Using of Residual Number System as a Mathematical Basis for Software Defined Radio

Вступ. У традицiйному виглядi, програмно-визначена радiосистема (Software Defined Radio, SDR) являє собою обчислювальне ядро, обладнане приймально-передавальними блоками. З метою прискорення обчислювальних операцiй у системах SDR, пропонується у якостi математичної основи застосування системи залишкових класiв. Результати попереднiх дослiджень, що проводились рiзними групами вчених з метою пошукiв шляхiв пiдвищення продуктивностi обчислювальних засобiв, методiв органiзацiї ефективної системи виявлення та виправлення помилок, а також побудови надiйних обчислювальних комплексiв, дають можливiсть стверджувати, що в межах позицiйних систем числення не можна очiкувати принципових зрушень в даних напрямках без суттєвого збiльшення робочих частот i ускладнення апаратної частини. Перевагою пропонованого методу є те, що програмна радiосистема може складатися з декiлькох ПЛIС i обслуговувати декiлька незалежних радiоканалiв, а перепрограмування властивостей дозволяє змiнювати число i складовi процесу обробки повiдомлень в залежностi вiд поточних умов роботи. Метод дослiдження. В роздiлi проаналiзовано паралельнiсть арифметичнi операцiї у системi залишкових класiв. Цi операцiї називаються модульними, оскiльки для обробки числових значень використовують невеликi залишки дiлення на певний набiр модулiв, а для додавання i множення потрiбно лише один тактовий цикл роботи обчислювальної системи. Для перетворення чисел iз двiйкової системи у RNS використовується алгоритм, заснований на застосуваннi китайської теореми про залишки. Проте такi операцiї, як подiл, порiвняння двох чисел i виявлення знака, є складними i ресурсо-затратними в RNS. Для цих проблемних операцiй було запропоновано кiлька рiшень. Вони полягають у вiдсутностi процесу перетвореннi залишку в бiнарну систему (зворотне перетворення) шляхом застосування цифро-аналогових перетворювачiв у RNS. З iншого боку, вибiр правильного набору модулiв є ще одним важливим питанням для побудови ефективного RNS з достатнiм динамiчним дiапазоном. Результати та аналiз. Пiдводячи пiдсумки деяких результатiв, можна зазначити, що система класiв залишкiв дозволяє значно полiпшити параметри обчислювача у SDR, а особливо у функцiональному блоковi Direct Digital Synthesizers (DDS) у порiвняннi з обчислювачем, побудованим на тiй же фiзичнiй i технологiчнiй основi, але в позицiйнiй обчислювальнiй системi, а також отримання нових бiльш прогресивних конструктивних i структурних рiшень. Експериментальнi результати показують, що представленi методи дають значнi переваги для цифрових фiльтрiв у SDR, якi характеризуються високим динамiчним дiапазоном i мають велику кiлькiстю ланок, особливо коли повнi перемножувачi не доступнi у цiльовiй архiтектурi FPGA, або коли цi перемножувачi повиннi використовуватися для рiзних цiлей. Висновки. Таким чином, запропонована система вносить явнi переваги перед iснуючими системами i показує переваги продуктивностi обчислювальних операцiй i може бути використана для побудови сучасних систем зв’язку. Запропонована архiтектура зменшує розмiри конвеєру суматорiв i перемножувачiв, що є дуже важливим фактором при розробцi високошвидкiсних SDR.Introduction. In the classic view, program-defined radio system (Software Defined Radio, SDR) is a central processor, equipped with receiving and transmitting units. In order to speed up computational operations in SDR systems it is proposed to use the system of residual classes as a mathematical basis. The results of research conducted by various groups of scientists in order to find ways to improve the performance of computing tools, methods of organizing an effective system for detecting and correcting errors, as well as building reliable computer systems, make it possible to assert that, within the limits of positional number systems, no fundamental changes can be expected in these areas without a significant increase in operating frequencies and hardware complications. The advantage of this method is that a software radio system can consist of several FPGAs and serve several independent radio channels, and reprogramming the properties allows you to change the number and components of message processors depending on current operating conditions. Research method. The equations in this section show the parallel nature of the RNS, free from bit transfers. These operations are called modular, because for it takes only one clock cycle to process the numerical values. To convert numbers from the binary position number system to RNS we use an algorithm based on the application of a distributed arithmetic. However, operations such as division, comparison of two numbers, and the detection of a sign are laborious and expensive in RNS Several decisions were proposed for these problem operations. They consist in the absence of the process of converting a residue into a binary system (reverse transformation) by using digital-to-analog converters in RNS. On the other hand, choosing the right set of modules is another important issue for building an effective RNS with a sufficient dynamic range. Results and analysis. Summing up some results, it can be noted that the system of residual classes allows to significantly improve the parameters of a computer in SDR especially in functional block a Direct Digital Synthesizers (DDS) in comparison with a computer built on the same physical and technological basis, but in a positional system calculation, and also to receive new more progressive constructive and structural solutions. The experimental results shows that the presented techniques offer interesting advantages for FIR filters characterized by high dynamic range and high number of taps especially when full custom multipliers are not available in the target FPGA architecture or when they must to be used for different purposes. Conclusion. Thus, the proposed system introduces clear advantages over existing systems and shows performance advantages and can be used to build modern communication systems. The proposed architecture reduces the size of the pipeline adders and multipliers which is a very important factor in the design SDR for fast work.В статье рассмотрены принципы построения и функционирования систем, определенных программным обеспечением (Software Defned Radio, SDR). С целью ускорения вычислительных операций в системах SDR предлагается применение системы остаточных классов в качестве математической основы построения систем. Преимуществом приведенного метода является то, что программная радиосистема может состоять из нескольких ПЛИС и обслуживать несколько независимых радиоканалов, а перепрограммирование свойств позволяет изменять число и составляющие процессоры сообщений в зависимости от текущих условий роботы. Приведены проблемы формирования выходного сигнала. Описаны особенности внедрения операций прямого и обратного преобразований с позиционных на непозиционые системы исчисления. Рассмотрена структурная модель SDR с прямыми цифровыми синтезаторами частоты, ЦАП, АЦП, цифровыми фильтрами в системе остаточных классов. Рассмотрены методы преобразования системы остаточных класов в аналоговый сигнал. Рассматриваются проблемы эффективного использования площади кристалла для SDR и уменьшения задержек в формировании выходного сигнала. Полученные результаты показывают широкие возможности применения программно определенной радиосистемы в системе остаточных классов

