**The main results of the Department for all time**

In the Laboratory for Nonlinear Dynamics of Electronic Systems (LNDES) – *Department #17*, on the initiative by Prof. K.O. Lukin, the Head of the Department #17, more than a dozen directions of scientific research were formed and successfully developed during the entire existence of the unit. The intensity of research in these directions directly depends on the priorities set by the National Academy of Sciences of Ukraine (NASU), the availability of funding through international projects, grants, contracts and other types of scientific and technical cooperation and other circumstances.

During the period of 2017-2023, under the leadership of K.O. Lukin, Department #17 carried out two **State Research Projects:** “New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and **techniques** for their emission and reception for the purpose of application in noise radar systems for the formation of radioimages” **(**“**Rukh**“**)**, (2017 – 2021), and “Digital and analog generation and processing of chaotic and pseudorandom signals for noise and quantum radar sensors and communication systems, as well as for multi-channel systems for forming coherent images in the sub-terahertz, optical and X-ray ranges**“****(“GRIFFON”)****,** (2022 – 2026).

The following results were obtained:

- A thorough comparison of the Noise Radar (NR) concept with the concept of ‘Quantum Radar’ (QR) was carried out and as a result it was proposed to use another term: ‘Quantum Radar Sensor’ (QRS) L2[1]. In addition, to implement QR, an extremely low temperature (about 7ºK) is required, which can only be achieved in special refrigerators, which makes QR unreasonably expensive. At the same time, the NR concept is much easier to implement in the microwave, millimeter wave, and sub-Terahertz ranges L2[23]. Recently, the use of light-emitting diodes (LEDs) and the spectral interferometry technique made it possible to construct a noise reflectometer even in the infrared and optical frequency ranges, which was experimentally proven in L2[10].

It was established that the QR concept has a good perspective in the development of QRS in ultraviolet, X-ray and gamma frequency ranges of electromagnetic radiation. In addition, application of a step-like the photon’s frequency varying in QRS is also proposed and considered, which provide a range profile measurement and range resolution capability in QRS. L2[20].

- Measurement of a thin-films thickness by the method of spectral interferometry of optical random signals generated by LED sources has been experimentally proven. The measurement method developed has a fairly good error, the relative value of the limit of the confidence interval of measurements at a confidence probability of 0.95 was 0.88%, while the absolute value is 0.17 μm L2[10].

The measurement of the distance by the method of spectral interferometry and heterodyne transfer of the spectrum from the optical range to the radio range has been implemented. The possibility of using radio frequency spectrum-analyzers, the resolution of which spectrum measurement allows obtaining reflectograms (*range profiles*) of long fiber-optic communication lines, is shown. In this case, the problem of the “dead zone” is solved via using a continuous signal instead of the traditional pulse measurement mode. A prototype of an optical correlation reflectometer was developed and experimentally tested.

- A new concept for design a self-organizing SMART system for information transmission and radar monitoring of vehicles on the autobahn is proposed based on a new method of multiplex transmission of code signals with an extended spectrum previously developed by the authors for the implementation of a multiple access with spatial code separation of channels. A new method of generating unique binary pseudorandom sequences (BPS) with quasi-ideal periodic and inverse-periodic autocorrelation is proposed. The method is developed on the basis of a modified discrete chaotic mapping with two delay parameters. The structure of the BPS generated by the proposed algorithms was investigated and studied by computer simulation, and the spectra of the periods of various BPS were found. The conducted analysis showed that BPS have correlation characteristics sufficiently close to the characteristics of M-sequences.
- A new method for information transmission using a broadband chaotic signal generated by a nonlinear dynamic system with a time-delayed feedback was suggested and elaborated. This proposed novel method differs from the previously known ones in that it uses a feature of chaotic systems, which consists in the possibility of forming a periodic structure in the signal spectrum directly in the process of its generation. In the non-coherent receiver, which does not require chaotic synchronization with the transmitter, an information message decoding algorithm is implemented that is close to the optimal one, which makes it possible to achieve immunity to interference and high accuracy of data recovery.

It is shown that the correct restoration of the transmitted binary message is possible at the level of additive broadband Gaussian interference in the communication channel, which significantly exceeds the level of the useful chaotic signal. The efficiency of the information transmission system based on the spectral manipulation of a chaotic signal using the proposed algorithm was demonstrated experimentally, which confirmed the theoretical conclusions. Signal processing in the transmitter and receiver is performed in the discrete time domain, which makes the proposed technique ready for implementation in DSP and FPGA.

- An adaptation of the chaotic signal generation algorithm based on a nonlinear dynamic system with delayed feedback is proposed for its implementation in FPGA.

A noise (random) signal generator in the variable frequency bandwidth within the range of 12-16 GHz was developed and implemented by modulating the voltage-controlled oscillator (VCO) with a low-frequency random signal generated digitally in the FPGA. The algorithm for generation and digital-analog processing of broadband random signals was tested using the developed software and the main parameters of noise and deterministic signals generated were evaluated.

- The method for processing of radar signals was improved and an advanced algorithm was developed for obtaining 2D radioimages in real time, which makes it possible to obtain images of radar scenes in the format of microwave video.
- Developed models of antenna arrays based on Vivaldi antennas for multi-channel SAR imaging systems. A comparative analysis was made with the parameters of real antennas. The mutual influence of antenna array elements is analyzed. The developed antenna meets all required performance in the selected frequency range.
- The Ku-band (wavelength 2 cm)
*Microwave Video Camera Demonstrator*which is a ground-based SAR with a transmitter and a multi-channel receiver, was developed and tested, as well as the necessary algorithms for the formation of 2D SAR images in real time with a 10ms frame rate, that enables formation of microwave video with high resolution L2[7]. - A new mathematical model has been developed to analyze the processes of the chaotic oscillations generation in Gunn diode systems, taking into account mutual coupling delays in electronic systems based on several implicit methods of numerical modeling of increased accuracy and order, which are designed to obtain non-stationary solutions to the so-called “non-stiff” problems. The conditions for solving the same problems have been found.
- The mode of excitation of hybrid volume-surface waves in a Clinotron with a ribbon electron beam and a biperiodic grating was theoretically investigated. It is shown that the advantage of the hybrid mode is an increase in both feedback and radiation efficiency due to the bulk wave. The simulation results showed an output power of tens of Watts in the frequency range from 0.5 to 0.7 THz, which is provided by a beam of 0.2 A and a voltage of 17 kV. The efficiency of interaction is about 1%. A frequency tuning range of about 5% by changing the accelerating voltage was demonstrated.
- A new mechanism for the generation of ultra-high energy cosmic rays from active galactic nuclei has been proposed and studied. It has been proven that taking into account the effects of quantum gravity leads to the emergence of a trans-Planck jump in the energy density and the momentum density of matter fields. In addition, the resulting pulse density reflects structures indicating a disk-like configuration near the equator and the outflow of collimated matter from the poles. The bipolar outflow/disc structure must be an essential part of the mechanism underlying the jets/accretion discs of active galactic nuclei. For the first time, the Membrane Paradigm of Black Hole physics in the Parik-Wilchek formalism was applied to Kerr’s solutions for the General Relativity equation. The description of black holes in terms of dual microscopic degrees of freedom is generalized, which affects the interpretation of gravitational and electromagnetic wave signals in the merging processes of compact relativistic objects in binary star systems L2 [32-34,36].
- Peculiarities of tunneling dynamics in the exactly solvable N=4 model of supersymmetric quantum mechanics with a multi-well potential and broken reflection symmetry were studied. The main advantages of application of iso-spectral, exactly solvable Hamiltonians in the study of quantum mechanical systems with two- and three-well potentials are given in the study of such phenomena as
*partial localization*and*coherent tunneling destruction*L2[35].

All obtained results have no analogues in Ukraine and the world.

The main achievements of the department’s staff in the developing the **research** areas are briefly described below L2[1-44], L1[1-120]:

**Dynamical chaos**in electromagnetic resonators with non-integrable boundaries and/or nonlinear reflecting inhomogeneities, chaotic dynamics in quantum billiards.

