Ретроспективный обзор троичных последовательностей с идеальной периодической автокорреляцией и устройств их генерации

Introduction. Perfect polyphase unimodular sequences, i.e. sequences with ideal periodic autocorrelation and single amplitude of symbols are widely used in modern radio communications and radars. Among them a special place is occupied by perfect ternary sequences (PTSs) with elements {–1, 0, 1}. PTSs are quite numerous and their length in comparison with perfect binary sequences is not limited from above. There is a well-known review of PTS families undertaken by Fan and Darnell in 1996. However, over the past two decades numerous new PTS families have been discovered. Connections between PTSs and circulant weighing matrices have been established and certain theorems on the existence of PTS existence for certain lengths have also been obtained. Therefore, there is a need for a new modern review of existing PTSs.Objective. This review of existing PTSs is intended for developers of radio electronic systems using perfect sequences. Materials and methods. Domestic and foreign sources of information (books, journal papers, conference proceedings, patents) were considered and analysed. A Web search was carried out based on keywords using resources of Yandex and Google, as well as in digital electronic libraries (Russian State Library (RSL), IEEE Xplore Digital Library), conference materials (Digital Signal Processing and its Application (DSPA), Sequences and their Applications (SETA), etc.). Results. In addition to the matter of collating an informational bibliography, the review shows the relationship between PTSs obtained at different times and their connection with circulant weighing matrices. The review also describes the generators of known PTS families (Ipatov, Hoholdt-Justensen, etc.). Conclusion. A retrospective review of PTSs is herein presented and the generators of certain known PTS families have been considered. The results of the study are relevant for use in modern radio communications and radar systems and in CW and LPI radars in particular. Введение. Идеальные многофазные унимодулярные последовательности, т. е. последовательности с идеальной периодической автокорреляцией и единичной амплитудой символов, широко используются в современной радиосвязи и радиолокации. Особое место среди них занимают идеальные троичные последовательности (ИТП) с элементами {–1, 0, 1}. ИТП достаточно многочисленны, а их длина в отличие от идеальных двоичных последовательностей не ограничена сверху. Известен обзор ИТП, сделанный Фаном и Дарнеллом в 1996 г. Однако за прошедшие два десятилетия были открыты новые многочисленные семейства ИТП, установлены связи между ИТП и циркулянтными взвешенными матрицами, получены теоремы о существовании ИТП с определенными параметрами. Поэтому возникла потребность в новом современном обзоре известных на сегодня ИТП. Цель работы. Обзор современных ИТП предназначен для разработчиков радиоэлектронных систем, в которых используются идеальные последовательности.Материалы и методы. Рассмотрены и проанализированы отечественные и зарубежные источники информации (книги, журнальные статьи, труды конференций, патенты). Поиск осуществлялся в сети Интернете по ключевым словам с использованием Интернет-ресурсов Yandex и Google, а также в цифровых электронных библиотеках (Российской Государственной библиотеке (РГБ), IEEE Xplore Digital Library), в материалах конференций (Цифровая Обработка Сигналов и ее Применение (DSPA), Sequences and Their Applica-tions (SETA), и др.). Результаты. Наряду с решением информационно-библиографической задачи в обзоре показана взаимосвязь полученных в разное время ИТП, их эквивалентность циркулянтным взвешенным матрицам, а также рассмотрены устройства генерации известных семейств ИТП (Ипатова, Хохолдта-Джастесена и др.). Заключение. Представлен ретроспективный обзор ИТП; рассмотрены генераторы известных семейств ИТП. Результаты исследования актуальны для применения в современных системах радиосвязи и радиолокации, в частности в CW- и LPI-радарах.

Class of Quadratic Almost Bent Functions That Is EA-Inequivalent to Permutations

The permutation relationship for the almost bent (AB) functions in the finite field is a significant issue. Li and Wang proved that a class of AB functions with algebraic degree 3 is extended affine- (EA-) inequivalent to any permutation. This study proves that another class of AB functions, which was developed in 2009, is EA-inequivalent to any permutation. This particular AB function is the first known quadratic class EA-inequivalent to permutation

ISOMORPHIC SIGNAL ENSEMBLES AND THEIR APPLICATION IN ASYNC-ADDRESS SYSTEMS

The object of consideration is async-address systems using code division of subscribers. The subject of the analysis is quasi-orthogonal ensembles of signals based on code sequences that have normalized characteristics of cross-correlation functions (CCF) and provide reliable separation of subscribers (objects) when exposed to imitation and signal-like interference. The purpose of the analysis is to create a model and methodology for construction a set of the best code sequences ensembles having the ability to quickly change the instance of the set to counter imitation and signal-like interference. The solution is based on algebraic models of code sequences and their CCF representation. The article proposes a comprehensive technique to construct signal ensembles set having normalized characteristics of the CCF. The quality of the primary ensemble of code sequences is ensured by the procedure for calculating the CCF optimized in the number of look over options. Optimization is based on the basic properties of the Galois field, in particular, on the Galois fields’ isomorphism property. It provides a significant reduction in calculations when choosing the primary ensemble of code sequences with the specified properties of the CCF. The very choice of the best (largest in size) code sequences ensemble relies on the solution of one of the classical combinatorics problems – searching for maximal clique on a graph. The construction of signals ensembles set having normalized characteristics of the CCF is ensured by the use of special combinatorial procedures and algorithms based on the multiplicative properties of Galois fields. An analysis of the effectiveness of known and proven procedures searching for maximal clique is also performed in this article. The work results will be useful in the design of infocommunication systems using complex signals with a large base and variable structure to provide protection from signal structure research and the effects of imitation and signal-like interferenc

