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Effective user service strategies in a multi-user MIMO system 多用户MIMO系统中有效的用户服务策略
Q3 Mathematics Pub Date : 2019-10-04 DOI: 10.31799/1684-8853-2019-4-69-81
A. Gorbunova, E. Medvedeva, Yuliya Gaidamaka Yu. V., V. Shorgin, K. Samouylov
Introduction: One of the main advantages of multiple antenna systems is the support of multi-user connections, simultaneouslytransmitting parallel data streams. This can significantly increase the overall system throughput. However, the spectral efficiency can be additionally increased through the usage of various dynamic strategies which take into account the current state of the system.Here we propose a method to evaluate the effectiveness of such strategies with the help of appropriate mathematical models. Purpose:Development of mathematical models for a multi-user MIMO system which would allow you to evaluate the average delay of a filetransfer. Results: Mathematical models of the MIMO system are presented in the form of discrete/continuous time queuing systemsfor three user service strategies. We provide formulas for estimating the average file transfer delay in a closed form, which simplifynumerical analysis as compared to the well-known methods using mathematical models in continuous time. This method allows you tofind the most effective strategy with less computational complexity. Another advantage of the constructed models is the opportunityof further research on the effect of file length distributions on the file transfer delay. The conclusions we made about the effectivenessof each strategy are consistent with our earlier work, which is confirmed by a numerical example. Practical relevance: The developedmathematical models for a multi-user MIMO system can be used to set the operating parameters of a real wireless MIMO system.
简介:多天线系统的主要优点之一是支持多用户连接,同时传输并行数据流。这可以显著提高整个系统的吞吐量。然而,可以通过使用考虑系统当前状态的各种动态策略来额外提高频谱效率。在此,我们提出了一种借助适当的数学模型来评估此类策略有效性的方法。目的:开发多用户MIMO系统的数学模型,使您能够评估文件传输的平均延迟。结果:针对三种用户服务策略,以离散/连续时间排队系统的形式给出了MIMO系统的数学模型。我们提供了以闭合形式估计平均文件传输延迟的公式,与使用连续时间数学模型的已知方法相比,该公式简化了数值分析。这种方法使您能够找到计算复杂度较低的最有效策略。所构建的模型的另一个优点是有机会进一步研究文件长度分布对文件传输延迟的影响。我们对每种策略的有效性得出的结论与我们之前的工作一致,并通过一个数值例子得到了证实。实际相关性:开发的多用户MIMO系统的数学模型可用于设置实际无线MIMO系统的操作参数。
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引用次数: 1
Analysis of frequency resource for FHSS mode FHSS模式的频率资源分析
Q3 Mathematics Pub Date : 2019-10-04 DOI: 10.31799/1684-8853-2019-4-62-68
Sergey Dvornikov, Sergey Dvornikov, A. Pshenichnikov
Introduction: When the radio frequency spectrum is as busy as it is today, it is especially important to ensure effective functioningof radio systems under various signal and interfering conditions. One of the research fields is radio frequency resource management.Purpose: Developing a system of proposals for choosing a frequency resource for radio system operation in the mode of frequencyhoppingspread spectrum (FHSS). Results: On the basis of the developed analytical apparatus, we have specified the conditions forpreliminary testing of working frequencies in the direct response mode in FHSS radio channels. Practical conditions are substantiatedfor achieving the required performance indicators from the parameters of the preliminary frequency testing process. A statementis proved that determines how the improvement of timely message delivery in a radio link with a pseudo-random adjustment of theoperating frequency depends on the growth of the array of allocated frequencies and on the speed of the program adjustment. A featureof the newly developed theoretical approaches is the formalization of radio system performance indicators based on the ratio of the timewithout taking into account the preliminary testing processes to the time required to implement the test mode with a fixed amount of aninformation message. The chosen criterion for selecting a frequency group is the permissible level of errors in the received test sequencewhose evaluation determines the group of specified unsuitable frequencies. On the basis of the conducted simulation, we have revealedthe relationships between the number of unsuitable frequencies and the gains provided by the timeliness of information transfer,depending on the performance indicators found during the testing of the working frequencies. Practical relevance: The developedsolutions, in their entirety, provide a better timeliness of message delivery in radio systems in FHSS mode.
