|Digital Signal Processing||
Analysis of quantized FIR filters
In this paper, VIP analysis is applied to optimal low-pass FIR filters with symmetrical impulse response synthesized on the basis of the Remez - Parks - McClellan algorithm (see, for example, the function cremez (...) in MATLAB). The description of controlled and initial parameters is given. Dependences of controlled parameters on initial parameters for continued and quantized coefficients îf low-pass filters are presented. The piecewise constant nature of the plotted curves is explained. The analysis of similar curves for direct structure narrowband and wideband filters at big and small relations of ripple levels of magnitude response in passband and stopband is carried out. Dependences of the maximum relative error of the magnitude response on the initial ratio of ripple levels for direct and cascade and also for direct and bound real filter structures are compared.
2. Mingazin A. Variation of initial parameters of weighted Chebyshev approximation in multiplierless FIR filter design (DSPA-2005)//7-th Int. Conf. Digital Signal Processing and its Applications (DSPA-2005), vol. 1, pp. 56-59.
3. Mingazin A. Design of multiplierless half-band digital FIR filters // Sovremennaya Elektronika, 2006, no. 3, pp. 44-46.
4. Mingazin A. Two examples of multiplierless perfect reconstruction lattice filter bank design //11-th Int. Conf. Digital Signal Processing and its Applications (DSPA-2009), vol.1, pp.99-103. 5.Mingazin A. Design FIR filters with arbitrary magnitude response and limited coefficient wordlength // Components & Technologies, 2014, no. 2, pp. 98-100.
6. Mingazin A. Variation of initial parameters in analysis problem of IIR filters // Components & Technologies, 2018, no.11, pp.-102.
7. Dehner G. On the design Cauer filters with coefficients of limited wordlength // AEU. 1975, vol. 29, no. 4, pp. 165-168.
8. Mehrnia A., Willson A. N. FIR filter design via extended optimal factoring // IEEE Trans. 2016, SP-64, no. 4, pp. 1061-1075.
9. Mehrnia A., Willson A. N. À lower bound for the hardware complexity of FIR filters // IEEE CAS Magazine, 2018, no. 1, pp. 10-28.
10. Mehrnia A., Willson A. N. Optimally factored IFIR filters // Circuits, Systems and Signal Processing, 2019, vol. 38, no. 1, pp. 259-286.
11. Vaidyanathan P. P, Mitra S. K. Very low sensitivity FIR filter implementation using structural passivity concept // IEEE Trans. 1985, CAS-32, no. 4, pp. 360-364.
12. Vaidyanathan P. P, Mitra S. K. Robust digital filter structures: a direct approach // IEEE CAS Magazine, 2019, no. 1, pp. 14-32.
The discrete structure of the zeros and poles location in the Z-plane of the recursive digital filters with a finite word length
Keywords: IIR digital filters, resolved positions of the zeros and poles, finite wordlength, discretized z-plane, plane algebraic curves.
2. Signal processing toolboxTM: User's guide. - The MathWorks, Inc. - 2017.
3. Lesnikov V., Chastikov A., Naumovich T., Armishev S. A new paradigm in design of IIR digital filters // 8th IEEE East-West Design and Test Symposium (EWDTS 2010). - St. Petersburg, Russia. - 17-20 Sept. 2010. - Pp. 282-285.
4. Lesnikov V., Chastikov A., Naumovich T., Armishev S. Implementation of a new paradigm in design of IIR digital filters // 8th IEEE East-West Design and Test Symposium (EWDTS 2010). - St. Petersburg, Russia. - 17-20 Sept. 2010. - Pp. 156-159.
5. Lesnikov V., Naumovich T. Number-theoretic and algebraic aspects of structural synthesis of digital filters // Global Signal Processing (GSP 2004). The International Embedded Solutions Event (The Embedded Signal Processing Conference). - Santa Clara, USA - 2004. - Pp. 27-30.
6. Lesnikov V., Naumovich T., Chastikov A. Number-theoretical analysis of the structures of classical IIR digital filters // 7th Mediterranean Conference on Embedded Computing (MECO 2018). - Budva, Montenegro. - 10-14 June 2018. - 4 p.