This direction was primarily developed by K. O. Lukin and O. V. Zemlyaniy. The studies of chaotic dynamics of electromagnetic fields in resonators with nonlinear reflecting walls, as well as non-linear radiophysical systems with delay were continued. The new methods for generating of chaotic signals in radio and microwave bands for noise radar and communication systems were developed. A new method of smoothing (correction) of spectral irregularities of chaotic oscillations in the ring oscillator with the delay time dependence of the instantaneous amplitude of generated oscillations (amplitude-dependent delay) was suggested. The possibility of a significant reduction in non-uniformity of the power spectral density of generated signals has been shown. A new method of quasi-orthogonal sequences forming using multidimensional discrete maps suitable for use in modern radar and communication systems was proposed and investigated (K. O. Lukin O. V. Zemlyaniy, V. E. Scherbakov.) L1[1–5]. Further development of research in this direction L2[9, 29 -31, 38-39].

**Chaotic and regular dynamics of charge carriers**in multilayer semiconductor structures with avalanche charge multiplication; new methods for generating periodic and random oscillations in the millimeter and terahertz ranges.

K. O. Lukin, P. P. Maksymov, L. V. Yurchenko are participated in development of this direction. The study of dynamic instability of currents in sharp two-span ** p-n** junctions and the improvement of the range, energy and spectral characteristics of semiconductor generators based on them, called avalanche generator diodes (AGD), was continued. The sharp of two-span Ge, Si, and GaAs

**junctions with different impurity atom concentrations, reverse bias voltages, and minority carrier lifetimes were investigated. The range, energy and spectral characteristics of AGD are determined by the concentration of impurity atoms, the size of the doping regions, the reverse shift voltage and the lifetime of minority carriers in the multiplying layer, which makes it possible to generate oscillations in the terahertz range. The effect of direct frequency conversion in**

*p-n***structures associated with the generation of a local oscillator signal in the**

*pn-i-pn***structure itself due to the presence of positive feedback on the drift current between avalanche**

*pn-i-pn***junctions has been discovered. Semiconductor photomultiplier tubes (SPMT) based on semiconductor avalanche**

*p-n***structures, the operating principle of which is based on avalanche-cascade multiplication of the primary photocurrent (K. O. Lukin, P. P. Maksymov, H. Cerdeira) have been researched L1[6- 10]. Further development of research in this direction was carried out in L2[8-9,12-13, 22-23,39].**

*pn-i-pn*A study of regular and chaotic oscillations in strongly nonlinear electronic and radiophysical systems, including self-oscillatory systems of terahertz band, with the aim of finding new methods for generation of chaotic signals needed for the design of new kinds of noise generators for noise radars has been done. A mathematical model for the efficient time-domain simulation of complicated ultra-wide-band auto-oscillations in a series chain of large-current GaN Gunn-diode microstrip circuits with time-delay coupling has been developed. The model allows one to perform self-consistent simulation of basic nonlinear effects in this kind of circuits assuming no restriction on the waveform (spectral composition) of the emerging oscillation signals, accounting for the presence of open (radiative) microstirp sections, considering non-instant response of active devices, and imposing minimal demands on the computer resources. On the basis of nonlinear modeling of time-delay active systems in the time domain, new effects have been found such as chaotic oscillations in an open (radiative) one-dimensional multi-device propagation system without dispersion, spontaneous generation of chains of high frequency pulses, nonlinear summation of power, bistability and hysteresis in the excitation of pulses and continuous wave oscillations (L. V. Yurchenko, V. B. Yurchenko) L1[11–15]. The study of new effects in these systems L2[39], new materials for radar applications L2[12], modeling of impulse-chaotic type of oscillations for hybrid multi-band systems L2[13] was extended, and a new mathematical model was developed based on several implicit methods of numerical simulation of increased accuracy and order, intended for obtaining non-stationary solutions of so-called “non-stiff ” problems.

**Generation and coherent processing of random signals;**implementation of signal processors based on FPGA for real-time operation of radar sensors.

K. O. Lukin, O. V. Zemlyaniy, P. L. Vyplavin, S. K. Lukin were performing research in this area. The developed methods of chaotization of auto-oscillating systems were used for creation of chaotic generators of radio and microwave bands for noise radar and communication systems. The possibility of usage in radar Arbitrary Waveform Generators (AWG) and FPGA, to generate noise complex signals has been shown. K. A. Lukin proposed a new method of processing the received signal in noise radar: the “step delay” method, the essence of which is the implementation of hopping change of delay of transmitted signal in the reference channel of the noise radar and subsequent evaluation of the cross-correlation function with the use of the analog correlator, which avoids application of high-speed ADC or delay lines in the radar reference channel and at the same time provide a high range resolution without the use of wideband ADC, as well as to increase the dynamic range of the noise radar. Elaboration of the methods for generating and processing of noise signals allowed to develop and implement the concept of a fully digital noise radar (*Software Defined Noise Radar*), which allows to develop radars with generation and processing of radar signals directly into *FPGA*, which enables completely new possibilities in the design of the radar allowing quick variation the type of transmitted signals and change their parameters L2[16–20]. Further development of research in this direction was carried out in L2[7,16,27,40].

In addition, techniques of time-frequency analysis of non-stationary random signals based on their two-parameter representations and algorithms for processing such signals developed in the Department. As a result of these studies, a monograph was published (A. A. Mogyla, K. O. Lukin) L1[21].

**Antennas with pattern****synthesizing**and reconfigurable antenna based on MEMS (micro-electro-mechanical system) switches.

K. O. Lukin, V. P. Palamarchuk, M. K. Zaets were involved in developing this area.

Within this framework, various options of antennas of new type – antennas with radiation **pattern** **synthesizing** proposed by K. O. Lukin L1[22-24] were examined L1[25-26]. The basic principle of such antennas is to implement a virtual (*or real*) antenna array due to the real (*or virtual*) displacement of the emitting or receiving physical antennas with a wide antenna pattern and the subsequent application of SAR (Synthetic Aperture Radar) for the antenna pattern synthesizing, or formation of the SAR images, including three-dimensional tomographic ones. Several modifications of the proposed antennas with radiation patterns synthesizing: spiral-slit scanning antenna; waveguide-slot antenna; scanning microstrip antenna were developed in the LNDES. For Noise Radars, fixed non-switched antenna arrays with time delays between its physical antenna elements exceeding the coherence time of the probing noise signals were also proposed, which make it possible to implement cross-correlation separation (*orthogonality*) of the signals received by each antenna element in a single-channel receiver.

The proposed antennas with radiation patterns synthesizing is suitable for use in surveillance radars, in radar sensors and radar tomography, as well as for the establishment of ground Noise SAR for monitoring structural changes and registration of the pre-catastrophic states of engineering facilities. In addition, W-band and Ku-band “video cameras” for 2-dimensional and 3-dimensional real-time imaging based on them is being developed (K. O. Lukin, V. P. Palamarchuk, P. L. Vyplavin, N. K. Zaets, D. M. Tatyanko, O. V Zemlyaniy, S. K. Lukin, A.O.Shelekhov). Further research developments in this direction was done in L2[7,42].

**Noise Radar Systems**

K.O. Lukin, V. P. Palamarchuk, A. A. Mogyla, P. L. Vyplavin, V. M. Konovalov were involved in development of this area. The main goal of research in this direction is to search for fundamentally new applications of Noise Radars and the proposed new type of antennas. Several novel millimeter wave Noise Radars and sensors have been developed and tested. First of all, it should be noted the development and testing of the world’s first X-band pulse-coherent Noise SAR, with coherent processing of the noise radar returns, which can operate in two different modes: (1) Surveillance mode and (2) Arc SAR mode. This radar was developed by LNDES and supplied to *DSTA, Singapore*.

The LNDES Antenna with pattern synthesizing (Kharkiv, 2008) |
The LNDES X-band pulse-coherent Noise SAR, (Singapore, 2008) |

The world’s first Ka-band bistatic ground Noise SAR has been developed, manufactured and tested, using the proposed antennas with radiation pattern synthesizing and intended for monitoring structural changes in various objects such as large buildings, bridges, TV towers, dams, etc., in order to record eye imperceptible structural changes and, therefore, identifying their pre-catastrophic states. The proposed SARs can also be used for monitoring transport areas: highways, railway junctions, seaports, as well as airport runways (K. O. Lukin, V. M. Konovalov, A. A. Mogila, P. L. Vyplavin, V. P. Palamarchuk) L1[27-32]. Further research developments in this direction was done in L2[3,16-19,21,28].

Bistatic Ka-band ground MIMO Noise SAR |

A method has been developed for suppressing the side lobes of the cross-correlation function for short-range radar with pseudo-random signals intended for detecting slow-moving objects in optically opaque media. For the same radar, a method for coherent compensation of powerful reflections by local stationary objects has been implemented. A method has been realized for processing the signal reflected by a nonmoving person, which acquired a Doppler frequency shift due to the person’s physiological activity during the interval of several periods of his breathing (K. O. Lukin, V. M. Konovalov) L1[31-32].

