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“Digital
Signal Processing” No. 4-2020 |
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Two-dimensional signal processing in space-frequency domain in fourier bases with variable parameters
A. V. Ponomarev, e-mail: ponva@mail.ru
Kalashnikov Izhevsk State Technical University, (Kalashnikov ISTU), Russia, Izhevsk
Keywords: theoretical foundations, information technologies of digital Fourier processing, negative effects of two-dimensional DFT, Fourier bases with variable parameters, periodicity of a two-dimensional signal, parametric periodicity of a two-dimensional signal.
Abstract
Information technologies of digital Fourier signal processing of one-dimensional (1-D) and two-dimensional (2-D) signals are effectively used in many subject areas. Discrete Fourier Transform (DFT) is the basis of digital Fourier processing. Two methods for determining 2-D DFT are considered, each of which is carried out using a two-stage application of 1-D DFT. 1-D DFT and 2-D DFT, apart from their advantages, have a number of disadvantages. These disadvantages are manifested in applications in the form of negative effects. Main negative effects are leakage effect, scalloping effect, picket fence effect, aliasing effect.
An effective method of dealing with these effects, both in one-dimensional and two-dimensional cases, is to use the operation of padding zeros to a signal. Significant disadvantages of this approach are large required memory size and the need for the great number of unproductive computations with zero elements.
There are three options for extending the reference area of a 2-D signal with zeros: zero-padding of the vertical, horizontal, and both vertical and horizontal periods of the two-dimensional signal. It is proved that each of the three options for padding zeros to the reference area samples generates its own set of Fourier bases with variable parameters.
The sets were called by the author as Fourier bases of the first, second and third type. The foundations of the theory of two-dimensional signal processing in the spatial-frequency domain in Fourier bases with variable parameters of the first type have been developed. Bases of two-dimensional exponential functions with a variable parameter of the first kind (2-D DEF-VP-1) are introduced and investigated. The basic properties of two-dimensional exponential functions of the first type with a variable parameter are proved. Algebraic and matrix forms of direct and inverse two-dimensional discrete Fourier transform with a variable parameter of the 1st type - 2-D DFT-VP-1 are introduced.
The generalization of the 2-D signal periodicity is carried out in the form of the parametric 2-D signal periodicity. The generalization of the cyclic shift of a 2-D signal in the form of a parametric cyclic shift of a 2-D signal is carried out. The main properties of the two-dimensional discrete Fourier transform with a variable parameter of the first type are investigated. The theoretical foundations of the theory of two-dimensional digital signal processing in Fourier bases with variable parameters of the first type make it possible to develop new and improve existing methods for two-dimensional Fourier - signal processing.
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30. Ponomareva O.V., Ponomareva N.V. [Filter modification based on frequency sampling by generalizing the difference equation of a non-recursive comb filter]. Modern information and electronic technologies, 2013, vol. 1, no. 14. – pp. 244 - 247.
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33. Ponomarev A.V. Systems Analysis of Discrete Two-Dimensional Signal Processing in Fourier Basis // Advances in Signal Processing. Theories, Algorithms, and System Control. Editor: Margarita Favorskaya, Lakmi C. Jain. // Springer. – 2020.
Analysis of the frequency responses of the quadrature correlation processing of complex signals
E.V. Kuzmin, e-mail: ekuzmin@sfu-kras.ru
Siberian Federal University (SibFU), Russia, Krasnoyarsk
Keywords: correlation processing, cross-correlation function, frequency response, phase shift keying signal, Fourier transform
Abstract
The frequency responses of classical correlator and two procedures for the quadrature corre-lation processing of complex signals based on the Fourier transform have been analytically ob-tained. The considered procedures imply the quadrature transformation of the incoming signal and differ in the method of forming the reference signal. The first method involves preparing the refer-ence signal in the same way as the input one, which is the most common case. The implementation of the second method is focused on a special case – processing a binary phase shift keying signal, while the reference signal is formed by samples of a pseudo-random sequence.