7. Weinstein C.J. Quantization effects in digital filters // Technical Report 468. - Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts. - 21 November 1969. URL: https://www.semanticscholar.org/paper/Quantization-Effects-in-Digital-Filters-Weinstein/0e52d6dbb14fb6c137527f7919e0bc380bd276f8.
8. Hess W. Digitale filter: eine einfuhrung. - Springer Fachmedien Wiesbaden GmbH. - 1993. 433 p.
9. Bomar B.W. Finite wordlength effects // Digital Signal Processing Handbook / Ed. V. K. Madisetti, D. B. Williams. - Boca Raton: CRC Press LLC. - 1999. Chapter 3.
10. Lesnikov V., Naumovich T., Chastikov A. Topography of z-plane which is discretized due to quantization of coefficients of digital biquad filters // 12th International Siberian Conference on Control and Communications (SIBCON 2016). - Moscow, Russia. - 12-14 May 2016, 4 p.
11. Lesnikov V., Naumovich T., A. Chastikov. The sampling of the z-plane due to the quantization of the digital filter coefficients // 7th Mediterranean Conference on Embedded Computing (MECO 2018), Budva, Montenegro. - 10-14 June 2018. - 4 p.
12. Lesnikov V., Naumovich T., Chastikov A. The topography of a third order IIR digital filter zeros and poles in the z-plane discretized due to the quantization of the direct form coefficients // 7th Mediterranean Conference on Embedded Computing (MECO 2019). - Budva, Montenegro. - 10-14 June 2019. Pp. 374-377.
13. Lesnikov V., Naumovich T., Chastikov A., Metelyov A. Topography of the z-plane discretized by quantizing the coefficients of the canonical form of recursive digital filter // Computer Vision in Advanced Control Systems 6 / M. Favorskaya, L.C. Jain, Eds.
14. Lesnikov V., Naumovich T., Chastikov A., Metelyov A. The discrete structure of the zeros and poles location in the z-plane of the arbitrary order IIR digital filters with a finite word length // IEEE East-West Design and Test Symposium (EWDTS 2019). - Batumi, Georgia. - 13-16 Sept. 2019.
15. Lesnikov V., Naumovich T., Chastikov A. Synthesis of recursive digital filters with finite word length: problems and their solutions // Problems of Advanced Micro- and Nanoelectronic Systems Development, 2019, Issue III, Moscow, IPPM RAS. Ñ. 46-53.
16. Hilbert D. The theory of algebraic number fields. Berlin Heidelberg New York: Springer Verlag, 1998. 360 p.
17. Ireland K., Rosen M. A classical introduction to modern number theory, 2nd ed. - New York: Springer-Verlag, 1990. 406 p.
18. Rovenski V. Modeling of curves and surfaces with MATLAB. - New York - Dordrecht Heidelberg London: Springer Science+Business Media, LLC, 2010. 452 p.
Adaptive Antenna Array for Operation in Interference and Multipath Conditions
Adaptive arrays use different criteria of operation, among which is a criterion of the Mean Square Error (MSE) between pilot and array output signals. This criterion is widely used in communication systems. The solution allows to suppress interferences in array output signal and to steer the main beam of the array towards the desired signal source, if there is no multipath of the signal.
However, if there is a multipath, the adaptive algorithm cannot minimize MSE. An equalizer, which has to suppress the multipath, cannot do its job well due to interference signals, which are not suppressed completely at array output. Such independent cascade solution (adaptive array and equalizer) is not effective, that was demonstrated in a diversity of publication on the topic.
The given paper proposes a solution of the problem, which is based on a simultaneous using of an adaptive antenna array and a feedback equalizer for signal receiving, if there are the sources of the interference and the desired signal multipath.
The paper presents the architecture of such array and equalizer, adaptive algorithm (Recursive Least Squares, RLS) and simulation results, confirming the efficiency of the solution in a circular array.
The simulation are conducted for the circular array with 3 antennas, which receives PSK-8 signal via two-rays channel in the presence of two interference sources with 30 dB Signal-to-Interference Ratio (SIR) each.
