Анализ автокорреляционной функции и функции неопределенности сложного радиолокационного сигнала с бинарной фазовой манипуляцией последовательностью Касами

Розглянуто метод формування послідовностей Касамі, їхні властивості. Наведені графіки результатів виконання програми для коду Касамі: автокорреляційні функції, перерізи по частотному зсуву, об’ємні графіки функції невизначеності та їхні перерізи на різних рівнях. Проаналізовані викиди боковиків АКФ, розрізнювальні здатності за дальністю та швидкістю.Introduction. Publications dedicated to pseudorandom sequences in radiolocation were reviewe. Conclusion about necessity of researching in this subject was made. Modeling of probing radiolocation signal with binary phase manipulation by Kasami sequence. The method of forming Kasami sequences and measuring their properties were considered. Example of generator for sequence with length 63 symbols is also shown. Technique of research. Graphical results for modeling of Kasami sequence with lengths of 255 binary values were shown. Amplitudes of side maximums of autocorrelation function are measured. Modeling of ambiguity function. In this article, graphical results for modeling Kasami sequence ambiguity function are shown. These includes 3-dimensional plot of function body and its cross-sections by plane of equal ranges and planes of function level, equal to 0.9, 0.7, 0.5, 0.4, 0.3, 0.2 and 0.1 of its maximum. Amplitude of side maximums, cross-section form and relative values of range and speed resolution were analyzed. Conclusion. These articles contain analyses of characteristics of previously shown plots included estimation of total value of side maximums of ambiguity function of Kasami sequence, ambiguity function cross-section form analysis and conclusion about ability of using these sequences as probe signal in radiolocation.Рассмотрен метод формирования последовательностей Касами, их свойства. Приведены графики результатов выполнения программы для кода Касами: автокорреляционные функции, сечения по частотному сдвигу, объемные графики функции неопределенности, а также их сечения на разных уровнях. Проанализированные выбросы боковиков АКФ, разрешающие способности по дальности и скорости

On Inversion in Z_{2^n-1}

In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z_{2^n-1}, and we described the binary weights of the inverses of the Gold and Kasami exponents. We studied the function \de(n), which for a fixed positive integer d maps integers n\geq 1 to the least positive residue of the inverse of d modulo 2^n-1, if it exists. In particular, we showed that the function \de is completely determined by its values for 1 \leq n \leq \ordb, where \ordb is the order of 2 modulo the largest odd divisor of d.Comment: The first part of this work is an extended version of the results presented in ISIT1

A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span

A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound expression on the linear span of sequences in the family is given. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences. A class of ideal autocorrelation sequences is also constructed and proved to have large linear span.Comment: 21 page

Анализ спектра сложного радиолокационного сигнала с бинарной фазовой манипуляцией последовательностью Касами

У роботі розглянуто принципи формування послідовності Касамі, наведена структурна схема генератора послідовності на основі регістрів зсуву і дано опис її роботи. Проаналізовані спектральні характеристики радіолокаційного сигналу з бінарною фазовою маніпуляцією послідовностями Касамі різної довжини. Розраховані амплітудні та фазові спектри такого сигналу.Introduction. This article contains short introduction to history of complicated signals and list of common sequences used in spectrum spreading. Method of creating Kasami sequences. Sequence creation method based on method of creating maximum length sequence is shown in this article. Creating the structural schema of Kasami sequences generator. Principles of Kasami sequence generator construction are shown in this article. Example of generator for sequence with length 63 symbols, which are created using method, mentioned in previous article, is also shown. Spectrum of Kasami sequences. This article contains amplitude and phase spectrum of two Kasami sequences with lengths of 1023 and 255 symbols. Theoretical formulas are created using Discrete Fourier Transform operation, and graphics are plotted using Fast Fourier Transform operation. Phase spectrum data is also was changed by unwrap operation for better visibility. Conclusion. This article contains analysis of previously shown spectrum characteristics. Several conclusions are made about correlation between sequence and spectrum characteristics. These conclusions include that made about amplitude spectrum form dependence of sequence length, type and basic impulse characteristics.В работе рассмотрены принципы формирования последовательности Касами, приведена структурная схема генератора последовательности на основе регистров сдвига и дано описание ее работы. Проанализированы спектральные характеристики радиолокационного сигнала с бинарной фазовой манипуляцией последовательностями Касами различной длины. Рассчитаны амплитудные и фазовые спектры такого сигнала

SPS pilot signal design and power transponder analysis, volume 2, phase 3

The problem of pilot signal parameter optimization and the related problem of power transponder performance analysis for the Solar Power Satellite reference phase control system are addressed. Signal and interference models were established to enable specifications of the front end filters including both the notch filter and the antenna frequency response. A simulation program package was developed to be included in SOLARSIM to perform tradeoffs of system parameters based on minimizing the phase error for the pilot phase extraction. An analytical model that characterizes the overall power transponder operation was developed. From this model, the effects of different phase noise disturbance sources that contribute to phase variations at the output of the power transponders were studied and quantified. Results indicate that it is feasible to hold the antenna array phase error to less than one degree per power module for the type of disturbances modeled