An algorithm is proposed for iterative symbol-by-symbol decoding of signal constructions based on orthogonal frequency-division multiplexing signals with the base increased using pseudorandom sequences and noise-immunity coding. The algorithm is based on the nonlinear transformation of the spectral components of the input implementation (constraining the spectral component amplitudes or their switching-off) in combination with the symbol-by-symbol decoding of the used class of noise-immune block codes. The results of the simulation of this decoding algorithm for the investigated signal constructions in the presence of the channel of narrow-band noise are reported and the stability of the signal constructions against the distorting effect of the discussed interference class is demonstrated. It is shown that a signal construction based on a low-density code in combination with the iterative symbol-by-symbol decoding algorithm is more efficient in terms of the noise immunity than a convolutional code in combination with the Viterbi decoding algorithm that implements the maximum likelihood rule. It is shown that the operation of switching-off the spectral components relative to their constraining is more efficient in terms of suppressing the distorting effect of the investigated noise complex.

A description of the algorithm for optimal symbol-by-symbol reception of signal structures based on block error-correcting codes in non-binary Galois fields is given. It is shown that the basis of this algorithm is the fast spectral transformation algorithm in the Walsh–Hadamard basis with the dimension of the Galois field. It is shown that the resulting complexity of the analyzed symbol-by-symbol reception algorithm is determined by the dimension of the dual code, which makes it promising to use it for block error-correcting codes with a high code rate (with low redundancy). The results of modeling the symbol-by-symbol reception algorithm for the purpose of studying the noise immunity for several frequency-efficient digital signals with quadrature-amplitude and amplitude-phase keying (with a frequency efficiency coefficient of 3, 4 and 6 bit/s/Hz) in combination with a correcting code with a parity check are presented. It is shown that the use of the symbol-by-symbol reception algorithm provides an energy gain of up to 1.5–3.0 dB in relation to the transmission and reception of the considered range of signals without coding.

The results of studies of the distorting effect for phase noise of digital signal modulators, generated by short-term instability of clock generators, on the degradation of probabilistic characteristics (bit error probability) when receiving digital signals with two-dimensional "constellations" (signals with multi-position phase shift keying and signals with amplitude-phase shift keying) are presented. Research is carried out for two models of phase noises with parameters of their power with uniform and normal laws of phase density distribution. Numerical estimates of energy losses are given, obtained by theoretical calculation and computer simulation of the algorithm for receiving digital signals using the considered models of phase noise with respect to additive white Gaussian channel noise. It is shown that the energy losses calculated using the analytical relation for these signals are fairly approximate estimates in relation to the simulation results. It is also shown that for signals with 2-position phase shift keying and for amplitude-phase keying with a keying order equal to 8, in the presence of phase noise with specified powers and distribution density laws, the bit error probabilities are practically equivalent to the theoretical values of the bit error probabilities for channel with additive white Gaussian noise - in this case, the energy loss is almost equal to 0. Signals with 8-position phase-shift keying are most susceptible to the distorting effect of phase noise - for the considered phase noise power parameter, the energy loss exceeds 1.5 dB. The method of reducing energy losses when receiving the considered series of digital signals is based on the use of clock generators with a decrease in the power of phase noise

The paper presents methods for describing distortions of signals during their propagation in transionospheric transmission lines, which cause inter-symbol and inter-channel interferences. A technique for estimating the statistical characteristics of the interference noise has been developed and their estimation for digital phase-shift keyed signals is carried out by simulating transionospheric lines. The probabilistic characteristics and asymptotic probabilities of erroneous reception of the considered signals with an increase in their frequency band are estimated using the calculated statistical characteristics for the lines of the P range.

A model of a radio line with fog, which is used to represent distortions of complex envelopes of digital signals because of the absorbing and dispersive properties of the propagation medium, has been considered. It is shown that with an increase in the frequency band of digital signals and with an increase in their order of manipulation (when using frequency-efficient signals), the influence of these distortions leads to energy losses in relation to propagation in free space. The quantitative estimation of energy losses for the digital signals used in applications with multi-position phase, quadrature-amplitude, and amplitude-phase manipulations and for a radio line with fog with a variation of its parameters has been carried out. It has been shown that for signals with multiposition phase and amplitude-phase manipulations (the frequency efficiency coefficient of the signals is 4 bits/s/Hz), the energy losses reach 3.5 and 1.0 dB, respectively.

