signala na fone shirokopolosnogo shuma (Analyzing of the adaptive line enhancement of narrowband signal using adaptive interpolated IIR filters) // Cifrovaya obrabotka signalov, M., 2021. Vol.2. pp. 42-47 8. M. Shafaati, M. Ahmadi and H. Mojallali, "Identification of IIR systems using harmony search algorithm," The 2nd International Conference on Control, Instrumentation and Automation, 2011, pp. 1148-1153 9. Feintuch P.L. An Adaptive Recursive LMS Filter // Proceedings IEEE, Vol. 64, No. 11, November 1976. pp. 1622-1624 10. Diniz P. Adaptive Filtering: Algorithms and Practical Implementation. Springer, 2020. 495 pp. 11. S. Koshita, Y. Kumamoto, M. Abe, M. Kawamata, Adaptive IIR Band-Pass/Band-Stop Filtering Using High-Order Transfer Function and Frequency Transformation, Interdisciplinary Information Sciences, 2013, Vol. 19, Issue 2, 2013, pp. 163-172
The preliminary results of the research show that the sharpness optimization radar image autofocusing method gives a better efficiency result compared to traditional image focusing algorithms. Using the methods of the golden-section search and Fibonacci numbers allows to reduce the autofocusing time of radar image by more than 5 times in relation to the direct search method. The type of image sharpness metric significantly affects the accuracy of radar image sharpness recovery. Following an in-depth analysis of preliminary research results, some recommendations on the choice of determine intensity image pixels degree parameter also are given. In particular, it was found that according to the criterion «quality/recovery time», the best metric is [I(x,y)] 2. C.V. Jakowatz, Jr., D.E. Wahl, P.H. Eichel, D.C. Ghiglia, and P.A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach., Kluwer Academic Publishers, Boston, 1996. 3. J.R. Fienup and J. J. Miller, «Aberration correction by maximizing generalized sharpness metrics», J. Opt. Soc. Amer. A, vol. 20, no. 4, pp. 609-620, April 2003. 4. L. Xi, L. Guosui, and J. Ni, «Autofocusing of ISAR images based on entropy minimization», IEEE Transactions on Aerospace and Electronic Systems, vol. 35, no. 4, pp. 1240-1252, October 1999. 5. Schulz, T.J.: «Optimal sharpness function for SAR autofocus», IEEE Signal Process. Lett., 2007, 14, (1), pp. 27-30. 6. Gao, Yang; Yu, Weidong; Liu, Yabo; Wang, Robert: «Autofocus algorithm for SAR imagery based on sharpness optimization», Electronics Letters, 2014, 50, (11), pð. 830-832. |