The solution with symbol-rate equalizer demonstrates the ability to steer of the main beam of array towards the information signal source, to suppress interference signals creating dips in radiation pattern of about -100 dB, and equalize the multipath channels with 0.05
. 0.5 dB final frequency response ripple dependently Signal-to-Noise Ratio (SNR) in array receivers (-30
2. Djigan V.I. Adaptivnaya fil`traciya signalov. Teoriya i algoritmy (Adaptive signal filtering: theory and algorithms). Moscow, Technosphera, 2013. 528 p. (in Russian)
3. Haykin S. Adaptive filter theory. Fifth edition. Pearson Education Inc., 2014. 889 p.
4. Zhuravlev A.K., Lukoshkin A.P. Poddybny S.S. Obrabotka signalov v adaptivny`x antenny`x reshetkax (Signal processing in adaptive arrays). Leningrad: Lenigrad University Publisher, 1983. 240 p. (in Russian)
5. Compton R.T. Adaptive antennas. Concepts and performance. Prentice Hall, 1988. 448 p.
6. Pistolkors A.A., Litvinov O.S. Vvedenie v teoriyu adaptivny`x antenn (Introduction in adaptive arrays theory). Moscow, Nauka, 1991. 200 p. (in Russian)
7. Allen B., Ghavami M. Adaptive array systems. Fundamentals and applications. John Wiley & Sons Ltd., 2005. 250 p.
8. Hudson J.E. Adaptive array principles. The Institution of Engineering and Technology, 2007. 253 p.
9. Monzingo R.A., Haupt R.L. Miller T.W. Introduction to adaptive arrays. (2-nd edition). SciTech Publishing, 2011. 510 p.
10. Qureshi S. Adaptive equalization // IEEE Communications Magazine. 1982. Vol. 20. ¹2. P. 916.
11. Qureshi S. Adaptive equalization // Proceedings of the IEEE. 1985. Vol. 73. ¹9. P. 13491387.
12. Litva J., Lo T.K.-Y. Digital beamforming in wireless communications. Artech House., 1996. 301 p.
13. Grigoriev L.N. Cifrovoe formirovanie diagrammy` napravlennosti v fazirovanny`x antenny`x reshetkax (Digital beamforming in phased arrays). Moscow, Radiotechnika. 144 p. (in Russian)
14. Lindskog E., Ahlen A., Sternad M. Combined spatial and temporal equalization using an adaptive antenna array and a decision feedback equalization scheme // Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing. Dertoit, USA, 2 12 May, 1995. Vol. 2. P. 1189-1192.
15. Perahia E., Pottie G.J. Adaptive antenna arrays and equalization for indoor digital radio // Proceedings of the International Conference on Communications. Dallas, USA, 23-27 June 1996. P. 592 P. 597.
16. Vaidyanathan C., Buckley K.M. An adaptive decision feedback equalizer antenna array for multiuser CDMA wireless communications // Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers. Pacific Grove, USA 36 November, 1996. Vol. 1. P. 340344.
17. Choy F. Cherniakov M. Combinations of adaptive antennas and adaptive equalizers for mobile communications // IEEE Region 10 Annual Conference. Speech and Image Technologies for Computing and Telecommunications. Brisbane, Australia, 4 December 1997. P. 497 500.
18. Lee J.-Y., Samueli H. Adaptive antenna arrays and techniques for high bit-rate QAM receivers // IEEE Journal on Selected Areas in Communication. 1999. Vol. 17. ¹ 4. P. 677688.
19. Maw-Lin Leou M.-L, Yeh C.-C., Li H.-J. A novel hybrid of adaptive array and equalizer for mobile communications // IEEE Trans. on Vehicular Technology. 2000. Vol. 49. ¹ 1. P. 110.
20. Ichikawa Y, Tomitsuka K., Obote S., Kagoshima K. Computational complexity reduced MMSE adaptive array antenna with space-temporal joint equalization // Proceedings of the IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting. Boston, USA, 8-13 July 2001. Vol. 4. P. 3033.
21. Preisig J. Challenges and analysis of adaptive multichannel equalization for large-N arrays // Proceedings of the 49th Asilomar Conference on Signals, Systems and Computers. 2015. Pacific Grove, USA, 8-11 Nov. 2015/ P. 239243.