导言:当无线电频谱像今天这样繁忙时,确保无线电系统在各种信号和干扰条件下有效工作就显得尤为重要。其中一个研究领域是射频资源管理。目的:为在跳频扩频(FHSS)模式下的无线电系统运行选择频率资源制定一套建议系统。结果:在研制的分析仪器的基础上,确定了FHSS无线电信道直接响应模式下工作频率的初步测试条件。根据初步频率试验过程的参数,确定了实现所需性能指标的实际条件。一个命题证明了在工作频率伪随机调整的无线电链路中,消息及时传递的改进如何取决于分配频率阵列的增长和程序调整的速度。新开发的理论方法的一个特点是基于时间的比率形式化无线电系统性能指标,而不考虑初步测试过程与使用固定数量的信息消息实施测试模式所需的时间。选择频率组的标准是接收到的测试序列中的允许误差水平,其评估决定了指定的不合适频率组。在进行仿真的基础上,我们揭示了不合适频率的数量与信息传递的及时性所提供的增益之间的关系,这取决于在测试工作频率期间发现的性能指标。实际意义:所开发的解决方案总体上为FHSS模式下的无线电系统提供了更好的消息传递时效性。
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引用次数: 2
ОЦЕНКА КОНФИДЕНЦИАЛЬНОСТИ СИСТЕМЫ ПЕРЕДАЧИ ИНФОРМАЦИИ НА ОСНОВЕ ХАОТИЧЕСКОГО ГЕНЕРАТОРА С ЗАПАЗДЫВАНИЕМ И ПЕРЕКЛЮЧАЕМЫМ ВРЕМЕНЕМ ЗАДЕРЖКИ 基于延迟和切换时间的混乱生成器对信息传输系统隐私的评估
Q3 Mathematics Pub Date : 2019-10-04 DOI: 10.31799/1684-8853-2019-4-54-61
V. I. Ponomarenko, Elena Navrotskaya, Danil Kul’minskii, Mikhail D. Prokhorov
Introduction: Communication systems based on the use of dynamical chaos have a number of positive features. Dynamical chaoshas the properties of random processes, which allows systems based on it to ensure the information transmission confidentiality.However, a quantitative security assessment of such systems is a complicated problem, since the methods for evaluating cryptographicstrength are well developed only for the classical encryption algorithms. Purpose: Development of a method for quantitative estimationof confidentiality of a binary signal hidden transmission in a communication system based on a chaotic time-delay oscillator withswitchable delay time. Results: A method is proposed for estimating the confidentiality of a binary information signal transmissionin a communication system using a chaotic time-delay oscillator with switchable delay time as a transmitter. The method is based onestimating the power of the key space for the chaotic communication system under study. We have considered the cases when sometransmitter parameters are known, and the most general case when all the transmitter parameters are unknown. A communicationsystem based on dynamical chaos may have a much higher confidentiality than the classical cryptographic algorithm using a cipher witha key length of 56 bits, but is significantly inferior in terms of cryptographic strength to a cipher with a key length of 128 bits. Practicalrelevance: The proposed method allows us to obtain a quantitative estimation of confidentiality of communication systems based ondynamical chaos, and compare it with the known strength of classical cryptographic algorithms.