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Non-orthogonal multiple access: main directions and
capabilities
Bakulin M.G., Moscow, MTUCI, e-mail: m.g.bakulin@gmail.com
Kreyndelin V.B., Moscow, MTUCI, e-mail: vitkrend@gmail.com
Shumov A.P., Ryazan, RGRTU, e-mail: magnit2250@mail.ru
Keywords: Non-orthogonal multiple access (NOMA), 5G and beyond, mobile communication, radio access technology.
Abstract
Currently, non-orthogonal multiple access (NOMA) is becoming an important technology that can give fifth-generation wireless networks (5G) new capabilities to meet the new requirements for low latency, high reliability, mass connectivity, increased fairness for users, high throughput that are already planned for future generations of wireless communication systems.
Multiple access is one of the fundamental principles of wireless communication systems. It has a significant impact on the nature of the use of the available frequency spectrum, throughput, delay in communication systems. For cellular systems, multiple access is a technology by which multiple users use shared radio resources to establish links with a base station (BS). Some of the widely used multiple access technologies in previous generations of cellular networks include time division multiple access (TDMA), frequency division multiple access (FDMA), code division multiple access (CDMA). These technologies refer to the so-called orthogonal multiple access (OMA). In OMA, user access is orthogonal, and ideally, users should not interfere with each other when sharing a communication channel.
The key idea behind NOMA is to remove the orthogonality condition when serving multiple users. The NOMA principle is a general concept, and several recently proposed 5G multiple access schemes can be considered as its special cases. This article discusses the basics of power-domain NOMA - NOMA in the power domain - with one or many antennas under up and down line conditions, discusses the basic principles of code-domain NOMA - NOMA in the code domain. The article discusses various resource allocation technologies, such as pairing users and placing capacities for systems with NOMA, discusses the main forms of cooperative NOMA and its variants.
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Optimal receiver for detecting set of signals with unknown parameters
V.A. Pakhotin, R.V. Simonov, K.V. Vlasova , S.V. Petrov, e-mail: VPakhotin@kantiana.ru
Keywords: radar, optimal reception, maximum likelihood method, optimal receiver, signal detection, probability of detection, signal resolution.
Abstract
The problem of separate detection of a set of signals with unknown parameters is considered. The known optimal receiver is unable to solve this problem. The problem is the need to pre-evaluate and resolve unknown signal parameters based on the information contained in the received implementation. A new structure of an optimal receiver is proposed, the basis of which is the transformed functionality of the likelihood ratio. Together with likelihood equations, it allows you to minimize the loss function, solving the problem of resolving signals and evaluating their complex amplitudes. Provided that the copy contains more signals than in the received implementation, the problem of estimating the number of signals contained in the received implementation is additionally solved. Output of proposed optimal receiver is vector of complex amplitudes, part of which components estimates amplitudes of signals contained in received implementation, and part is connected with level of noise maximums. When using the Neumann-Pirson test, the probability of false alarm is limited to a small value (percentage). In this case, exceeding the threshold level by the individual components of the amplitude vector determines their number and the fact of their presence in the received implementation. The proposed optimal receiver, when operating in sliding mode, allows setting a scale on the indicator for separate estimation of probability of detection of signals in the received implementation. The basis of theory and results of model studies of potential possibilities of the proposed optimal receiver are presented. It is shown that in case of mutual attenuation of two signals, their separate detection is more effective than joint detection.
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Calculating the time of entering synchronism at the synchronization stage using a cyclic character prefix in LTE OFDMA technology
T.P. Kiseleva, Post-graduate student of the Department of radio systems of the Moscow technical University of communication and Informatics (MTUCI), Russian Federation, Moscow e-mail: golzev2011@yandex.ru
Keywords: LTE OFDM, Zadoff-Chu sequence (ZC), synchronization, timing,correlation function, OFDM symbol, cyclic prefix, Rayleigh channel, signal-to-noise ratio (SNR).