**Radar****tomography and radiometry on the basis of the ground Noise SAR**

K. O. Lukin, P. L. Vyplavin, V. V. Kudryashov, V. P. Palamarchuk, M.K. Zaets and S. K. Lukin were involved in developing of this area. The formation of tomographic and radiometric images based on antennas with a radiation pattern synthesizing and the MIMO (*multiple input, multiple output)* radar concept (multiple input, multiple output – multi-channel reception, multi-channel transmission) was proposed by K. O. Lukin and was actively developed by the department staff. Methods have been elaborated for generating 2- and 3-dimensional coherent images in the MM wavelength range using MIMO Noise SAR with time-division of the received signals. SAR imaging experiments in the LNDES laboratory and field trials were carried out to obtain 2- and 3-dimensional coherent images, allowing the generation of radio holograms and radio tomograms, respectively.

The LNDES team that developed the ground MIMO Noise SAR for radar tomography: standing – P. L. Vyplavin, K. O. Lukin, V. V. Kudryashov, V. P .Palamarchuk; sitting – S. K. Lukin |

Using the developed noise ground-based 8-mm range SAR, a series of measurements were carried out on the territory of the National Reserve “Sofia of Kyiv” in order to measure displacements in the bell tower building. Coherent radioimages and differential interferograms of the Cathedral were obtained, and the stability of its interior and the outer surface of the bell tower was recorded when the ambient temperature was constant. A displacement of approximately 0.1 mm was detected when the metal elements of the building were heated during sunrise with an instrumental measurement error of no worse than 0.03 mm.

The effect of long-term stability of the probe signal to the accuracy of differential interferometric measurements using this SAR was investigated. The research made it possible to obtain an error in object displacement measurements of no worse than 10 μm with a signal-to-noise ratio of 45dB in the absence of atmospheric interference. This result agrees with the Cramer-Rao theoretical criterion for the maximum achievable precision of phase measurements. The method of augmentation of the SAR data has been proposed to depict the way of compensating the signals received through the side the side lobes L1[33-36].

In 2013, to demonstrate the capabilities of ground-based Noise SARs, experiments were implemented with capturing radioimages of folding objects. The vigilance was carried out together with the staff of I. Kozhedub Kharkiv University of the Air Force under supervision by Colonel K. S. Vasyuta.

Ka-band ground Noise SAR based on the antenna with pattern synthesizing for monostatic and MIMO-configurations was used during the field trials. SAR and tomographic images of various models of military vehicles were obtained during these trials L1[37].

a) | b) |

c) | d) |

Photographs ( |

In particular, this opens a possibility of developing radar imaging systems enabling formation of 2- and 3-dimensional images, as well as measurement of the distance to an object and estimation of its velocity in the covered operation mode. Further development of research in this direction presented in L2[7,19,21,24,40,42,44].

The proposed antenna with pattern synthesizing became the basis of the SAR radiometer designed to get radiometric images in the length-azimuth plane. This direction of research was proposed by K. O. Lukin and was developed by V. V. Kudryashov, V. P. Palamarchuk, P. L. Vyplavin and S. K. Lukin. Algorithms for radiometric SAR imaging with one or two antennas with pattern synthesizing were obtained, and first experimentally capturing the radiometric images of thermal radio sources in the plane of the range-azimuth using bistatic SAR radiometer L1[38-42].

**Optical noise reflectometers**and micro- and nano-scale detectors based on LED sources and methods of spectral interferometry.

This area of research was suggested by K. O. Lukin as a generalization of the principles of the noise radar technology for optical measuring systems and is actively developing by D. M. Tatyanko, Yu. A. Shiyan, O. V. Zemlyaniy in collaboration with Dr. M. Danailov ‘Ellectra’ Synchrotron, Trieste, Italy and with PFEE department of NURE (Kharkiv). The feasibility of the spectral interferometry method and wideband optical radiation of ultra-bright LEDs in *Coherence optical tomography* and *Low-coherence optical tomography* was shown. Optical instruments based on spectral interferometry are convenient for measuring micro- and nano-distances and generating standard frequency grids for optical telecommunication systems. The conducted research also made it possible to solve the problem of measuring the phase shifts of the envelope of modulated optical signals. New optical radiation power detectors based on trap detectors were developed, which made it possible to increase the accuracy of optical radiation power measurements and improve the characteristics of measuring instruments, including devices based on low-coherence spectral interferometry (K. O. Lukin, D. M. Tatyanko, O.V. Zemlaniy) L1[43-48]. Further development of research in this direction are shown in L2[10-11,23,27].

**New methods of wireless radio communication for vehicles**

K. O. Lukin, V. M. Konovalov, V. E. Scherbakov were involved in developing of this area. A fundamentally new method for constructing communication systems between independent vehicles on highways has been proposed, for which two US patents have been received (K.O.Lukin, V. M. Konovalov, D. Breed –*Detroit**, USA*) L1[49-50]. The key idea of the method is that in the proposed space-code division communication system, a unique code for each car is associated not with the car itself, but with *its current position* on the autobahn. In addition, a new concept for constructing a multiplex system of short-range communication between vehicles (*DSRC-VVDT *system) has been proposed. Within the framework of this concept, a mathematical model of the system has been developed that takes into account the requirements of US and European standards (K. O. Lukin, V.E. Scherbakov) L1[51–53].

**New methods in quantum theory**

K. O. Lukin proposed a new method for describing the motion of quantum mechanical (QM) particles in potential wells. The method is based on the representation of the wave function that describes the state of a QM particle in the form of a superposition of successive reflections of a spreading wave packet from the walls of the well, which makes it possible to take into account its self-interference over a finite number of reflections. The method is asymptotically consistent with the traditional quantum mechanical approach to solving such problems, based on representing the solution in the form of an expansion over the eigenstates of a particle in a potential well. A generalization of the method to the case of nonlinear boundary conditions is proposed. Together with scientists from the National Scientific Center KIPT (Prof.Yu.L. Bolotin and Dr. V. Cherkasky), a model of a compound billiard was considered, consisting of two ring billiards, chaotic and regular ones, connected by a narrow waveguide, which is suitable for studying the fundamental properties of both quantum and wave chaos. K.O. Lukin, in collaboration with Nuclear Physics Department of Odessa National Polytechnic University, developed a theory describing motion of a QM particle in a dissipative-fluctuation field at the presence of a Quantum Potential (first introduced by D. Bohm). It is shown that the Schrödinger equation describes the motion of those particles for which there is an exact compensation of the disturbance of their motion by the force of the quantum potential, which, in particular, explains the *Hamiltonian nature of modern Quantum Mechanics*. To describe the motion of those particles for which such compensation is not complete, a more complex equation containing a stochastic term should be used. In this case, the resulting equation qualitatively coincides with the well-known equation of the GWR theory (Ghirardi, Weber, Rimini), which enables a description of QM particles under condition of micro- and macro-world interaction, L1[54–57]. Further development of research in this direction was done in L2[1,20].

- Research in the field of
**Microwave Vacuum Electronics**

Research in this direction was done by K.O. Lukin in collaboration with the Department #11 IRE NASU and Seoul National University (South Korea). Vacuum microwave integrated circuits (VMICs) have been proposed for use in receiver input units of aircraft communications and radar systems. The use of VMIC will improve the resistance of receivers to the effects of ionizing radiation and powerful electromagnetic pulse radiation L1[58].

The theory of multimode and multi-frequency self-oscillations in the generators of diffraction radiation (DRGs) with an open resonator (OR) was also developed for studying both steady-states and transients of self-oscillations in such DRGs. Solutions are obtained that describe the stable mode of two-mode two-frequency generation during the interaction of an electron beam with the fundamental and higher modes of the DRG OR. Similar studies were carried out for the Clinotron, where self-modulation modes were also discovered and ways to increase the efficiency of devices of this type were found L1[59–63]. Some results of further developments in this direction published in L2[2,4-6,14-15, 22, 25-26,41].

**New methods in advanced relativistic theory**.

Book L2[43] is devoted to the application of the concept of discrete space-time to overcome the consequences of the old traditional assumptions of the space-time continuum by introducing finite differences x, t, distance and time respectively, as well as accounting the electric and magnetic dipole currents of the physical vacuum in relativistic theories.