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The relevance of the problem is determined by the number of complex problems that exist in present Samara municipal retail trade system, which is manifested in the lack of regulation, a glut of sales area, poorly developed infrastructure. The purpose of this article is to form a quantitative base for determining the municipal needs in the floor space. Leading method to study this problem is the method of empirical observations and mathematical modeling. The study results: the article contains the analysis of sales area availability on the example in the urban district and presents a quantitative method to determine predictive values for retail trade turnover. Practical significance: the paper is aimed to develop managerial decisions in the sphere of municipal trade regulation. © 2016 Suraeva et al

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It was studied the long-term dynamics of influenza A viruses circulation in the Southern Central Siberia. Also, we studied of birds population dynamic as the main carriers of viral infection, as well as spatial and temporal distribution of positive samples containing specific antibody to influenza viruses subtypes H5 and. H7 and. genomic RNA of these subtypes. It was considered the cases of mortality wild. and. synanthropic birds in the region. It was shown a correlation between the identified centers of the virus influenza, the deaths of birds and. human disease with significant excess seasonal epidemic threshold, including a subtype Н1NЫЦ

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The interface engineering plays important role in fabrication of the tandem and perovskite based solar cells. Recent experiments show that the interface effects caused by the coupling of the electron bands and the pairing of geometry of contacting surfaces. In particular, it has been experimentally revealed that the transition from planar to the rough interface improves many photoelectric parameters of the device. It means that the value of the fractal dimension of the interface may be key factor in device performance. It is possible to formulate two problems: firstly, the understanding on simple models why the electrical properties at fractal interfaces are improved, and, secondly, to discuss one of the most promising approaches in modern electronics, namely technology of radiation applications in the creation of rough interfaces. Thirdly, the problem of photodegradation is analyzed in detail in the structures containing the fractal interfaces. On the basis of the constructed models, it was found: i) increase of roughness (fractal) of interface structure can enhance the role of total internal light reflection effect, thereby increasing the effective light path, and therefore, the number of generated e-h-pairs; ii) the curvature of the surface leads to the shift of Tamm levels both to the borders of allowed bands, and to the middle of the band gap; it opens the way of the control of carrier recombination on the interface; iii) surface Tamm orbitals interact differently each with other on the convex and concave areas; it leads to the different probability of defect formation and, consequently, reduces the fractal interface, inhibiting the effect of increasing of the photocurrent associated with the fractal interface (new channel of photodegradation)

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