Introduction. The multipath resistance of GNSS antennas is largely determined by the gain slope of the amplitude radiation pattern at sliding angles (angles close to the horizon). The gain slope of the antenna radiation pattern is determined by the size of its ground plane. This article investigates the dependence between the gain slope and ground plane diameter R of a quadrupole antenna.

Aim. To analyse the impact of the diameter of conventional and high-impedance ground planes on the backscatter radiation pattern of a quadrupole antenna at sliding angles.

Materials and methods. Computer simulations were carried out in CAD CST Studio Suite using the methods of finite element analysis (FEM), finite difference time domain (FDTD) and template based post-processing.

Results. Quadrupole antennas with a capacitive high-impedance ground plane and a conventional flat ground plane were simulated. The dependence of the average gain slope at sliding angles on the diameter of the ground plane was determined at low f_н and upper f_в GNSS frequencies. The analysis of the down/up ratio, the rolloff gain and the multipath ratio for R= 1…20 of the wavelength of capacitive high-impedance and ground planes conventional flat was performed. It was established that higher gain slopes can be obtained using different types of ground planes; however, lower backscatter radiation values are achievable only using high-impedance structures. It was observed that the same slope of the radiation pattern (about 1 dB/°) for GNSS lower frequencies can be obtained at different R=12λ₀, and, presumably, at 20λ₀.

Conclusion. A high-impedance ground plane with a diameter of R=12λ₀  is preferable for a quadrupole antenna at low GNSS frequencies. A further increase in the ground plane size will insignificantly improve its characteristics.

Introduction. Electronically scanned antennas (ESA) appeared about a century ago. Although the methods of their design and production have been sufficiently studied, some individual parameters are yet to be revealed. One of such parameters is the minimum step of movement, along with a related parameter – the accuracy of beam alignment in a given direction. From the electrodynamic problem of radiation, it is obvious that the step is associated with the number of radiators and the accuracy of phase adjustment in analogue phase shifters, or with the quantization step in the case of using phase shifters with a discrete step.

Aim. To discover a connection between the design parameters of ESA and the step of beam steering; to investigate the dependence between the step and the parameters of the phase shifter and types of beam forming phased array circuits; to create a mathematical apparatus for calculating the minimum step of beam movement for the sum and difference radiation patterns.

Materials and methods. Analytical relations were determined for calculating the step depending on the geometric dimensions and location of the radiators. A software application was developed for calculating radiation patterns. A software and hardware complex was designed for beam control of an experimental C-band ESA.

Results. A method was developed for calculating the minimum step of ESA scanning. Mathematical relations for calculating the minimum step and accuracy of the ESA beam setting were obtained. A comparison of the experimental and theoretical data on the minimum step of movement of the sum and difference beams of a C-band ESA with the ratio D/λ=10 in the X coordinate and D/λ=5 in the Y coordinate showed good agreement.

Conclusion. The created mathematical apparatus makes it possible to calculate the minimum step of electron beam scanning with sufficient accuracy. The experimentally measured steps of the beam movement for an array of 144 elements confirmed the obtained analytical relationships. In an ESA with a small number of elements (N < 10), the minimum step of movement can be variable. The theoretically achievable minimum step of beam movement is determined by the phase shift of the least significant bit of the phase shifter and the electrical length of the antenna aperture.

Introduction. Random deviations of the antenna phase centre of a synthetic aperture radar (SAR) are a source of phase errors for the received signal. These phase errors frequently cause blurring of the radar image. The image quality can be improved using various autofocus algorithms. Such algorithms estimate phase errors via optimization of an objective function, which defines the radar image quality. The image entropy and sharpness are well known examples of objective functions. The objective function extremum can be found by fast optimization methods, whose realization is a challenging computing task.

Aim. To synthesize a versatile and computationally simple autofocusing algorithm allowing any objective function to used without changing its structure significantly.

Materials and methods. An algorithm based on substituting the selected objective function with a simpler surrogate objective function, whose extremum can be found by a direct method, is proposed. This method has been referred as the MM optimization in scientific literature. It is proposed to use a quadratic function as a surrogate objective function.

Results. The synthesized algorithm is straightforward, not requiring recursive methods for finding the optimal solution. These advantages determine the enhanced speed and stability of the proposed algorithm. Adjusting the algorithm for the selected objective function requires minimal software changes. Compared to the algorithm using a linear surrogate objective function, the proposed algorithm provides a 1.5 times decrease in the standard deviation of the phase error estimate, with an approximately 10 % decrease in the number of iterations.

Conclusion. The proposed autofocusing algorithm can be used in synthetic aperture radars to compensate the arising phase errors. The algorithm is based on the MM-optimization of the quadratic surrogate objective functions for radar images. The computer simulation results confirm the efficiency of the proposed algorithm even in case of large phase errors.

Introduction. Landing is the most challenging and dangerous part of the helicopter flight. The development of systems facilitating safe landing is a priority task for both Russian and foreign engineering companies. Landing on unprepared sites covered with snow and ice may be determined by the need to deliver cargo and ammunition in combat conditions, during search and rescue operations, evacuations of victims, etc.