基于动态混沌的通信系统有许多积极的特点。动态混沌具有随机过程的特性,使得基于动态混沌的系统能够保证信息传输的保密性。然而,这种系统的定量安全评估是一个复杂的问题,因为评估密码强度的方法只针对经典的加密算法。目的:建立一种基于可切换时延混沌振荡器的通信系统中二进制信号隐藏传输保密性的定量估计方法。结果:提出了一种估计通信系统中二进制信息信号传输保密性的方法,该通信系统使用具有可切换延迟时间的混沌时滞振荡器作为发射机。该方法基于所研究的混沌通信系统的密钥空间功率估计。我们考虑了某些发射机参数已知的情况,以及所有发射机参数未知的最一般情况。基于动态混沌的通信系统可能比使用密钥长度为56位的经典密码算法具有更高的机密性,但在加密强度方面明显不如使用密钥长度为128位的密码算法。实际意义:提出的方法使我们能够获得基于动态混沌的通信系统机密性的定量估计,并将其与已知强度的经典密码算法进行比较。
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引用次数: 0
Encoder-decoder models for recognition of Russian speech 俄语语音识别的编码器-解码器模型
Q3 Mathematics Pub Date : 2019-10-04 DOI: 10.31799/1684-8853-2019-4-45-53
Nikita Markovnikov, I. Kipyatkova
Problem: Classical systems of automatic speech recognition are traditionally built using an acoustic model based on hidden Markovmodels and a statistical language model. Such systems demonstrate high recognition accuracy, but consist of several independentcomplex parts, which can cause problems when building models. Recently, an end-to-end recognition method has been spread, usingdeep artificial neural networks. This approach makes it easy to implement models using just one neural network. End-to-end modelsoften demonstrate better performance in terms of speed and accuracy of speech recognition. Purpose: Implementation of end-toendmodels for the recognition of continuous Russian speech, their adjustment and comparison with hybrid base models in terms ofrecognition accuracy and computational characteristics, such as the speed of learning and decoding. Methods: Creating an encoderdecodermodel of speech recognition using an attention mechanism; applying techniques of stabilization and regularization of neuralnetworks; augmentation of data for training; using parts of words as an output of a neural network. Results: An encoder-decodermodel was obtained using an attention mechanism for recognizing continuous Russian speech without extracting features or usinga language model. As elements of the output sequence, we used parts of words from the training set. The resulting model could notsurpass the basic hybrid models, but surpassed the other baseline end-to-end models, both in recognition accuracy and in decoding/learning speed. The word recognition error was 24.17% and the decoding speed was 0.3 of the real time, which is 6% faster than thebaseline end-to-end model and 46% faster than the basic hybrid model. We showed that end-to-end models could work without languagemodels for the Russian language, while demonstrating a higher decoding speed than hybrid models. The resulting model was trained onraw data without extracting any features. We found that for the Russian language the hybrid type of an attention mechanism gives thebest result compared to location-based or context-based attention mechanisms. Practical relevance: The resulting models require lessmemory and less speech decoding time than the traditional hybrid models. That fact can allow them to be used locally on mobile deviceswithout using calculations on remote servers.
问题:传统的自动语音识别系统是使用基于隐藏马尔可夫模型和统计语言模型的声学模型来构建的。这种系统显示出很高的识别精度,但由几个独立的复杂部分组成,这可能会在构建模型时造成问题。最近,一种使用深度人工神经网络的端到端识别方法得到了推广。这种方法使得只使用一个神经网络就可以很容易地实现模型。端到端模型软化在语音识别的速度和准确性方面表现出更好的性能。目的:实现用于连续俄语语音识别的端到端模型,在识别精度和计算特性(如学习和解码速度)方面对其进行调整,并与混合基础模型进行比较。方法:使用注意力机制创建语音识别的编码器模型;应用神经网络的稳定化和正则化技术;增加训练数据;使用单词的部分作为神经网络的输出。结果:在不提取特征或使用语言模型的情况下,使用注意力机制识别连续俄语语音,获得了编码器-解码器模型。作为输出序列的元素,我们使用了训练集中的部分单词。所得到的模型不能超过基本的混合模型,但在识别精度和解码/学习速度方面都超过了其他基线端到端模型。单词识别误差为24.17%,解码速度为实时的0.3倍,比基线端到端模型快6%,比基本混合模型快46%。我们证明了端到端模型可以在没有俄语语言模型的情况下工作,同时证明了比混合模型更高的解码速度。在没有提取任何特征的情况下,在原始数据上训练得到的模型。我们发现,对于俄语,与基于位置或基于上下文的注意力机制相比,混合类型的注意力机制给出了最好的结果。实际相关性:与传统的混合模型相比,所得到的模型需要更少的内存和更少的语音解码时间。这一事实可以让它们在移动设备上本地使用,而不需要在远程服务器上进行计算。
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引用次数: 1
An exact solution method for Fredholm integro-differential equations Fredholm积分微分方程的精确解方法
Q3 Mathematics Pub Date : 2019-08-22 DOI: 10.31799/1684-8853-2019-4-2-8
Kyriaki D. Tsilika
Introduction: Linear boundary value problems for Fredholm ordinary integro-differential equations are seldom consideredwith integral boundary conditions in the literature. In our case, integro-differential equations are subject to multipoint or nonlocalintegral boundary conditions. It should be noted that finding exact solutions even for multipoint problems or problems with nonlocalintegral boundary conditions with a differential equation is a difficult task. Purpose: Finding the uniqueness and existencecriterion of solutions for Fredholm ordinary integro-differential equations with multipoint or nonlocal integral boundary conditionsand obtaining exact solutions in closed form of such problems. Results: Within the class of abstract operator equations, for thespecial case of Fredholm integro-differential equations with multipoint or nonlocal integral boundary conditions, a criterion for theexistence and uniqueness of an exact solution is proved and the analytical representation of the solution is given. A direct methodanalytically solving such problems is proposed, in which all calculations are reproducible in any program of symbolic calculations.If the user sets the input parameters and the initial conditions of the problem, the computer codes check the conditions of existenceand uniqueness and of solution generate the analytical solution. The stages of the solution method are illustrated by twoexamples. The article uses computer algebra system Mathematica to demonstrate the results.