The book’s main contribution to the discussion is our assumption that bosons, electrons, and positrons have a positive rest mass of +m_{0} or a negative rest mass of -m_{0}. If they are so close to each other that they cannot be observed individually, we get the result of “nothing observable,” or “NOTHING” for short. If particles move away from each other (for example, as a result of mutual repulsion of masses of opposite sign) and can be distinguished by an observer, the result will be “something observed” or “SOMETHING”. Therefore, the clear difference between NOTHING and SOMETHING becomes hidden if particles with positive mass +m_{0} or negative mass -m_{0} can exist, as required by the theory. Therefore, creating particles of positive mass +m_{0} and negative mass -m_{0} from nothing implies that matter with positive or negative mass can be created from nothing.

Particles or substances with the same mass sign attract each other, and particles with the opposite sign repel each other. This should lead to the assembly of galaxies with both positive and negative mass.

Another particularly important result of the book is that it may convince young scientists of the benefits of studying the finite difference effect in relativistic theories.

*We clearly understand that overcoming the influence of infinitesimals dx, dt on physical concepts may take a long time. *

The development of research in this direction will be continued in future projects.

It should be noted that all the recent achievements of the department of nonlinear dynamics of electronic systems would have been impossible without theoretical and experimental studies carried out in previous years. A number of results were also obtained by specialists from Department #17 of the IRE NASU together with other organizations within the framework of international cooperation.

Developments were carried out in the following areas (1989-2005):

**The study****of nonlinear phenomena in electronic and radiophysical systems**

A theory of self-oscillations in resonant self-oscillators with long-term interaction of electrons with a synchronous field was created, in particular, in generators of diffraction radiation (DRGs) L1[64], L2[2] which became the basis for an interactive system of computer modeling and design of these devices. These results expanded knowledge about the properties of induced diffraction and Cherenkov radiations and made it possible to patent a new method for *electromagnetic waves amplification* (K. O. Lukin L1[120]). Developed self-consistent theory of the autodyne effect in DRG (K. O. Lukin, A. B. Lebedev) L1[69]. Discovery of parametric instability of an electrons ensemble in the field with phase inversion made it possible to propose the design of an electron-vacuum generator based on this instability (K. O. Lukin) L1[64-70]. A nonlinear stationary theory of Reflex DRG with M-fold interaction of the reflected electron beam with the Gaussian field of an open resonator (OR) was constructed and the mechanism of multiple energy exchange of the electron beam with the OR field was investigated. A linear analytical theory of Reflex DRG (RDRG) with M-fold interaction of the electron beam (RDRG-M) with a Gaussian electric field distribution was also elaborated. Analytical formulas were obtained for the increment of the oscillations amplitude growth, the frequency electronic tuning and the starting current of RDRG-M. The theory is valid for arbitrary values of M, which is especially important when studying the scenario of transition from harmonic oscillations to dynamic chaos, (K. O. Lukin, P. P. Maksymov) L1[68, 71,72].

**Investigation****of the chaotic dynamics of the electromagnetic field and electrons in systems with nonlinearly reflecting surfaces and barriers**

A formulation and method for solving initial-boundary value problems of electrodynamics of a new type are proposed, when the mode approximation is not valid for description of the OR field (K. O. Lukin), and it becomes necessary to take into account the time delay in the feedback channel. For the first time, nonlinear boundary conditions were used for the components of the electromagnetic field (V. P. Shestopalov, K. O. Lukin, A. M. Sharkovsky) L1[73-75] and this approach was generalized for electronics problems and applied to the study of the main characteristics of the proposed semiconductor photomultiplier (K. O. Lukin, H. A. Cerdeira, A. A. Colavita) L1[76]. A new method for the numerical solution of initial boundary value problems for the equations of the drift-diffusion model in ** pn-i-pn**-structures with an abrupt boundary between the

*p**and*layers was proposed, (K. O. Lukin, P. P. Maksymov) L1[77-80].

**n****The study of electromagnetic dynamical chaos in a 2D rectangular cavity**

with an array of active microwave devices on the reflecting border as well as the strong nonlinear self-oscillations in a chain of Gunn diode circuits with possibility of nonlinear power combining for compact THz Devices design (V. B. Yurchenko, L. V. Yurchenko) L1[81,82 ]

**The study of the propagation of electromagnetic signals in a non-conducting medium**

A new approach to describing the propagation of non-stationary electromagnetic signals in a neutral medium with dipole currents (a highly rarefied gas formed by atomic hydrogen) is proposed. The main effects associated with the propagation of the front of an electromagnetic pulse, as well as radio signals of finite duration, at distances on the order of the size of the Universe were studied and it was proposed to use the resulting calculations to estimate distances to pulsars (H. F. Harmuth, K. O. Lukin) L1[83]. In this case, the presence of attenuation of the electrons of the atom, associated with the radiation reaction, leads to an increase in the period of oscillations in such a medium and, accordingly, to an additional contribution to the frequency Red-shift of the propagating signals.

**Development of methods for spectral, correlation and fractal processing of chaotic signals, including non-stationary ones**

A new two-parameter model of random nonstationary signals with finite energy was proposed and justified, allowing their representation in the form of an integro-summatory expansion over a system of functions, which forms an orthonormal basis in the Hilbert space of realizations of a random signal over the Hilbert space of their local samples (A.A. Mogila). Based on the results obtained, new approaches to analysis of the reflected radar signals have been developed, a new algorithm for modeling non-stationary radar signals with given probabilistic characteristics has been obtained, based on the established relationship between the correlation functions of one- and two-parameter representations (A. A. Mogila, K. O. Lukin) L1[84-86]. An algorithm for experimental evaluation of the uncertainty function of a narrow-band, ergodic, stationary noise signal using a simulator of a uniformly and rectilinearly moving point target was also justified. A measuring stand and measurement technique have been developed. With their help, an assessment was made of the resolution and accuracy of measuring range and radial speed when using signals of the type under consideration as probing signals (K. O. Lukin, A. A. Mogila, Yu. O. Oleksandrov, T. K. Lukina).

**Research of chaotic self-oscillations in generators based on BWOs and development of self-generators of chaotic oscillations. Autodyne effect in stochastic oscillation generators**

A technical solution was found that ensured a reduction in starting currents and sufficient broadband of the oscillatory system in backward wave tubes of type “O” (BWTO), which made it possible to obtain record values of the generated frequency band and the power of continuous generation of noise signals, characterized by a continuous frequency spectrum and a rapid decrease in correlations. Based on these *Weakly Resonant* BWOs, a *self-oscillator of a wideband chaotic oscillations, as well as *a nonlinear amplifier with ring delayed feedback were created for the first time.

In the course of studying the self-oscillatory modes of a Weakly Resonant BWO, the *autodyne effect *was discovered in stochastic oscillatory mode, which allowed not only to measure the distance to a target, but also its velocity. (K. O. Lukin, V. O. Rakityansky, V. V. Kulik, O. V. Zemlyaniy) L1[87-89].

**Wideband****correlation receiver****of****noise signals**

Several wideband digital-analog correlation receivers of relay type with programmable (adjustable) delay line (PDL) were developed: (1) based on universal synchronous 8-bit registers; (2) based on computer memory; (3) digital-to-analog PDL based on multiplexers and “vernier” delay line. These receivers do not contain expensive ADC. High-speed digital memory chips of random or serial access were used as the elements of PDL. The idea of building PDL operating at the carrier frequency of the Ka-band signal using the segments of waveguide channel switching its length by means of high-speed PIN-switches was implemented. Correlator of sequential type was built on its base. Using different types of digital integrated circuits, enables design of different PDL with characteristics meeting the requirements for the modern correlation receivers. In particular, they were used in the development of the first noise radar (K. О. Lukin, Yu. О. Оlexandrov, V. L.Virchenko, V. S.Korostelev, A. A. Mogyla) L1[90, 91, 94].

**Noise Radars****systems based on Chaotic Signals**

A number of research prototypes of Noise Radar systems based on the use of *chaotic* probing signals and coherent reception of their returns using the advanced methods for correlation and spectral processing were developed in the Department #17 by 2003. They are intended for such functions as car collision avoidance, sector or circular surveillance, remote monitoring of the environment and major engineering objects, etc. The first research sample Noise Radar used chaos generator was constructed in Ka-band and was successfully tested L1[92-99]. The experience acquired during its design and trials enabled development of a W-band CW Noise Radar for car collision avoidance systems (K. O. Lukin, A. A. Mogyla, Yu. O. Olexandrov, V. O. Rakityansky, V. V. Kulik) L1[90-93].