22. Pletneva I.D., Djigan V.I. Modelirovanie obrabotki signalov v cifrovy`x antenny`x reshetkax (Simulation of signal processing in digital antenna arrays) // Modern Telecommunication Systems: Proceedings of the Moscow Institute of Electronic Engineering. Moscow, Russia, 2007. P. 3643. (in Russian)
The Doppler frequency shift estimation problem occurs in almost all radio communication and radar systems, and is especially relevant in aviation and satellite communication systems, as well as in positioning systems.
In this work, the authors propose a method for the Doppler frequency shift estimation from information single-tone signals with phase-shift-keying modulation based on the symbols phase values.
The proposed method allows real-time estimation of the Doppler frequency shift of the received signal. A feature of this method is that there is no need to transmit a special test signal. Estimation is carried out directly by the information signal based analyses the symbols phases. The information bit sequence is unknown. Also note that relatively small sequences of information BPSK symbols are required to obtain an estimation.
Addition, the methods of correct processing on the phase circle are proposed.
2. Johnson E.E., Koski E., Furman W.N., Jorgenson M., Nieto J. Third-Generation and Wideband HF Radio Communications. Artech House, Inc, Boston, 2013.
3. Karpukhin E.O., Mazepa R.B., Mikhaylov V.Y. Research perspective signal-code constructions based on FH-OFDM when exposed doppler shift frequency // H&ES Research. 2016, V. 8, ¹ 1, pp. 1216.
4. Liu Q. Doppler measurement and compensation in mobile satellite communications systems. MILCOM 1999. IEEE Military Communications. 31 Oct. 3 Nov., 1999, pp. 316320.
5. Tirer T., Weiss A.J. High Resolution Localization of Narrowband Radio Emitters Based on Doppler Frequency Shifts. Signal Processing. 2017, V. 141, pp. 288298.
6. Kundu D., Nandi S. Statistical Signal Processing. Frequency Estimation. Springer, 2012.
7. Rife D., Boorstyn R. Single tone parameter estimation from discrete-time observations. IEEE Transactions on Information Theory. V.20, I. 5, Sep. 1974, pp. 591598.
8. Beletskaya S.Y., Gnezdilov D.S., Kryzhko I.B., Tokarev A.B. Frequency measurement algorithm based on set of spectrum template. Bulletin of Voronezh state technical University. 2014, V. 10, ¹ 1, pp. 8587.
9. Hua J., Meng L., Zhao X., Li G., Wang D., You X. A Doppler shift estimator in radio propagations. Radio Science. 2009, V. 44, I. 4.
10. Chen G., Zhao Z., Nie X., Shi S., Yang G., Su F. Doppler estimating and compensating method based on phase. Journal of Systems Engineering and Electronics V. 20(4). 2009, ¹ 8,pp. 681686.
11. Johnson Ì., Freitag L., Stojanovic Ì. Improved Doppler tracking and correction for underwater acoustic communications // in Proc. ICASSP `97, Munich, Germany, Apr. 1997, pp. 575578.
12. Grishin Y.P, Ipatov V.P., Kazarinov Y.M, Kolomensky Y.A., Ulyanicky Y.D. Radio Engineering Systems.Moscow, Radio I svyaz, 1990.
13. Botashev B.M., Skripkin A.A. Pat. RU ¹ 2233452. The method of extracting information about the Doppler frequency shift of the carrier signal and a device for its implementation. 2004.
14. Burenin A.V. Pat. RU ¹ 2565237. Evaluation of complex signal carrier frequency Doppler shift. 2015.
15. Okunev Y.B. Digital transmission of information by phase-shifte-keying signals. Moscow. Radio I svyaz, 1991.
16. Nelson H.F. Beebe. The Mathematical-Function Computation Handbook. Springer, 2017.
17. Egorov V.V., Smal M.S. Signal-to-noise ratio estimation for signals with phase-shift keying modulation scheme // Telecommunications, 2013, ¹ 5, pp. 2934.