The paper describes an algorithm for optimal symbol-by-symbol reception of signal structures based on signals with multiphase keying and block correcting codes in non-binary Galois fields. It is shown that the basis of the developed algorithm for symbol-by-symbol reception is the spectral transform in the Walsh–Hadamard basis and the resulting complexity of the reception algorithm is determined by the dimension of the dual code, which makes it promising for block correction codes with a high code rate. The results of simulation of the reception algorithm are given in order to analyze the noise immunity of several signal structures based on phase-shift keyed signals and on parity-check codes in non-binary Galois fields.

— Mathematical models of trans-ionospheric radio lines with signal phase fading because of the influence of Earth’s ionosphere have been presented. An important radio line parameter, which is its phase stationarity time, associated with the statistical characteristics of random temporal and spatial fluctuations in the electron density of ionospheric inhomogeneities, has been considered. The estimates of the time stationarity of radio lines for the maximum and average velocity of ionospheric inhomogeneities of the considered radio line models with the standard mid-latitude ionosphere parameters have been obtained.

Descriptions of mathematical models of signal propagation in forests are given. These models are based on forest representation as a continuous quasi-homogeneous medium and characterized by an effective complex dielectric constant. It is shown that when propagating along the considered channels the spectral components of digital signals acquire partial phase and amplitude shifts which causes distortions of complex envelope signals and energy losses during reception with respect to propagation in free space. The simulation was carried out using models of signal propagation in forests with typical characteristics to assess the probabilistic characteristics of reception.

Models of signal propagation in forests are presented, based on the representation of forests as a continuous quasi-homogeneous medium and characterized by an effective complex permittivity. The values of the effective permittivity are a functional of the total volumetric concentration of the components of vegetation relative to the main medium - the atmosphere, of the frequency of signals, of the electrical and taxometric characteristics of forests. It is shown that when propagating along the lines under consideration, the spectral components of digital signals acquire partial phase and amplitude shifts, which causes distortions of the complex envelopes of signals and energy losses during reception with respect to propagation in free space. Modeling was carried out using models of signal propagation in forests with typical characteristics to estimate the probabilistic characteristics of receiving digital signals with 4-level phase shift keying with frequency band extension. It is shown that for these signals with a frequency band of 10...20 MHz with a center frequency of the P-band with horizontal polarization, the energy loss with respect to propagation in free space with equivalent attenuation exceeds 1.2 dB due to the distortion of the complex envelopes of the signals. A smaller effect on the probabilistic characteristics of receiving signals with vertical polarization is also shown - the energy loss in this case reaches 0.5 dB.

A description of signal propagation along satellite ionospheric radio channels is given. It is shown that when propagating along these radio channels, the complex envelopes of digital signals are distorted with a significant expansion of their frequency band that occurs due to the dispersion properties of the Earth’s ionosphere. A model of signal distortions during propagation along these radio channels, whose effect is equivalent to linear filtering, is given. A description of the algorithm for compensating these distortions by forming a filter inverse to the filter of the ionospheric radio channel is given. The inverse filter parameters are calculated by processing the pilot signals. The condition for the correct operation of the distortion compensation algorithm has been determined: the estimated value of the period of inclusion of pilot signals in the signal stream is given, which must be consistent with the stationarity time of the radio channel link, one of its important parameters. The results of modeling the compensation algorithm when receiving digital signals with 16-position phase shift keying used in satellite information systems are presented, which are more promising than signals with binary phase shift keying in terms of frequency efficiency, but are much more susceptible to the distorting influence of the earth’s ionosphere. The possibility of compensating distortions for the considered class of signals during propagation and achieving probabilistic characteristics during reception, which practically coincide with the probabilistic characteristics during propagation in free space, is shown.

The results of the analysis for phase noise influence of generators as part of digital signal modulators on the error-performances of receiving signals with two-dimensional "constellations" (Phase Shift Keying signals, Quadrature Amplitude Manipulation signals and Amplitude and Phase Shift Keying signals) are presented. Numerical estimates of energy losses for reception are given for set of these digital signals under consideration using models of phase multiplicative noise and additive channel noise with respect to channels with only additive channel noise depending on the power of phase noise.