Abstract
In this paper, a comparative analysis of the time of entering into synchronism at the synchronization stage by the correlation function of the cyclic prefix (CP) of the OFDM symbols of LTE technology is carried out in the case of building the CP on binary pseudo – random sequences (PSP) transferred to the interval of the cyclic prefix from the end of the characters, or building the CP on the basis of short sequences of Zadoff – Chu (ZC (u, n)).
The calculation formulas for calculating the time of entering into synchronism when used in relation to the correlation functions of the CP are given, while the energy values of the signal – noise ratio (SNR) for the correlation functions of the CP are proposed to be replaced by the ratio of the Merit- factor, which in this paper corresponds to the value of the ratio of the maximum value of the correlation function of the CP to the modulus of the average value of the side lobes (MFs). In the calculations of the time of entering into synchronism, we used calculations of the probability of correct detection with the values of the thresholds obtained from the expression of the probability of a false alarm equal to F=10-3, 10-4, 10-5, 10-6.
Since the MFs relations differ for different values of the roots u of the ZC(u,n) sequences, the sequences with the roots (indices) u were selected in the simulation process, allowing to obtain the maximum value of the MFs.
The results of calculations for the specified false alarm probabilities for the ideal (without interference) and Rayleigh channel with the addition of additive white Gaussian noise (AWGN) at the values of the SNR=10dB, 0dB ratios are shown in tables and graphs for the case of averaging the number of OFDM symbols over the duration of half an LTE frame (70 symbols) of the downlink (DL) direction in the band of the central 72 subcarriers of the frame for OFDM symbols that do not contain service information of the base cellular station.
Mathematical modeling of CP correlation functions was performed in the MATLAB operating environment for sequences with the number of elements N=9,11,13,17,19,31,37.
References
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Using the Viterbi algorithm when transmitting overlapping elementary signals
V.A. Vershinin,
Russia, Rybinsk
e-mail: vershinin-vladimir@yandex.ru
Keywords: overlapping signals, intersymbol interference, frequency efficiency, complex envelope, Viterbi algorithm, noise immunity.
Abstract
Frequency efficiency, noise immunity, and implementation complexity are the most important parameters for transmitting binary messages. One of the ways to increase frequency efficiency is the conscious or controlled introduction of intersymbol interference into the transmitted signal with an acceptable reduction in noise immunity. The purpose of the work is to consider one of the ways to implement this direction using the Viterbi algorithm in the reception. The variants of the transmitted signal formation and reception are considered. The noise immunity of the transmission under the influence of interference in the form of white noise is estimated. The considered method of transmitting binary messages provides a fairly good frequency efficiency without using a spectrum shaper with an acceptable reduction in noise immunity.
Two message elements (a pair of elements) are transmitted simultaneously using orthogonal signals of duration T. Pairs of message elements are received for transmission with an interval of T / 2. Thus, the signals corresponding to the sequentially transmitted pairs of elements partially overlap in time by the amount of T / 2. As a result, there is intersymbol interference at reception.
The frequency band in which 99% of the signal power is concentrated, 2.36/T, the specific cost of the band is 0.59, the peak factor is 2. For comparison, with minimum shift modulation (MSK), the frequency band is 1.18/T, the specific cost of the band is 1.18, the peak factor is 1.41. Thus, the transmission method under consideration has twice the unit cost, but 1.41 times the peak factor.
When transmitting in the high-frequency range, it is advisable to form and process the transmitted signal using a complex envelope.
The reception uses the Viterbi algorithm, which implements the maximum likelihood rule and minimizes the probability of error in intersymbol interference. The noise immunity of the considered transmission method is somewhat worse than with MSK.
References
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The usage of three signal fetures for classification and blanking of discrete interfering reflections
V.G. Bartenev, Russian Technological University MIREA, Moscow, Russia, e-mail: bartenev_v@mirea.ru
Keywords: doppler velocity, inter-frequency correlation coefficient, effective scattering surface.