18. Mardia K.V. Statistics of Directional Data. Academic Press, 1972.
19. Jammalamadaka S.R., SenGupta A. Topics in Circular Statistics, World Scientific Publishing Co., Singapore, 2001.
20. Kalitkin N.N. Numerical Methods. Moscow. Nauka, 1978.
The voice recordings used in this study were collected in the Republican Scientific and Clinical Center for Neurology and Neurosurgery (Minsk, Belarus). A total of 54 people were recorded, including 39 healthy (23 men, 16 women) and 15 ALS patients with signs of bulbar dysfunction (6 men, 9 women). The average age in the healthy group was 41.9 years (SD 16.3), and the average age in the ALS group was 57.7 years (SD 9.0). For discriminating between the two classes of normal and pathological cases two widely spread machine learning algorithms: linear discriminant analysis (LDA) and k-Nearest Neighbors (k-NN) were used. For determining classification accuracy k-fold cross-validation method (with k=4) was used. Since the dimensionality of the feature sets was low we have performed exhaustive search through all possible feature subset to find the best one.
The experiments showed that the use of the proposed methods of acoustic voice analysis and classification according to the method of k nearest neighbors made it possible to obtain the detection system with accuracy of 95.7% (sensitivity 91.5% and specificity of 97,4%).
2. Yunusova Y. et al. Detection of bulbar ALS using a comprehensive speech assessment battery// Proceedings of the International Workshop on Models and Analysis of Vocal Emissions for Biomedical Applications. 2013. pp. 217-220.
3. Horwitz-Martin R.L. et al. Relation of automatically extracted formant trajectories with intelligibility loss and speaking rate decline in amyotrophic lateral sclerosis. Proceedings of Interspeech. 2016. pp. 12151219.
4. Spangler T. et al. Fractal features for automatic detection of dysarthria // IEEE EMBS International Conference on Biomedical Health Informatics. 2017. pp. 437440.
5. Tomik B., Guiloff R.J. Dysarthria in amyotrophic lateral sclerosis: A review // Amyotrophic Lateral Sclerosis. 2010. vol. 11, ¹ 1-2. pp. 4-15.
6. Benba A., Jilbab A., Hammouch A. Discriminating between patients with Parkinsons and neurological diseases using cepstral analysis / A. Benba, // IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2016. vol. 24, no. 10. pp. 11001108.
7. Norel R. et al. Detection of amyotrophic lateral sclerosis (ALS) via acoustic analysis // Proceedings of Interspeech 2018. pp. 377381.
8. Guerra C., Lovey D. A modern approach to dysarthria classification // Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEMBS). 2003. vol. 3. pp. 22572260.
9. Liss J.M., LeGendre S., Lotto A.J. Discriminating dysarthria type from envelope modulation spectra // Journal of Speech, Language, and Hearing Research. 2011. vol. 53, no. 5. pp. 1246-1255.
10. An K. [et al.] Automatic early detection of amyotrophic lateral sclerosis from intelligible speech using convolutional neural networks // Proceedings of Interspeech 2018. P. 1913-1917.
11. Vashkevich M. et al. Features extraction for the automatic detection of ALS disease from acoustic speech signals // Proceedings of inter. conf. Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). 2018. pp. 321-326.
12. Gvozdovich A.D., Rushkevich Yu.N., Vashkevich M.I. Detektirovanie bulbarnyh narushenij pri bokovom amiotroficheskom skleroze na osnove analiza rechevogo signala (Detection of bulbar amyotrophic lateral sclerosis based on speech analysis) // Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radiojelektroniki (Reports of the Belarusian State University of Informatics and Radioelectronics). 2018. vol. 116. no 6. pp. 52-58.
13. Illa A. et al. Comparison of speech tasks for automatic classification of patients with amyotrophic lateral sclerosis and healthy subjects // Proceedings of IEEE Inter. Conf. on Acoustics, Speech and Signal Processing (ICASSP). 2018. pp. 6014-6018.
14. Wang J. et al. Towards Automatic Detection of Amyotrophic Lateral Sclerosis from Speech Acoustic and Articulatory Samples// Proceedings of Interspeech. 2016. pp. 1195-1199.
15. Bandini A. et al. Classification of bulbar ALS from kinematic features of the jaw and lips: Towards computer-mediated assessment // Proceedings of Interspeech. 2017. pp. 1819-1823.
16. Baken, R.J., R.F. Orlikoff Clinical measurement of speech and voice, 2nd edition // Thomson Learning, 2000. 864 p.
17. Moran R.J. et al. Telephony-based voice pathology assessment using automated speech analysis // IEEE Transactions on Biomedical Engineering. 2006. vol. 53, no. 3. pp. 468-477.