Fredholm常积分-微分方程的线性边值问题在文献中很少考虑积分边界条件。在我们的例子中,积分-微分方程受制于多点或非局部积分边界条件。需要注意的是,即使对于多点问题或具有非局部积分边界条件的微分方程问题,找到精确解也是一项困难的任务。目的:寻找具有多点或非局部积分边界条件的Fredholm常积分-微分方程解的唯一性和存在性判据,并得到该问题的闭形式精确解。结果:在抽象算子方程中,对于具有多点或非局部积分边界条件的Fredholm积分微分方程的特殊情况,证明了精确解存在唯一性的判据,并给出了解的解析表示。本文提出了一种直接的分析方法来解决这类问题,其中所有的计算在任何符号计算程序中都是可重复的。如果用户设置问题的输入参数和初始条件,计算机代码检查解的存在唯一性和解的存在唯一性条件,生成解析解。通过两个实例说明了求解方法的各个阶段。本文利用计算机代数系统Mathematica对结果进行了演示。
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引用次数: 1
Models of decision support in socio-cyber-physical systems 社会-网络-物理系统中的决策支持模型
Q3 Mathematics Pub Date : 2019-06-21 DOI: 10.31799/1684-8853-2019-3-55-70
A. Smirnov, T. Levashova
Introduction: Socio-cyber-physical systems are complex non-linear systems. Such systems display emergent properties. Involvement of humans, as a part of these systems, in the decision-making process contributes to overcoming the consequences of the emergent system behavior, since people can use their experience and intuition, not just the programmed rules and procedures.Purpose: Development of models for decision support in socio-cyber-physical systems.Results: A scheme of decision making in socio-cyber-physical systems, a conceptual framework of decision support in these systems, and stepwise decision support models have been developed. The decision-making scheme is that cybernetic components make their decisions first, and if they cannot do this, they ask humans for help. The stepwise models support the decisions made by components of socio-cyber-physical systems at the conventional stages of the decision-making process: situation awareness, problem identification, development of alternatives, choice of a preferred alternative, and decision implementation. The application of the developed models is illustrated through a scenario for planning the execution of a common task for robots.Practical relevance: The developed models enable you to design plans on solving tasks common for system components or on achievement of common goals, and to implement these plans. The models contribute to overcoming the consequences of the emergent behavior of socio-cyber-physical systems, and to the research on machine learning and mobile robot control.