**Pulse-Coherent surveillance****Noise Radar and Noise SARs**

The world’s first X-band pulse-coherent surveillance Noise Radar has been developed in 2005. It is intended for detecting, monitoring and measurement of range, velocity and azimuth of the objects in the field of view. An important feature of this radar is that it partially implements one embodiment of the modern concept of *software-defined radar* that is to replace as much as possible radar analog units by their computer analogues, which allow forming the probing signal, processing the radar returns in a computer and displaying the results in the screen. With the aim of improving methods and equipment of Noise Synthetic Aperture Radars (SAR), the Noise SAR in which the phase center of receiving and transmitting antenna moves along an arcuate path, was created on the base of the the X-band Noise Radar hardware that is of particular interest in the development of Noise SAR due to the simplicity of implementation of such movement (K. O. Lukin, V. P. Palamarchuck, A. A. Mogyla, Yu. O. Olexandrov, P. L. Vyplavin, M. K. Zaets, V. V. Kulik).

**Differential SAR Interferometry and Noise Radars**

The first SAR with a continuous noise signal has been developed in Department #17 for joint research at the European Commission Space Research Institute (JRC EC-Ispra) in Ispra, Italy in 1998 L1[99]. The results obtained experimentally confirmed the applicability of noise signals for getting coherent images. The elaborated transmitter had a number of qualities that made it possible to use Noise SAR in differential interferometry. Department #17 developed Ka-band Noise interferometric Noise SAR for remote monitoring of the condition of the Chernobyl Nuclear Power Plant sarcophagus and other engineering structures. The realized SAR used a coherent transmit-receive path and the movement of the phase center of the transmit-receive antenna along a stably repeating trajectory. To ensure rapid movement of the phase center of the ground SAR transmitter, a new type of antennas was proposed and developed – scanning antennas with pattern synthesizing (K. O. Lukin) L1[100-102].

**Scanning Antennas with Radiation Pattern Synthesizing**

Research in this direction was started in the Department #17 in 1999 in collaboration with Department #21 (V.M. Skresanov’s group) in connection with the development of forward-looking radars. The main idea of this approach was proposed by K. O. Lukin and consists of combining the application of the concept of aperture synthesizing with the implementation of moving an elementary transceiver antenna along a fixed real aperture. The spiral-slot antenna with aperture synthesizing proposed in L1[99, 100] and developed in L1[103], is one of the possible technical solutions that implements this principle. Another embodiment of the new principle is proposed in the so-called waveguide tape scanner (Tape Scanner) L1[102]. Compared to a spiral scanner, this antenna has greater frequency bandwidth and does not require the use of a rotary joint to receive and (or) transmit a microwave signal. Later on we proposed a 2D Tape Scanner, which allows us to significantly expand the viewing sector in the azimuthal plane and provide discrete scanning of the beam in the elevation plane L1[104]. One of the promising applications of such antennas could be surveillance radars for the territory of modern airports.

**Spectral Interferometry of Stationary Random Signals**

By 2000, in the Department #17, research was carried out to generalize such a fundamental concept as coherence to the case of interference of stationary random signals in the spectral region (spectral interferometry L1[64,89]). We have proposed a modification of the double spectral processing method L1[96-98], based on measuring the frequency coordinates of spectrum maxima and minima allowing absolute measurements of distances with high accuracy. A distance meter was developed using noise signals and the method of spectral interferometry in the X-band (K. O. Lukin, V. O. Rakityansky, V. V. Kulik, A. A. Mogila) L1[96-98].

**Development of electron-optical systems (EOS) with longitudinal compression and their applications**

The theory of electron-optical systems with longitudinal compression was developed and a number of three-electrode guns with output power from a few milliwatts to hundreds of kilowatts in continuous operation were manufactured. These guns made it possible to effectively and independently control the energy and density of the electron beam with very low power consumption for the control (M. S. Zinchenko, V. I. Afanasyev). The research in the field of high-perveance electron optics and its applications were continued (V. I. Afanasyev, K. O. Lukin).

**EOS synthesis,****well-posed solution to the dense electron beam synthesis problem**

The problem of EOS synthesis was considered in its general form and precise formulation, without any approximations or restrictions on beam focusing methods. Well-posed Dirichlet-Neumann problem has been derived and numerically solved for this purpose instead of ill-posed Cauchy problem for the Poisson equation arising according to conventional approach. A possibility of synthesis of dense laminar electron (ion) beams with an arbitrarily specified spatial structure (with certain restrictions) has been shown when using strong magnetic fields of special configurations (L. V. Yurchenko, V. B. Yurchenko) L1[105,106].

**Generalization of dynamic theory of quantum particles**

A new form of equations of semi-quantum dynamics has been derived that allows one to apply the theory (of the higher than conventional quasi-classical approximation) to the analysis of electron motion in mesoscopic quantum superlattices with a possibility of transition to quasi-quantum dynamical chaos in a strong high-frequency electromagnetic field (L. V. Yurchenko, V. B. Yurchenko) L1[107,108].

**Cosmic Microwave Background anisotropy and polarization measurements**

Within the framework of the European Space Agency project on the “PLANCK Surveyor” deep-space satellite radio-telescope development for the Cosmic Microwave Background anisotropy and polarization measurements, research on the telescope beam simulations have been carried out. A method has been developed for super-fast computing of mm- and sub-mm-wave beams of large multi-reflector antenna systems with implementation of physical optics method on each reflector that is particularly important for broadband multi-beam systems with large aberrations and multi-mode (oversized) corrugated feed horns (V. B. Yurchenko) L1[109-112].

**Development of the methods for creating super-short optical and high-frequency electromagnetic pulses using the “time lens” technique**

A method for reducing the aberrations and improving the accuracy of the “time lens” systems for compressing super-short optical pulses has been proposed. The method is based on a more accurate adjustment (at the level of the third-order terms) of the effects of frequency dispersion and phase modulation used in the time-lens technique (V. B. Yurchenko) L1[113].

**Advancement of the theory of temperature-electrical instability in metals at the helium temperatures**

Appearance of multi-valued current-voltage characteristics, electrical current instability, and hysteresis in the switching effects under the conditions of temperature-electrical instability in metals in the case of the Corbino disk geometry has been carried out (V. B. Yurchenko) L1[114].

**Research on the nonlinear electron transport in semiconductors**

Theoretical analysis of the effect of nonlinear electron super-emission from a semiconductor in a strong high-frequency electromagnetic field has been carried out L1[115]. A method for increasing the efficiency of thin-film thermoelectric converters due to the use of the energy non-equilibrium electrons has been proposed, etc (V. B. Yurchenko) L1[116-119].

These results were included in the annual and final reports on the **State Research Projects: **

- “Digital and analog generation and processing of chaotic and pseudorandom signals for Noise and Quantum Radar Sensors and communication systems, as well as for multi-channel systems for forming coherent images in the sub-terahertz, optical and X-ray ranges”. State Research Project “GRIFFON”, Kharkіv, 2022 – 2026, K.O. Lukin and others.
- “New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques for their radiation and reception for the purpose of application in Noise Radar systems for the formation of radioimages”. State Research Project “Rukh” Report, Kharkіv, 2021, K.O. Lukin and others.
- “Chaotic and pseudorandom signals of the microwave and millimeter wavelength ranges, techniques for their radiation and reception for use in Noise Radars and radioimaging systems”. State Research Project “Krok” Report, Kharkіv, 2016, K.O. Lukin and others.
- “Methods for generation, radiation and reception of random and chaotic signals and their application in radar and communication”. State Research Project “Versiya” Report, Kharkіv, 2011, K.O. Lukin and others.
- “Methods for generation, radiation and processing of chaotic signals and their application in short-range radar and communication systems” State Research Project “Variant” Report, Kharkіv, 2006, K.O. Lukin and others.
- “Electrodynamics of open structures, development of sources and radio systems, including noise ones, in millimeter and submillimeter wavelength ranges.” State Research Project “Start” Report, Kharkіv, 2003, K.O. Lukin and others.
- “Dynamic chaos in radiophysical and electronic systems with nonlinear wave transformation at boundaries and its applications”. State Research Project “Kontakt” Report, Kharkіv, 2000, K.O. Lukin and others.
- “Development of new methods of chaosization of nonlinear electronic systems for design of wideband generators of stochastic oscillations and their application in radioengineering systems.” State Research Project “Triplet” Report, Kharkіv, 1995, K. O. Lukin and others.
- “Theoretical and experimental studies of nonlinear dynamics of electronic and electron-optical systems with the aim of creating effective electron guns and sources of electromagnetic oscillations.” State Research Project “Kvadro” Report, Kharkіv, 1992, K.O. Lukin and other.
- “Spatiotemporal chaos in distributed radiophysical and electronic systems.” State Research Project “Chaos – M” Report, Kharkіv, 1992, K.O. Lukin and others.