18. Little M. A. et al. Suitability of Dysphonia Measurements for Telemonitoring of Parkinson's Disease // IEEE Transactions on Biomedical Engineering. 2009. vol. 56, no. 4. pp. 1015-1022.
19. Azarov I.S., Vashkevich M.I., Petrovsky A.A. Algoritm ocenki mgnovennoj chastoty osnovnogo tona rechevogo signala (Algorithm for estimating the instantaneous frequency of the fundamental frequency of a speech signal)// Cifrovaja obrabotka signalov (Digital Signal Processing). 2012. No. 4. pp. 49-57.
20. Rilov A.S. Analiz rechi v raspoznajushhih sistemah [Speech analysis in recognition systems]. Minsk: Bestprinto, 2003. 264 p. (in Russian)
21. Nakano T., Goto M., Hiraga Y. An automatic singing skill evaluation method for unknown melodies using pitch interval accuracy and vibrato features // Proceedings of Interspeech 2006. pp. 17061709.
22. Aronson A.E. et al. Rapid voice tremor, or flutter, in amyotrophic lateral sclerosis // Annals of Otology, Rhinology & Laryngology. 1992. vol. 101, no. 6. pp. 511518.
23. Vashkevich M., Petrovsky A., Rushkevich Yu. Bulbar ALS detection based on analysis of voice perturbation and vibrato // Proceedings of inter. conf. Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA). 2019. pp. 267-272.
24. Flach P. Machine learning: The art and science of algorithms that make sense of data. Cambridge University Press. 2012. 409 p.
Noise immunity of a modem based on dynamic chaos according to Veshkurtsev law in a channel with Gaussian noise
Analysis of noise immunity of the proposed modem in a channel with Gaussian noise other than "white" noise was performed. It has been found that the noise immunity of a modem depends on the mathematical expectation of noise in a complex manner. It can be increased by 10 dB at a fixed error probability or reduced to an error probability of 0.5 in the range of 40 dB signal-to-noise power ratios with a lower range limit of minus 10 dB.
For the wired communication channel, recommendations have been developed to combat the interfering factor in the form of mathematical noise expectation. In radio channel, compensation of mathematical noise expectation at modem input is performed automatically due to operation of antenna-feeder system. Thus, the noise stability of the modem remains the same with the probability of mistakes at the level of 110^(-45).
2. Veshkurtsev Yu.M. Noise immunity of modem during reception of signal with distribution of instant values according to Tikhonov law//Digital signal processing, 2019. ¹ 2. pp. 49 - 53.
3. Veshkurtsev Yu.M. Interference immunity and efficiency of the new modulation method/Yu.M. Veshkurtsev//International scientific journal Science and Peace. - 2019. - ¹ 3 (67). Volume 2. pp. 32 - 45.
4. Veshkurtsev Y.M. Modulation and demodulation method of signal//Telecommunications, 2019. No. 5. pp. 66 - 69.
5. Tikhonov, V.I. Statistical Radio Engineering. - Moscow: Sov. Radio, 1966. - 678 p.
6. Veshkurtsev Yu.M. Study of noise immunity of modem of digital systems with amplitude manipulation during operation in channel with Gaussian noise/Yu.M. Veshkurtsev//Instruments and systems. Management, control, diagnostics, 2019. ¹ 9. pp. 21 - 26.
The results of modeling and field experiments illustrating the effectiveness of the proposed solutions are given. Additionally, the use of sharpness optimization autofocus as an alternative to PGA, as well as the use of a stripmap mode of imaging radar operation are considered.
2. O. Frey, C. L. Werner, I. Hajnsek and R. Coscione, "A Car-Borne SAR System for Interferometric Measurements: Development Status and System Enhancements," IEEE International Geoscience and Remote Sensing Symposium, 2018, pp. 6508 -6511.
3. O. Frey, C. L. Werner, U. Wegmuller, A. Wiesmann, D. Henke and C. Magnard, "A car-borne SAR and InSAR experiment," IEEE Intern. Geoscience and Remote Sensing Symposium, 2013, pp. 93-96.