社会-信息-物理系统是复杂的非线性系统。这样的系统显示出涌现的特性。作为这些系统的一部分,人类参与决策过程有助于克服突发系统行为的后果,因为人们可以利用他们的经验和直觉,而不仅仅是编程的规则和程序。目的:发展社会-网络-物理系统中的决策支持模型。结果:建立了社会-信息-物理系统中的决策方案、决策支持的概念框架和逐步决策支持模型。决策方案是,控制论组件首先做出决定,如果他们不能做到这一点,他们会寻求人类的帮助。阶梯式模型支持社会-网络-物理系统组成部分在决策过程的常规阶段做出的决策:态势感知、问题识别、备选方案的开发、首选备选方案的选择和决策实施。通过规划机器人执行常见任务的场景来说明所开发模型的应用。实际相关性:开发的模型使您能够设计解决系统组件的共同任务或实现共同目标的计划,并实现这些计划。这些模型有助于克服社会-网络-物理系统突发行为的后果,并有助于机器学习和移动机器人控制的研究。
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引用次数: 3
Optical data signals in fiber optic communication links with fading 具有衰落的光纤通信链路中的光数据信号
Q3 Mathematics Pub Date : 2019-06-21 DOI: 10.31799/1684-8853-2019-3-94-104
I. Juwiler, I. Bronfman, N. Blaunstein
Introduction: This article is based on the recent research work in the field of two subjects: signal data parameters in fiber optic communication links, and dispersive properties of optical signals caused by non-homogeneous material phenomena and multimode propagation of optical signals in such kinds of wired links.Purpose: Studying multimode dispersion by analyzing the propagation of guiding optical waves along a fiber optic cable with various refractive index profiles of the inner optical cable (core) relative to the outer cladding, as well as dispersion properties of a fiber optic cable due to inhomogeneous nature of the cladding along the cable, for two types of signal code sequences transmitted via the cable: return-to-zero and non-return-to-zero ones.Methods: Dispersion properties of multimode propagation inside a fiber optic cable are analyzed with an advanced 3D model of optical wave propagation in a given guiding structure. The effects of multimodal dispersion and material dispersion causing the optical signal delay spread along the cable were investigated analytically and numerically.Results: Time dispersion properties were obtained and graphically illustrated for two kinds of fiber optic structures with different refractive index profiles. The dispersion was caused by multimode (e.g. multi-ray) propagation and by the inhomogeneous nature of the material along the cable. Their effect on the capacity and spectral efficiency of a data signal stream passing through such a guiding optical structure is illustrated for arbitrary refractive indices of the inner (core) and outer (cladding) elements of the optical cable. A new methodology is introduced for finding and evaluating the effects of time dispersion of optical signals propagating in fiber optic structures of various kinds. An algorithm is proposed for estimating the spectral efficiency loss measured in bits per second per Hertz per each kilometer along the cable, for arbitrary presentation of the code signals in the data stream, non-return-to zero or return-to-zero ones. All practical tests are illustrated by MATLAB utility.
本文以光纤通信链路中的信号数据参数、非均匀材料现象引起的光信号色散特性和光信号在这类有线链路中的多模传播两方面的最新研究成果为基础。目的:通过分析光纤内缆(芯)相对于外包层不同折射率分布的导光波沿光缆的传播,以及光纤包层沿光缆的非均匀性导致的光纤的色散特性,研究通过光缆传输的归零和非归零两类信号码序列的多模色散特性。方法:利用光波在给定导向结构中传播的先进三维模型,分析了光纤内部多模传播的色散特性。分析和数值分析了多模态色散和材料色散对光缆中光信号延迟传播的影响。结果:得到了两种不同折射率光纤结构的时间色散特性,并以图形表示。色散是由多模(如多射线)传播和电缆沿线材料的非均匀性引起的。对于光纤的内(芯)和外(包层)元件的任意折射率,说明了它们对通过这种引导光学结构的数据信号流的容量和频谱效率的影响。介绍了一种新的方法来发现和评估光信号在各种光纤结构中传播时色散的影响。对于数据流中任意表示的码信号,非归零或归零信号,提出了一种估计沿电缆每公里每赫兹每秒比特数的频谱效率损失的算法。所有的实际测试都用MATLAB工具进行了说明。
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引用次数: 0
Random processes with random transitions between stable states 稳定状态间随机转换的随机过程
Q3 Mathematics Pub Date : 2019-06-21 DOI: 10.31799/1684-8853-2019-3-82-93
V. I. Khimenko
Introduction: Studying random processes with several stable states and random transitions between them is important because it opens a wide range of practical problems. The detailed information structure is not studied well enough, and there is no unified approach to the description and probabilistic analysis of such processes.Purpose: Studying the main probabilistic characteristics of random processes with two stable states, and probabilistic analysis of control over chaotic transitions under various control actions.Results: We show the ways to represent and preliminarily analyze random processes with two stable states on the phase plane and in the pseudophase space. A general probabilistic model for the processes in question is proposed in the form of a two-component probabilistic «mixture» of distributions. A probabilistic analysis was carried out for the principles of control over random transitions between different states. We have defined the basic probabilistic characteristics for the processes in a management action with a variety of spectral-correlation properties and a changeable threshold for random transitions. The Poisson model of a random transition flow is analyzed with an example of «high» threshold levels.Practical relevance: The methods of visual, qualitative and analytical research in studying dynamic systems with several stable states can be combined. The proposed probabilistic models, regardless of the physical nature of the processes under consideration, can be used in problems of probabilistic analysis, control over probabilistic structure of random transitions, and simulation of physical, technical or biological systems with random switching.