**Scientific results by chronology:**

## 2023

Annual Scientific & Technical Activities Report

**“Digital and analog generation and processing of chaotic and pseudorandom signals for Noise and Quantum Radar Sensors and communication systems, as well as ****for multi-channel systems for forming coherent images ****in the sub-terahertz, optical and X-ray ranges”**

**State Research Project “GRIFFON”**

- The algorithm for generation and digital-analog processing of broadband random signals was tested using the developed software, and the parameters of noise and deterministic signals generated were evaluated. The obtained results correspond to high international standards. (K.O. Lukin, D.M. Tatyanko, O.V. Zemlyaniy)
- Developed models of antenna arrays based on Vivaldi antennas for multi-channel systems of SAR imaging. A comparative analysis was made with the parameters of real antennas. The mutual influence of antenna array elements is analyzed. The antenna array that was developed meets the required performance in the selected frequency range. The obtained results correspond to high international standards. (K.O. Lukin, V.P. Palamarchuk, A.O. Shelekhov)
- A new mathematical model has been developed to analyze the processes of the chaotic oscillations generation in Gunn diode systems, taking into account mutual coupling delays in electronic systems based on several implicit methods of numerical modeling of increased accuracy and order, which are designed to obtain non-stationary solutions to the so-called “non-stiff” problems. The conditions for solving the same problems have been found. The results obtained meet high-level international standards and can be used to create new radar systems. (L.V. Yurchenko).
- New algorithms were developed in the MathCad and MatLab environments for processing and determining the parameters of signals with deterministic random sequences. The obtained results correspond to high international standards. (V.M. Konovalov)
- A new research approach and method is proposed, mathematical models and methods for assessing the effect of Doppler frequency shift on the quality of correlation compression of noise signals and quasi-orthogonal code sequences are developed for the technical implementation of the self-organizing SMART system of information transmission and radar monitoring of vehicles. The proposed new approach, research method and concept of a self-organizing SMART system have no analogues in Ukraine and the world. (K.O. Lukin, V.E. Shcherbakov, Yu.A. Shiyan)
- The Ku-band microwave video camera demonstrator (wavelength 2 cm), which is a ground-based SAR with a transmitter and a multi-channel receiver, was developed and tested, as well as the necessary algorithms for the formation of 2D SAR images in real time with an update rate of 10ms, that is, for the formation of microwave video with high resolution. Obtained results have no analogues in Ukraine and the world. (K.O. Lukin, V.P. Palamarchuk, D.M. Tatyanko, O.V. Zemlyaniy, A.O. Shelekhov)
- A generalization of the hydrodynamic description of Black Holes for dual microscopic degrees of freedom is obtained. The results of the study are important for the interpretation of signals of gravitational and electromagnetic waves emitted by objects of this type. Obtained results exceed high international standards. (O.J. Nurmagambetov).

## 2022

Annual Scientific & Technical Activities Report

**“Digital and analog generation and processing of chaotic and pseudorandom signals for Noise and Quantum Radar Sensors and communication systems, as well as ****for multi-channel systems for forming coherent images ****in the sub-terahertz, optical and X-ray ranges”**

**State Research Project “GRIFFON”**

** **An adaptation of the chaotic signal generation algorithm based on a nonlinear dynamic system with delayed feedback is proposed for its implementation in FPGA. The obtained results correspond to high international standards. (O.V. Zemlyaniy).

- A noise (random) signal generator in the controlled frequency band in the range of 12-16 GHz was developed and implemented by modulating the voltage-controlled oscillator (VCO) with a low-frequency random signal generated digitally in the FPGA. The obtained results correspond to high international standards. (K.O. Lukin, V.P. Palamarchuk, O.V. Zemliany).
- The method for processing radar signals has been improved and an advanced algorithm has been developed for obtaining 2D radioimages in real time, which makes it possible to obtain images of radar scenes in the format of microwave video. The obtained results exceed modern international standards. (K.O. Lukin, D.M. Tatyanko).
- A working model for estimating the spectral density of flicker noise in low-noise generators at infra-low frequencies is proposed. The obtained result corresponds to modern international standards. (V.M. Konovalov, K.O. Lukin).
- A theoretical model of broadband oscillation generation processes in the Gann diode system under frequency-dependent feedback delay conditions has been developed. The conditions for creating noise signals of increased chaotic complexity have been found. The obtained results correspond to high international standards. (L.V. Yurchenko)
- For the first time, the Membrane Paradigm of Black Hole physics in the Parik-Wilchek formalism was applied to Kerr’s solutions for the General Relativity equation. The description of black holes in terms of dual microscopic degrees of freedom is generalized, which affects the interpretation of gravitational and electromagnetic wave signals in the merging processes of compact relativistic objects in binary star systems. The obtained result exceeds modern international standards. (Nurmagambetov O.J.)

## 2021

Annual Scientific & Technical Activities Report

**“New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques for their radiation and reception for the purpose of application in Noise Radar Systems for the formation of radioimages”**

**State Research Project «Rukh»**

Authors:

K.O. Lukin, O.J. Nurmagambetov, O.V. Zemlyaniy, P.P. Maksimov, L.V. Yurchenko, D.M. Tatyanko, Yu.A. Shiyan, S.K. Lukin, A.O. Shelekhov, S.S. Ponomarenko, V.P. Palamarchuk, V.M. Konovalov, M.K. Zayets, P.G. Sushchenko, V.E. Shcherbakov

- A thorough comparison of the Noise Radar (NR) concept with the concept of ‘Quantum Radar’ (QR) was carried out and as a result it was proposed to use another term: ‘Quantum Radar Sensor’ (QRS).
- In addition, to implement QR, an extremely low temperature (about 7ºK) is required, which can only be achieved in special refrigerators, which makes QR unreasonably expensive. At the same time, the NR concept is much easier to implement in the microwave, millimeter wave, and sub-Terahertz ranges L2[23]. Recently, the use of light-emitting diodes (LEDs) and the spectral interferometry technique made it possible to construct a noise reflectometer even in the infrared and optical frequency ranges, which was experimentally proven in L2[10].
- It was established that the QR concept has a good perspective in the development of QRS in ultraviolet, X-ray and gamma frequency ranges of electromagnetic radiation. In addition, application of a step-like the photon’s frequency varying in QRS is also proposed and considered, which provide a range profile measurement and range resolution capability in QRS.
- Measurement of a thin-films thickness by the method of spectral interferometry of optical random signals generated by LED sources has been experimentally proven. The measurement method developed has a fairly good error, the relative value of the limit of the confidence interval of measurements at a confidence probability of 0.95 was 0.88%, while the absolute value is 0.17 μm L2[10].
- The measurement of the distance by the method of spectral interferometry and heterodyne transfer of the spectrum from the optical range to the radio range has been implemented. The possibility of using radio frequency spectrum-analyzers, the resolution of which spectrum measurement allows obtaining reflectograms (range profiles) of long fiber-optic communication lines, is shown. In this case, the problem of the “dead zone” is solved via using a continuous signal instead of the traditional pulse measurement mode. A prototype of an optical correlation reflectometer was developed and experimentally tested.
- A new concept for design a self-organizing SMART system for information transmission and radar monitoring of vehicles on the autobahn is proposed based on a new method of multiplex transmission of code signals with an extended spectrum previously developed by the authors for the implementation of a multiple access with spatial code separation of channels. A new method of generating unique binary pseudorandom sequences (BPS) with quasi-ideal periodic and inverse-periodic autocorrelation is proposed. The method is developed on the basis of a modified discrete chaotic mapping with two delay parameters. The structure of the BPS generated by the proposed algorithms was investigated and studied by computer simulation, and the spectra of the periods of various BPS were found. The conducted analysis showed that BPS have correlation characteristics sufficiently close to the characteristics of M-sequences.
- A new method for information transmission using a broadband chaotic signal generated by a nonlinear dynamic system with a time-delayed feedback was suggested and elaborated. This proposed novel method differs from the previously known ones in that it uses a feature of chaotic systems, which consists in the possibility of forming a periodic structure in the signal spectrum directly in the process of its generation. In the non-coherent receiver, which does not require chaotic synchronization with the transmitter, an information message decoding algorithm is implemented that is close to the optimal one, which makes it possible to achieve immunity to interference and high accuracy of data recovery.