Abstract
The first known method for blanking signals of discrete interfering reflections, based on the single formation about speed of the object, with it classification, if it has a small radial velocity in analyzed range element [1]. Therefore, this signal is blanked, reducing the flow of false marks at the output of the radar. The main disadvantage of this method is its low efficiency, due to the usage of a limited number of pulses. In addition, an attempt to set the highest possible speed threshold to increase the efficiency of this method which leads to an increase in the probability of blanking useful targets with a low radial speed. A two-frequency method of classifying and blanking discrete correlated interference is more efficient. This method is based on processing the reflected signals at each carrier frequency of the radar in the form of two observation samples in each element of the range and includes the formation of estimates of the interperiod Doppler phase difference, followed by their subtraction for unambiguous measurement of the speed of the detected discrete object [2]. The estimate of the inter-frequency inter-period phase difference obtained in this way is compared with the phase threshold (in fact, with the speed threshold), on the basis of which a decision is made to block the reflected signals from slowly moving interfering point objects, if this threshold was not exceeded. Although this method allows for more efficient classification of signals due to the higher accuracy of estimating the interperiod phase difference at each radar carrier frequency, however, this method with a single speedl feature is characterized by the lack of blanking useful targets with low radial velocities.
To exclude blanking of useful signals from targets with low radial velocities for signals received at two carrier frequencies, was added the formation of a second signal feature in the form of a module of the inter-frequency correlation coefficient, which is used to estimate the longitudinal size of the classified objects and which, if not exceeding the threshold, is classified as an interfering signal based on the correlation feature. In this case, the speed and correlation coefficient are assigned logical units, the coincidence of which is recorded in each element of the range using the logical function "And", on the basis of which a decision is made to blank the reflected signal in this element of the range [3]. Although this method allows using speed and correlation features to increase the efficiency of blocking interfering reflections, however, not taking into account the power of the reflected signal can lead to erroneous classification, when signals from a target with a small radial speed and a large size can be taken as interfering reflections, for example, an airliner flying from an angle relative to the radar.
In order to exclude blanking of useful signals from targets with small radial velocities and a large longitudinal size, it is proposed to form a third signal feature in the form of an estimated power of the received signals (an effective scattering surface), which is compared with the threshold in each element of the rang, if this threshold is not exceeded. And only after combining the correlation, speed, and the effective scattering surface, if they coincide, a decision is made to blank the reflected signal in this range element [4]. This article is devoted to this method.
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Method for increasing the sensitivity of video cameras based on binning with restoration of spatial resolution
V.N. Drynkin, e-mail: drynkinv@gosniias.ru
T.I. Tsareva, e-mail: tsareva@gosniias.ru
U.V. Pavlov, e-mail: pavlov@gosniias.ru
D.V. Mysin, e-mail: mysin@gosniias.ru
State research institute of aviation systems (FGUP “GosNIIAS”), Russia, Moscow
Keywords: digital image processing, increasing the sensitivity of video cameras, procedure of binning of adjacent pixels.
Abstract
The reduced resolution is a limiting factor in the use of binning in video cameras and video surveillance systems.
The article describes an experimentally tested method for increasing the sensitivity of video cameras, based on a method for increasing the sensitivity and frame rate using the procedure for binning adjacent pixels of the photodetector matrix for a sequence of video frames, followed by restoring the spatial resolution.
In the proposed method, the sequence of video frames subjected to binning is shifted by at least one pixel of the radiation receiver matrix diagonally so that a space-time grid with a staggered arrangement of samples in the adjacent video frames is formed. This allows us to restore the spatial resolution of video frames using a three-dimensional interpolation spatiotemporal low-pass filter with the passband of the three-dimensional spatial-frequency response in the form of an octahedron.
The synthesized three-dimensional interpolation spatiotemporal low-pass filter is a cascade connection of a three-dimensional, two-dimensional, and one-dimensional recursively-non-recursive blocks.
Experiments with Foucault calibration targets have shown that when using 2×2 binning, the original resolution is restored by more than 80%, and when using 4×4 binning – by at least 40%.
The proposed method for increasing the sensitivity of video cameras can be used in various fields of image processing, including video surveillance systems, technical vision, medicine, non-destructive testing, etc.
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