引言:研究具有几个稳定状态的随机过程以及它们之间的随机跃迁很重要,因为它打开了一系列广泛的实际问题。详细的信息结构研究得不够好,对此类过程的描述和概率分析也没有统一的方法。目的:研究具有两个稳定状态的随机过程的主要概率特性,并对不同控制行为下混沌过渡的控制进行概率分析。结果:我们展示了在相平面和伪相空间上表示和初步分析具有两个稳定状态的随机过程的方法。提出了一个有关过程的通用概率模型,其形式为分布的双组分概率“混合”。对不同状态之间随机转换的控制原理进行了概率分析。我们已经定义了管理行动中过程的基本概率特征,具有各种谱相关特性和随机转换的可变阈值。以“高”阈值水平为例,分析了随机过渡流的泊松模型。实际相关性:在研究具有几个稳定状态的动态系统时,视觉、定性和分析研究的方法可以结合起来。所提出的概率模型,无论所考虑过程的物理性质如何,都可以用于概率分析、随机转换概率结构的控制以及具有随机切换的物理、技术或生物系统的模拟问题。
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引用次数: 0
Nested code sequences of Barker — Mersenne — Raghavarao Barker - Mersenne - Raghavarao的嵌套代码序列
Q3 Mathematics Pub Date : 2019-06-21 DOI: 10.31799/1684-8853-2019-3-71-81
M. Sergeev, V. Nenashev, A. Sergeev
Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.
开放无线信道的无噪声编码问题对数据传输具有重要意义。本文的研究结果旨在激发人们对从拟正交矩阵衍生出的新码和基的科学兴趣,作为修订信号处理算法的基础。目的:寻找由Mersenne和Raghavarao拟正交矩阵的行组成的新的码序列,以及复杂而高效的Barker - Mersenne - Raghavarao码。结果:研究了由Mersenne、Raghavarao和Hadamard的拟正交循环矩阵行导出的嵌套码序列,给出了嵌套Barker、Mersenne和Raghavarao码及其组合的自相关函数的特征估计,特别是主峰与最大正、负“旁瓣”的比值。我们在拟正交矩阵的基础上合成了新的码,包括嵌套码,它们比已知的Barker码及其嵌套结构具有更好的特性。这些结果意义重大,因为这项研究影响了有用信息的分离、检测和处理方法的建立和发展。由于新的应用领域需要对新的原始码合成方法进行研究、修改、推广和扩展,因此工作结果具有长期的影响。实际相关性:所获得结果的实际应用保证了定位系统精度的提高,并在噪声背景中检测到有用的信号。特别是,这些结果可以用于具有高距离分辨率的雷达系统,当检测物理物体时,包括隐藏的物体。
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引用次数: 14
Adaptive control of time-varying non-linear plants by speed-gradient algorithms 时变非线性对象的速度梯度自适应控制
Q3 Mathematics Pub Date : 2019-06-21 DOI: 10.31799/1684-8853-2019-3-37-44
O. Tomchina, D. N. Polyakhov, O. I. Tokareva, Alexander L. Fradkov
Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.
许多现实世界系统的运动本质上是用非线性和非平稳模型来描述的。控制这类植物的许多方法都是基于构造非平稳的内部模型。但非平稳性模型参数变化较大,误差较大。本文仅假设目标参数的变化率是有限的,而初始不确定性可能相当大。目的:用速度梯度法合成具有显式参考模型的非线性时变系统的自适应控制算法。结果:得到了闭环系统解与参考模型解的最大偏差的估计。结果表明,在参数变化足够慢且初始不确定度很小的情况下,系统的极限误差可以任意小。采用直接方法设计的系统和基于识别方法设计的系统都得到了考虑。通过实例说明了自适应调节器的合成过程和合成系统的分析。实际意义:获得的结果使我们能够在非平稳条件下建立和分析具有参考模型的广泛的自适应系统。
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引用次数: 2
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Informatsionno-Upravliaiushchie Sistemy
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