It is shown that the correct restoration of the transmitted binary message is possible at the level of additive broadband Gaussian interference in the communication channel, which significantly exceeds the level of the useful chaotic signal. The efficiency of the information transmission system based on the spectral manipulation of a chaotic signal using the proposed algorithm was demonstrated experimentally, which confirmed the theoretical conclusions. Signal processing in the transmitter and receiver is performed in the discrete time domain, which makes the proposed technique ready for implementation in DSP and FPGA.

- A new mechanism for the generation of ultra-high energy cosmic rays from active galactic nuclei has been proposed and studied. It has been proven that taking into account the effects of quantum gravity leads to the emergence of a trans-Planck jump in the energy density and the momentum density of matter fields. In addition, the resulting pulse density reflects structures indicating a disk-like configuration near the equator and the outflow of collimated matter from the poles. The bipolar outflow/disc structure must be an essential part of the mechanism underlying the jets/accretion discs of active galactic nuclei.
- Peculiarities of tunneling dynamics in the exactly solvable N=4 model of supersymmetric quantum mechanics with a multi-well potential and broken reflection symmetry were studied. The main advantages of application of iso-spectral, exactly solvable Hamiltonians in the study of quantum mechanical systems with two- and three-well potentials are given in the study of such phenomena as partial localization and coherent tunneling destruction
- The mode of excitation of hybrid volume-surface waves in a Clinotron with a ribbon electron beam and a biperiodic grating was theoretically investigated. It is shown that the advantage of the hybrid mode is an increase in both feedback and radiation efficiency due to the bulk wave. The simulation results showed an output power of tens of Watts in the frequency range from 0.5 to 0.7 THz, which is provided by a beam of 0.2 A and a voltage of 17 kV. The efficiency of interaction is about 1%. A frequency tuning range of about 5% by changing the accelerating voltage was demonstrated.

All obtained results have no analogues in Ukraine and the world.

## 2020

Annual Scientific & Technical Activities Report

**“New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques for their** **radiation**** and reception for the purpose of application in Noise Radar Systems for the formation of radioimages”**

**State Research Project «Rukh»**

- A mathematical model has been created for the numerical calculation in the time domain of the processes of generating ultra-wideband oscillations in a system of Gunn diodes, combining several different frequency ranges. Options for devices that provide an increase in output voltage or output current under nonlinear mixing conditions of the individual diodes oscillations are considered. The results obtained correspond to high-level international standards and can be used to generate noise signals with improved spectral characteristics in a wide frequency range. (L.V. Yurchenko).
- The method of spectral interferometry with the application of noise signal modulation of the radiation of a broadband optical source was developed for measuring the lengths of optical fibers by noise reflectometers on optical fiber transmission lines; based on this method, a scheme was developed, a model of a fiber-optic reflectometer for measuring the length and distances to inhomogeneities of an optical fiber was built and investigated. The obtained results correspond to high-level international standards and allow determining the thickness of multilayer optically transparent film structures with interferometric accuracy. (K.O. Lukin, D.M. Tatyanko).
- A method of digital signal processing in optical noise reflectometers has been developed, which consists in the application of spectral analysis of noise signals and the construction of algorithms for obtaining optical fiber reflectograms based on this analysis. The obtained results correspond to international high-level standards and allow obtaining two-dimensional images of the area under investigation. (K.O. Lukin, D.M. Tatyanko, O. V. Zemlyaniy, S. K. Lukin).

## 2019

Annual Scientific & Technical Activities Report

**“New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques of their radiation and reception for the purpose of application in Noise Radar Systems for the formation of radioimages”**

**State Research Project «Rukh»**

- A method of information transmission using chaotic signals for the organization of a secure communication channel is proposed, which is based on a new method of spectral manipulation of a chaotic signal. Numerical modeling results were obtained, experimental layouts were created using AD9910 digital frequency synthesizer chips and 7Z007S programmable logic array (FPGA). The obtained result meets high-level international standards. (K. O. Lukin, O. V. Zemlyanyi, D. M. Tatyanko).
- The complex current voltage characteristic (CVC) of avalanche generator diodes (AGD) was studied, which describes the dynamics of the reverse current in the
and*p-*regions of the*n-*junction depending on the value of the constant reverse bias voltage on the diode. A mathematical model was developed for modeling the modes of amplification; mode and damping of two synchronous oscillations, as well as the conditions of their implementation in the AGD were studied. The obtained result exceeds international high-level standards. (K.O. Lukin, P.P. Maksymov).*p-n* - A new type of resonant tunneling (RTD) and laser diode (LD) circuit for visible optical communication is proposed. The scheme can convert carrier-free modulation pulses into microwaves emitted synchronously with optical pulses that also acquire microwave modulation. The conditions for the realization of these effects were found, taking into account the feedback delay between RTD and LD. The RTD-LD scheme with a resonator antenna can be used for the synchronous generation of microwave and microwave-modulated optical pulses. The obtained result exceeds high international standards. (L.V. Yurchenko).
- The concept, model and analytical expressions for calculating the power spectral density of flicker noise of low-noise generators in an arbitrary frequency range, including ultra-low frequency regions, are proposed. This provides developers of special equipment with a tool for evaluating the noise characteristics of low-noise generators in any frequency range. The obtained result meets high-level international standards. (V.M. Konovalov, K.O. Lukin).

## 2018

Annual Scientific & Technical Activities Report

**“New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques of their radiation and reception for the purpose of application in Noise Radar Systems for the formation of radioimages”**

**State Research Project «Rukh»**

- The possibility of generating a noise signal in the operating frequency range of the radar by heterodyning using a narrowband noise signal as a local oscillator signal was theoretically investigated. The expansion of the signal band of the local oscillator leads to the disappearance of the peak in the spectrum of the generated signal and a decrease in the level of the side lobes of its ACF. The conducted experiment on transferring the noise signal up in frequency without filtering the lower sideband and the frequencies of the local oscillator narrowband signal confirmed the simulation results. Obtained results have no analogues in Ukraine and the world. (K. Lukin, O. Zemlyaniy)
- A hardware and software toolkit was created to estimate the range profile when using the method of gradual change of delay in Noise Radar, and experimental estimates of the range profile were obtained with its help. Obtained results have no analogues in Ukraine and the world. (K.O. Lukin, O.V. Zemlianiy, V.P. Palamarchuk, S.K. Lukin)
- The algorithm for generating a broadband chaotic signal with a comb spectrum was created and researched, the core of which is the process of iteration of the functional difference equation, which is implemented on a real time scale. Experiments on covert transmission of information by the method of spectral manipulation were carried out. The results obtained indicate the possibility of applying the method of spectral manipulation to optical fiber communication lines. Obtained results have no analogues in Ukraine and the world. (K.O. Lukin, O.V. Zemlyaniy)
- Self-consistent modeling in the time domain of active systems with Gunn diodes connected by sections of a microstrip transmission line was performed and the self-excitation of Gunn diodes and the conditions for the occurrence of one or another type of oscillation were studied. The results highlight the importance of using a proper biasing algorithm when designing high-frequency oscillators with delay effects that can lead to different modes of oscillation. The alternative method we propose, which has no analogues in the world, allows us to carry out self-consistent computer modeling that is optimal in time and cost in various systems with parallel and serial connection of active microwave elements for the development of noise generators. (L.V. Yurchenko)
- As part of the Software Defined Radar concept, new multi-channel correlator circuits based on the Xilinx Virtex 6 FPGA programmable logic integrated circuit using the X6-1000M board from Innovative Integration Inc. were implemented and researched. A layout of a hardware-software device based on a relay correlator, which does not use the multiplication function, was developed and implemented, which significantly saves FPGA chip resources and speeds up the process of signal correlation processing. The obtained result has no analogues in the world. (K.O. Lukin, D.M. Tatyanko)
- The study of the scenario of intermittency of regular and chaotic oscillations in avalanche-generator diodes based on reverse-biased sharp Si
junctions with a discrete change in the reverse bias voltage was carried out. The obtained result has no analogues in the world and is promising for the creation of generators of broadband and ultra-broadband chaotic signals of the microwave range for their use as information carriers in communication systems, Noise Radar. (K.O. Lukin, P.P. Maksimov).*p–n*

