|Digital Signal Processing||
Algorithms for parametric fast Fourier transform
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Keywords: multichannel receiving system, signal processing, mutual influence, mutual impedance matrix, scaling factor, optimal weight, load impedance optimization.
A model of mutual influence between the receiving system's channels is based on changing the distance scale between the elements of a certain reference antenna system for which the matrix of mutual impedances can be calculated analytically is used in this paper. An antenna system in the form of thin vibrators is used as a reference antenna system. The multichannel receiving system considered in the work consists of an antenna system, a matching circuit, a unit of low-noise amplifiers, and a weight signal processing unit. The signal source is located in the far field. There are external antenna noise and amplifiers' inner noises in a multichannel receiving system. The matching circuit solves the problem of transmitting the maximum signal power from the antenna system to the low noise amplifier.
The analysis of the mutual influence between the channels on signal-to-noise ratio in the multichannel receiving system is carried out. An increase in the number of channels at a fixed aperture value leads to an increase in the degree of mutual influence between the channels. The receiving system's channels mutual influence leads to correlation of antenna noise and a decrease in the efficiency of signal processing. With a strong degree of receiving systems channels mutual influence the output signal-to-noise ratio is practically independent of the number of channels and is equal to the signal-to-noise ratio at the output of a single-channel receiving system. It is also noted that the choice of the optimal weight vector allows increasing the stability of the multichannel receiving system to an increase in the degree of mutual influence of the channels.
The influence of the antenna system size aperture on the output signal-to-noise ratio is considered. Increasing the size of the aperture leads to a decrease in the degree of mutual influence and to increase in the efficiency of signal receiving. However with a large number of receiving channels there is a mismatch between the elements of the antenna system and the low-noise-amplifiers.
The analysis showed the need to take into account the mutual influence between the channels when choosing the processing weight vector and the spatial structure of the system. Increasing in the degree of receiving systems channels mutual influence leads to a decrease in the signal-to-noise ratio at the output of the multichannel receiving system. Taking into account signal distortions and noise correlation caused by mutual influence during signal weighting allows increasing the value of the output signal-to-noise ratio.
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Mathematical modeling of the processes of information exchange of discrete messages via communication channels based on generating probability functions of a random variable
The article proposes a new mathematical apparatus for modeling the processes of bringing discrete messages through communication channels with decisive feedback, based on the theory of generating probability functions of a random variable. The substantiation of the validity of the use of this device for modeling a wide range of processes of information exchange of discrete messages and confirmation of the reliability of mathematical models obtained with its help is given.
At the same time, it is shown that the developed method of studying the probabilistic-temporal characteristics of delivering multi-packet messages using generating probability functions does not contradict the results obtained in the traditional way, however, it can significantly reduce computational costs and automate the process of obtaining the result.
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10. Potapov, S. E. a Study of the process of transmission of information through virtual routes in radio communications systems with moving objects [Text] / Theory and equipment telecommunications : nauch.–tekhn. jour. – Voronezh, JSC "Concern "Sozvezdie", 2019. – Vol. 3. – P. 11-23. – ISSN 1995-7009.
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The use of binary-sign stochastic quantization made it possible to carry out analytical calculation of integral operations in the transition from the analog form of modified periodograms to their calculation in discrete form. As a result, the calculation of the PSD estimate was reduced to processing discrete values of functions which are the result of the integral cosine and sine Fourier transforms for window functions. A set of such functions can be generated analytically depending on the used window functions and the requirements for spectral analysis. The main operations of processing these functions are addition and subtraction operations. The need to perform multiplication operations is practically eliminated, which increases the efficiency of spectral analysis.
The study of metrological properties of computational algorithms was carried out using numerical experiments. In this case, test sets of models of complex signals were used. The procedure of binary-sign stochastic quantization for models of complex numerical code signals was carried out on the basis of discrete-event simulation modeling. The test strategy for numerical experiments was aimed at the ability to detect weak components in complex signals. The results of the numerical experiment showed that the developed approach allows performing spectral analysis at a sufficiently low signal-to-noise ratio.
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Estimation of the probability density function of QAM signals
The purpose of this work is to estimation the probability density function of the complex envelope of the QAM signal.
The histogram method and the maximum likelihood method for estimate the probability density function of the coefficients of the complex envelope of the QAM signal are used. The results of numerical simulation are presented. It is shown that in the case of using the histogram method, a significant sample size is required, which is unacceptable when analyzing signals received from channels with fast changing characteristics. Therefore, the authors considered the application of the maximum likelihood method. An analytical expression is derived of the probability density function of the complex envelope for the case of signals with QAM-4 and QAM-16.