4. P. Eichel, D. Ghiglia, and C. Jakowatz, "Speckle processing method for synthetic-aperture-radar phase correction", Optics Letters, vol. 14, 1989, pp. 1-3.
5. D.E. Wahl, P.H. Eichel, D.C. Ghiglia, and C.V. Jakowatz Jr., "Phase gradient autofocus - a robust tool for high resolution SAR phase correction," Aerospace and Electronic Systems, IEEE Transactions on, vol. 30, is. 3, 1994, pp. 827 - 835.
6. Ch. V. Jakowatz, D.E. Wahl, P.H. Eichel, D.C. Ghiglia, P.A. Thompson. Spotlight-mode synthetic aperture radar: a signal processing approach. Springer. 1996.
7. S. Chen, F. Lu, J. Wang, M. Liu, "An improved phase gradient autofocus method for one-stationary bistatic SAR," IEEE Intern. Conf. on Signal Processing, Communications and Computing pp. 1-5, 2016.
8. M. P. Hayes and S. A. Fortune, "Recursive phase estimation for image sharpening," in Image and Vision Computing New Zealand, Dunedin, New Zealand, 2005.
9. T. J. Kragh, "Monotonic iterative algorithm for minimum-entropy autofocus," in Proc. Adaptive Sensor Array Processing (ASAP) Workshop, Lexington, MA, June 2006.
10. R.L. Morrison Jr., M.N. Do, and D.C. Munson, Jr. "SAR Image Autofocus By Sharpness Optimization: A Theoretical Study," IEEE Journal, pp. 1-13, 2003
11. M. P. Hayes, H. J. Callow, and P. T. Gough, "Strip-map Phase Gradient Autofocus," Proceedings of IEEE 6th Digital Signal Processing Workshop, 1994, pp. 53-56.
12. D.G. Thompson ; J.S. Bates ; D.V. Arnold, "Extending the phase gradient autofocus algorithm for low-altitude stripmap mode SAR," Proceedings of the 1999 IEEE Radar Conference. Radar into the Next Millennium, 1999, pp. 36-40.
13. Y. Gao, W. Yu, Y. Liu, R. Wang, C. Shi, "Sharpness-Based Autofocusing for Stripmap SAR Using an Adaptive-Order Polynomial Model", IEEE Geoscience and Remote Sensing Letters, 2014, Vol. 11, Is. 6, pp. 1086-1090.
14. V. Androsov, S. Vityazev, A. Kharin, V. Vityazev, "An Approach to Autofocus in Car-borne Radar Imaging Systems," 2018 IEEE East-West Design & Test Symposium, 2018, pp. 1-4.
15. I.G. Cumming, F.H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Norwood, MA: Artech House, 2005.
16. W.G. Carrara, R.S. Goodman, and R.M. Majewski, Spotlight Synthetic Aperture Radar. Signal Processing Algorithms, Artech House, Boston, London, 1995.
17. Robert L. Morrison, Jr., Minh N. Do. and David C. Munson, Jr. SAR Image Autofocus By Sharpness Optimization: A Theoretical Study, IEEE Journal, 2003.
Quantization of the ZC sequence both when used as a PSS in the DL direction, and as a preamble and probing and demodulated sequences in the UL transmission direction reduces the computational load and hardware complexity and, as a result, the cost of mobile systems.
2. ETSI TS 136 211 V10.0. 0 (2011-01). Technical Specification. - European Telecommunications Standards Institute, 2011 - 104 p.
3. Kiseleva T. P. Investigation of the properties of the cyclic autocorrelation function of the Zadov Chu sequence depending on the quantization characteristics of the sequence elements.- Digital signal processing, no. 4,2018. 40-44 p.
4. Calculation of the BS coverage area using the Hata model- [Electronic resource] access Mode: https://studopedia.ru/19_218637_tema--raschet-zoni-pokritiya-bs-s-pomoshchyu.html (accessed 16.07.2019)
5. Gelgor A. L., Popov E. A. LTE technology for mobile data transmission: a textbook. SPb.: Polytechnic University press, 2011 - 204 pages
6. Channels with fading [Electronic resource] - access Mode: https://siblec.ru/telekommunikatsii/teoreticheskie-osnovy-tsifrovoj-svyazi/15-kanaly-s-zamiraniyam (accessed 12.07.2019)
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