## 2017

Annual Scientific & Technical Activities Report

**“New methods for generating chaotic and random signals of the microwave, terahertz and optical ranges of electromagnetic waves, methods and techniques of their radiation and reception for the purpose of application in Noise Radar Systems for the formation of radioimages”**

**State Research Project «Rukh»**

- The theory of the generation of oscillations in the millimeter and terahertz ranges in resonators with coupled modes has been developed, and the fundamental regularities of the generation of powerful oscillations in DRG with such systems have been studied. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin.)
- With the help of theoretical methods, it is shown that under the influence of an external signal, avalanche-generator diodes AGDs generates periodic, quasi-periodic and chaotic oscillations of the terahertz range, depending on the amplitude and frequency of the external signal. This approach can be used for the development of generators in the terahertz range. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin, P.P. Maksymov).
- New algorithms for the formation of two-dimensional and three-dimensional (tomographic) SAR images were developed, and for the first time, tomographic images were obtained using Ground Noise SAR in the 4-mm wavelength range. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin, V.P. Palamarchuk, A.A. Shelekhov.)
- A computer model of the chaos generator was developed, which is a nonlinear dynamic system with delayed feedback and a nonlinear element with a variable parameter. An experimental layout of a broadband generator of chaotic oscillations based on a microprocessor device was created and the spectral characteristics of its output signal were evaluated. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin, O.V. Zemlyaniy)
- The spectrum of the total radiation at the output of the Fabry-Perot fiber-optic interferometer, which is formed due to reflections of the broadband radiation of LED sources from multilayer structures (thin films), was analyzed. The software for processing and visualization of the results of the experiment on measuring the thickness of optically transparent layered structures by the method of spectral interferometry was developed and tested. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin, O.V. Zemlianiy, D.M. Tatyanko).
- A method of measuring the distance in an optical fiber by signal correlation processing has been developed. An optical reflectometer based on correlation was developed and experimentally investigated. The obtained experimental data show the possibility of measuring the length of the optical fiber and the distance to inhomogeneities in it. This reflectometer also does not have a “dead zone” and can be used for metrological support of fiber-optic communication lines. The obtained results have no analogues in Ukraine and the world. (K.O. Lukin, D.M. Tatyanko).
- То develop new types of generators with self-excitation of complex impulse and chaotic forms of generated signals due to multiple overreflections and nonlinear shift of waves with multiple delays of different durations
**in collaboration with scientists from**the National University of Ireland (NUI Maynuth, Ireland), a study of RF properties and measurement of complex dielectric constant and frequency dispersion of new promising low-absorbing and high-contrast dielectric materials (fluoride glasses) as dielectric elements of wave reflection and communication delay for pulse and chaotic signal generators, in the Ka and W wave ranges (in the frequency range up to 100 GHz). The obtained results have no analogues in Ukraine and the world (L.V. Yurchenko)

**Preliminary scientific results**

## 2016

Annual Scientific & Technical Activities Report

**“Chaotic and pseudorandom signals of the microwave and millimeter wavelength ranges, techniques for their radiation and reception for use in Noise Radars and radioimaging systems” State Research Project «Krok»**

- An interferometer for measuring distances in the micrometric range based on a fiber-optic Fabry-Perot interferometer and a broadband LED source of infrared radiation and the method of low-coherence spectral interferometry was developed and tested. There are no analogues in Ukraine and abroad. (K.O. Lukin, D.M. Tatyanko, L.V. Yurchenko, Yu.A. Shiyan.)
- The use of antennas with the synthesis of the directional pattern for three-dimensional scanning is proposed. The main characteristics of such an antenna are studied and its modifications are described. Technical solutions of antennas with virtual movement of the emitter are provided. There are no analogues in Ukraine and abroad. (K.O. Lukin, V.P. Palamarchuk, M.K. Zaets, L.V. Yurchenko.).
- With the help of theoretical methods, it is shown that avalanche-generator diodes AGDs under the influence of an external signal generate periodic, quasi-periodic and chaotic oscillations depending on the amplitude and frequency of the external signal. There are no analogues in Ukraine and abroad. (K.O. Lukin, P.P. Maksimov.).
- The implementation of a multi-channel parallel relay-type correlator based on FPGA is proposed and tested. At the same time, an approach was used that allows efficient use of FPGA resources and, therefore, makes it possible to increase the number of parallel channels of the correlator, which allows to increase the operating range of the Noise Radar. There are no analogues in Ukraine and abroad. (K.O. Lukin, O. V. Zemlyaniy.).
- A new method of measuring distances to vibrating objects using broadband noise signals, based on spectral interference of stationary broadband random signals, is theoretically proposed and studied. . There are no analogues in Ukraine and abroad. (K.O. Lukin, Yu.A. Shiyan.).
- New algorithms for the formation of two-dimensional and three-dimensional (tomographic) SAR images were developed, and for the first time, tomographic images were obtained using Ground Noise SAR in the 8-mm wavelength range. There are no analogues in Ukraine and abroad. (K.O. Lukin, V.P. Palamarchuk, A.A. Shelekhov.).
- A new method for generating quasi-orthogonal chaotic code signals and binary pseudo-random sequences with quasi-ideal autocorrelation has been developed, allowing to forming a virtually “unlimited” family of binary codes that fully meet the requirements of the MIMO-systems. There are no analogues in Ukraine and abroad. (V.E. Shcherbakov, K.O. Lukin.).
- A model of the interaction of the beating heart and lungs with the surface of the chest is proposed, which makes it possible to obtain estimates of the displacement of the chest during heartbeat and breathing. The simulation results were compared with scattered experimental data and showed quite satisfactory agreement. The developed model makes it possible to significantly simplify the design of relevant radar systems. There are no analogues in Ukraine and abroad. (V.M. Konovalov.).

## 2015

Annual Scientific & Technical Activities Report

**“Chaotic and pseudorandom signals of the microwave and millimeter wavelength ranges, techniques for their radiation and reception for use in Noise Radars and radioimaging systems” State Research Project «Krok»**

- The previously proposed concept of building a new type of scanning receiving-transmitting antennas – antennas with the synthesis of a directional pattern – was developed, and another variant of the antenna – a spiral-slot antenna – was investigated. The main characteristics of such an antenna are studied and its modifications are described, as well as the use of these antennas for three-dimensional scanning is proposed. Technical solutions for antennas with virtual movement of the emitter are provided. There are no analogues in Ukraine and abroad. (K.O. Lukin, V.P. Palamarchuk, M.K. Zaets, L.V. Yurchenko.).
- New sources of powerful electromagnetic oscillations – avalanche generator diodes (AGDs) based on sharp Si and GaAs
junctions at a constant reverse bias voltage – have been studied by theoretical methods. The dynamics were studied and the mode of operation of two-frequency AGDs was determined, in which the maximum energy characteristics are achieved. For the first time, regular attractors in the phase plane of integral characteristics of AGDs are given. There are no analogues in Ukraine and abroad. (K.O. Lukin, P.P. Maksimov.).*p-n* - Spectral characteristics of chaotic self-oscillations in a nonlinear dynamic system with delayed ring-type feedback were studied for the case when the inertial properties of the system elements are taken into account. An approach based on replacing a nonlinear system with a linear one with time-varying parameters was used. A method of information transmission using a chaotic signal generated by this system is proposed. The effectiveness of the considered method of information transmission to ensure covert operation of the communication system at the presence of complex interference is shown. There are no analogues in Ukraine and abroad. (K.O. Lukin, O. V. Zemlyaniy.).
- A new approach to the design of a self-organized MIMO-system for data transmission in real time between vehicles located in the highway within the radius of 1 kilometer using the EU DSRC standard is proposed. The method makes it possible to implement in practice a multiple access with spatial code distribution of channels and information transmission using broadband chaotic and unique binary pseudo-random sequences. There are no analogues in Ukraine and abroad. (K.O. Lukin, V.E. Shcherbakov.).
- Prepared and carried out experiments on SAR images formation using ground-based Noise SAR of 8-mm band. Algorithms for the formation of two-dimensional and three-dimensional SAR images in the millimeter range of wavelengths were developed. There are no analogues in Ukraine and abroad. (K.O. Lukin, V.P. Palamarchuk, A.A. Shelekhov.).