Aim. Development of a method for remote assessment of the snow and ice cover based on the results of oblique sensing of the underlying surface with a radio signal with vertical polarization.

Materials and methods. In the MatLab environment, the authors conducted numerical simulations of Fresnel reflection coefficients of echo signals with vertical polarization in the 40–90 degree sensing range in the operating frequency range when solving the direct and inverse problem of reconstruction of the parameters of snow and ice layers.

Results. Intervals of the Brewster angle values were obtained at which the value of the Fresnel reflection coefficient from the boundaries of the snow and ice cover takes minimal. Thus, was found to be – 47...55°, – 55...58° and – 58...61° for dry snow, dry firn and dry ice, respectively. The depth resolution when using an ultra-wideband LFM signal with a frequency from 2 to 8 GHz is about 4 cm. The methodological error in determining the dielectric permittivity of layers by the Brewster angle comprises not more than 3 %.

Conclusion. The error in determining the relative permittivity and the depth of k layers under an increase in the RMS values of the noise level from 3.8 to 4.8 with a step of 0.1 for 100 implementations of each with a probability of 0.95 does not exceed 10 %, which confirms the validity of this method. The implementation of which allows you to automate the process of evaluating the possibility of a safe landing, thereby reducing the decision-making time and increasing the level of safety.

Introduction. Super-thin films of zinc oxide regarded as transparent electrodes can be integrated in effective semiconductor heterostructures for use in modern infrared photo electronics and solar power installations. The most important parameter of zinc oxide thin layers is their surface nanorelief, which can be effectively studied using SEM spectroscopy. SEM images allow for a quantitative description of the surface depending on the synthesis conditions using the method of multifractal analysis. Such an approach reveals quantitative relationships between the fractal parameters of the surface topography of the layers in these systems and the temperature regimes used for their final annealing in conventional sol-gel technology.

Aim. To reveal quantitative relationships between the fractal parameters of the surface topography of layers in the Zn–O & Zn–Cd–O systems and the temperature conditions of their final annealing. The MFA method was used for a quantitative description of the surface state depending on the synthesis conditions.

Materials and methods. Super-thin films in the ZnO and ZnO–CdO systems were synthesized using a modified sol-gel technology. The temperature-concentration ranges of the parameters of the modified technological process, which allows high-quality layers of the material to be reproducibly obtained on a glass substrate, were determined. The surface morphology was investigated by SEM spectroscopy depending on the temperature of the final annealing of the layers. SEM images of the surface served as a basis for multifractal analysis (MFA) of the surface area and volume of nanoforms, which are formed on the surface of the obtained layers thus determining their surface relief.

Results. Renyi’s numbers and the parameters of fractal ordering in MFA were chosen as fractal parameters for describing the nano-geometry of the layer surface. MFA was applied to the description of both the surface areas and volumes of nanoforms. Quantitative correlations between Renyi’s numbers, as well as the parameters of fractal ordering for the areas and volumes of surface nanoforms, and the temperature of the final annealing were found.

Conclusion. The numerical values of Renyi’s numbers for the surface and volume characteristics of the surface of layers were used to assess the effect of the fractality of the surface on the molar surface energy of the film. Consideration of the fractal geometry of nanoforms with their characteristic sizes smaller than 5·103μm shows the possibility of both an increase in the surface energy of the resulting film and its decrease when changing the characteristic sizes of nanoforms. The latter effect is due to the formation of a highly porous surface at the nano level

Introduction. For hazardous industries, the reliability of information and measuring equipment must ensure an almost complete absence of failure events, with their probability as low as 10-6. This requirement can be satisfied using various approaches, one of which is reservation. Reservation methods are classified into several types depending on such factors, as the operating mode of an object, failure types, frequency rate, etc. Majority redundancy schemes are rarely used in measuring equipment, particularly in measuring channels, largely because this method was initially aimed at improving the reliability of discrete digital devices. Thus far, no mathematical support for applying the method of majority reservation in measuring channels of analogue values has been developed. This gap determined the relevance of this study.

Aim. To develop a methodological support for applying the method of majority reservation with the purpose of improving the level of measurement accuracy.

Materials and methods. Both Russian and foreign sources published over the past 40 years on the topic of processing small samples when designing measuring channels for information and measuring systems were reviewed. The nonparametric Mann-Whitney rank test was applied to process small samples. Other research methods included mathematical modelling, as well as the mathematical apparatus of measurement theory andтsystems theory.

Results. A measuring module with a redundant structure was simulated. Parametric and nonparametric rank criteria were considered. An algorithm allowing identification of the failure of a channel in a measuring module with a redundant structure was developed. The computational complexity of the developed algorithm is estimated by a polynomial of the second degree.

Conclusion. The use of nonparametric rank criteria for processing small samples, as well as diagnostic situations for various combinations of these criteria, supports statistically grounded decision on the state of measuring channels. In the future, this method will be applied for diagnostic control of the serviceability of technological equipment used in fuel combustion, namely in boiler plants and installations for thermal waste destruction.