The results obtained can application in the problems of estimating the SNR of information signals with QAM modulation.
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Moreover, in cases where the SNR is large enough, most of the known methods, both test and blind, do not allow obtaining a "good" estimate with a small size of analyzed data. An increase in the size of the analyzed sample will lead to a decrease in the efficiency when timely deciding on the select of the optimal state of the communication system.
A problem of this kind arises in channels with fast changing propagation conditions, as well as in the functioning of an adaptive data transmission system in a difficult signal-interference environment.
The article proposes method of estimation the signal-to-noise ratio using data signals of short duration. This problem is reduced to solving the inverse problem or the problem of inverse modeling, moreover the noise component dispersion value is estimated.
The proposed method makes it possible to quickly estimate the variance of the noise component, on the basis of which current estimates of the bit error rate and signal-to-noise ratio can be obtained.
2. Smal M.S. Non-test methods for HF channel state estimation in adaptive radio links. Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg, 2018.
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The PUCCH format 0 detection algorithm modification in the fifth-generation new radio
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9. ETSI TS 38.104. 5G; NR; Base Station (BS) radio transmission and reception (3GPP, TS 38.104 version 16.4.0 Release 16).
Two variants of the formation of the transmitted signal are considered. In the first variant, the number of values of the message element is 2, in the second variant, the number of values of the message element is 4. Each value of the message element corresponds to a simplex signal. The specific bandwidth costs for the first and second options are 1.18 and 1.09, respectively, peak factor 2 and 2.63. It is shown that the second option allows for significantly better noise immunity, but the peak factor of the transmitted signal increases.
The possibility of forming and processing a high-frequency transmitted signal using a complex envelope is considered. At the same time, the main part of the algorithm of formation and processing is carried out in the low-frequency region. The transmitted signal is formed from a complex envelope using a quadrature modulator. When receiving, the complex envelope is formed using a quadrature demodulator and low-pass filters.
When modulating with a minimum shift (a known transmission method), the specific cost of the band is 1.18, the peak factor is 1.41. The noise immunity is the same as in the first variant under consideration. The second option makes it possible to obtain significantly better noise immunity than with modulation with minimal shift, but the peak factor increases.
2. Vershinin V.A. Ispol'zovanie algoritma Viterbi pri peredache perekryvajushhimisja jelementarnymi signalami [Using the Viterbi algorithm when transmitting overlapping elementary signals]// Cifrovaja obrabotka signalov [Digital signal processing].– 2020.– ¹4. (in Russian)
System identification of narrowband systems using adaptive interpolated IIR filters
When the signal passes through the structure of the interpolated adaptive filter, additional spectral components appear. To exclude additional spectral components, a low-order smoothing filter is used. Therefore, the use of an interpolated filter assumes the construction of a two-stage system, including an interpolated IIR adaptive filter and an FIR or IIR smoothing filter.
It was shown that the use of a structure consisting of an adaptive interpolated and smoothing filter gives a significant advantage over classical structures in the direct modeling of narrowband filters. With a slight increase in the computational costs required to implement the smoothing filter and some increase in the data memory, it is possible to achieve a much more accurate convergence and to increase the convergence rate of adaptation algorithms. An additional advantage is an increase in filter stability for some parameters of the adaptation algorithms.
The two-stage scheme makes it possible to construct stable adaptive filters based on classical algorithms with an improvement in the identification accuracy of an unknown system. In this work, the LMS and RLS algorithms were used without any special modifications, the changes made to the structure of the adaptive IIR filter are also minimal.
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Autofocus algorithm for increasing the resolution of on-board radar imaging systems by the sharpness optimization method
The preliminary results of the research show that the sharpness optimization radar image autofocusing method gives a better efficiency result compared to traditional image focusing algorithms. Using the methods of the golden-section search and Fibonacci numbers allows to reduce the autofocusing time of radar image by more than 5 times in relation to the direct search method. The type of image sharpness metric significantly affects the accuracy of radar image sharpness recovery. Following an in-depth analysis of preliminary research results, some recommendations on the choice of determine intensity image pixels degree parameter also are given. In particular, it was found that according to the criterion «quality/recovery time», the best metric is [I(x,y)]2 (β = 2).
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