Резюме. Цель статьи – рассмотреть подходы к методам повышения качества прогнозирования и классификации несбалансированных данных и выбрать методы, позволяющие повысить точность классификации редких событий. При прогнозировании появления редких событий методами машинного обучения ученые сталкиваются с проблемой несоответствия качества обученных моделей их реальной способности правильно спрогнозировать появление редкого события. Предмет исследования в статье – обучение моделей при исходных несбалансированных данных. Объект исследования – информация об инцидентах и опасных событиях на объектах железнодорожного электроснабжения. Проблема несбалансированных данных выражается заметной диспропорции между типами наблюдаемых событий – количествами представителей различных классов. Методы. При работе с несбалансированными данными, в зависимости от характера задачи, качества и объема исходных данных, применяют различные методы повышения качества моделей классификации и прогнозирования Data Science. Часть этих методов направлена на работу с признаками и параметрами моделей классификации. К ним относятся методы FAST, CFS, нечёткие классификаторы, GridSearchCV и другие. Другая группа методов ориентирована на формирование репрезентативных подмножеств из исходного массив данных – сэмплов. Методы сэмплинга данных позволяют исследовать влияние пропорции классов на качество машинного обучения. В частности, в рамках настоящей статьи подробно рассматривается метод NearMiss. Результаты. Проблема дисбаланса классов при анализе количества инцидентов на объектах железнодорожного транспорта существуют с 2015 года. Несмотря на снижение доли опасных событий на объектах железнодорожного электроснабжения в течении трех лет с 2018 года, не исключен рост количества таких событий. Статистика долей опасных событий на уровне месяца демонстрирует отсутствие тренда на снижение и наличие пиков. В таких условиях эффективным периодом наблюдений за количеством инцидентов и опасных событий является месяц. Визуализация соотношения классов показала отсутствие выраженной границы между представителями класса большинства (инцидентами) и класса меньшинства (опасные события). Исследовалось соотношение классов в двух и трех измерениях в натуральных величинах и с применением метода главных компонент. Такая «близость» классов является одной из причин ошибок прогноза. В рамках работы проведен анализ имеющегося исследовательского опыта повышения качества машинного обучения при работе с несбалансированными данными. Определены и уточнены используемые для описания степени дисбалансов классов термины. Изучены сильные и слабые стороны различных методов работы с такими данными, приведено описание сильных и слабых сторон 50 методов. Из методов работы с количеством представителей классов при решении задачи классификации (прогнозирования появления) редких опасных событий на железнодорожном транспорте выбран метод NearMiss. Указанный метод позволяет проводить эксперименты с пропорциями представителей классов и методами отбора представителей классов. По результатам серии экспериментов удалось добиться повышения точности классификации редких опасных событий от 0 до 70-90%.

Signal structures based on OFDM signals and error-correcting codes resistant to the influence of spectrum-concentrated noise are described. An algorithm for receiving such signal structures with the use of weight functions is presented. It is shown by theoretic analysis and simulations that the class of Kravchenko weight functions based on atomic functions represents nearly optimal windows in terms of the minimum error reception probability.

Statistical models of satellite ionospheric radio channels are considered in the article, the influence of which causes fading of signals during their propagation (amplitude and phase variations of signals) due to random temporal and spatial fluctuations of the electron density of ionospheric irregularities. These models are based on the use of empirical laws regarding the densities of the amplitudes and phases of digital signals from the output of signal demodulators. A technique for estimating the probability of erroneous reception of digital signals with phase shift keying using the considered fading models is presented. Estimates of energy losses end errorperformance degradation during propagation along ionospheric satellite radio channels with scintillation index parameters typical for the P- and L-frequency bands, with respect to propagation in free space, have been made.

The article describes the results of an iterative algorithm for symbol-by-symbol receiving signal structures based on signals with orthogonal frequency multiplexing, pseudorandom sequences and error-correcting low-density codes. The results of emulation this iterative reception algorithm for the signal structures in the presence of channel concentrated interferences are given and the stability of signal structures to the distorting influence of the considered class of interference is shown. It is shown that a signal design based on a low-density code in combination with an iterative algorithm for symbol-by-symbol reception is more effective with respect to noise immunity compared to a convolutional code in combination with a Viterbi reception algorithm implementing the maximum likelihood rule.

The models of distortions of digital broadband signals during their propagation through transionospheric channels which are equivalent to a linear filter with an impulse response determined by a number of parameters, in particular, the central frequency of the signals, are presented. Distortions of the phase-frequency characteristics of digital broadband signals due to the dispersion properties of the ionosphere causes time scattering and the appearance of interference noise which reduces the reliability of information systems and with certain characteristics of the radiochannel destroys their operation. This determines the relevance of developing computational procedures for processing digital signals that reduce the effectiveness of this type of interference, a characteristic property of which is the linear dependence of their power on the power of information signals. The description of the algorithm for adaptive compensation of these distortions based on the use of information signals and the formation of an inverse filter is given, which corresponds to the general concept of "blind" processing. The possibility of the considered distortion compensation for digital wideband signals with phase shift keying and achievement of probabilistic characteristics of erroneous reception providing an acceptable quality of a radiochannels for information systems has been shown by means of computer simulations.