Generalized discrete Fourier transform with non-linear phase : theory and design

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in various engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. Among these popular transforms, DFT is a linear phase transform and widely used in multicarrier communications due to its performance and fast algorithms. In this thesis, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase exploiting the phase space is developed. It is shown that GDFT offers sizable correlation improvements over DFT, Walsh, and Gold codes. Brute force search algorithm is employed to obtain orthogonal GDFT code sets with improved correlations. Design examples and simulation results on several channel types presented in the thesis show that the proposed GDFT codes, with better auto and cross-correlation properties than DFT, lead to better bit-error-rate performance in all multi-carrier and multi-user communications scenarios investigated. It is also highlighted how known constant modulus code families such as Walsh, Walsh-like and other codes are special solutions of the GDFT framework. In addition to theoretical framework, practical design methods with computationally efficient implementations of GDFT as enhancements to DFT are presented in the thesis. The main advantage of the proposed method is its ability to design a wide selection of constant modulus orthogonal code sets based on the desired performance metrics mimicking the engineering .specs of interest. Orthogonal Frequency Division Multiplexing (OFDM) is a leading candidate to be adopted for high speed 4G wireless communications standards due to its high spectral efficiency, strong resistance to multipath fading and ease of implementation with Fast Fourier Transform (FFT) algorithms. However, the main disadvantage of an OFDM based communications technique is of its high PAPR at the RF stage of a transmitter. PAPR dominates the power (battery) efficiency of the radio transceiver. Among the PAPR reduction methods proposed in the literature, Selected Mapping (SLM) method has been successfully used in OFDM communications. In this thesis, an SLM method employing GDFT with closed form phase functions rather than fixed DFT for PAPR reduction is introduced. The performance improvements of GDFT based SLM PAPR reduction for various OFDM communications scenarios including the WiMAX standard based system are evaluated by simulations. Moreover, an efficient implementation of GDFT based SLM method reducing computational cost of multiple transform operations is forwarded. Performance simulation results show that power efficiency of non-linear RF amplifier in an OFDM system employing proposed method significantly improved

Fast Decoder for Overloaded Uniquely Decodable Synchronous CDMA

We consider the problem of designing a fast decoder for antipodal uniquely decodable (errorless) code sets for overloaded synchronous code-division multiple access (CDMA) systems where the number of signals K_{max}^a is the largest known for the given code length L. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has a much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder only has a 1-2 dB degradation at BER of 10^{-3} when compared to ML

On correlation distribution of Niho-type decimation d=3(pm−1)+1d=3(p^m-1)+1

The cross-correlation problem is a classic problem in sequence design. In this paper we compute the cross-correlation distribution of the Niho-type decimation $d=3(p^m-1)+1$ over $\mathrm{GF}(p^{2m})$ for any prime $p \ge 5$. Previously this problem was solved by Xia et al. only for $p=2$ and $p=3$ in a series of papers. The main difficulty of this problem for $p \ge 5$, as pointed out by Xia et al., is to count the number of codewords of "pure weight" 5 in $p$-ary Zetterberg codes. It turns out this counting problem can be transformed by the MacWilliams identity into counting codewords of weight at most 5 in $p$-ary Melas codes, the most difficult of which is related to a K3 surface well studied in the literature and can be computed. When $p \ge 7$, the theory of elliptic curves over finite fields also plays an important role in the resolution of this problem

Cross Z-Complementary Pairs for Optimal Training in Spatial Modulation Over Frequency Selective Channels

The contributions of this article are twofold: Firstly, we introduce a novel class of sequence pairs, called “cross Z-complementary pairs (CZCPs),” each displaying zero-correlation zone (ZCZ) properties for both their aperiodic autocorrelation sums and crosscorrelation sums. Systematic constructions of perfect CZCPs based on selected Golay complementary pairs (GCPs) are presented. Secondly, we point out that CZCPs can be utilized as a key component in designing training sequences for broadband spatial modulation (SM) systems. We show that our proposed SM training sequences derived from CZCPs lead to optimal channel estimation performance over frequency-selective channels

Doppler Shift Tolerance of Typical Pseudorandom Binary Sequences in PMCW Radar

In the context of all-digital radar systems, phase-modulated continuous wave (PMCW) based on pseudorandom binary sequences (PRBSs) appears to be a prominent candidate modulation scheme for applications such as autonomous driving. Among the reasons for its candidacy are its simplified transmitter architecture and lower linearity requirements (e.g., compared to orthogonal-frequency division multiplexing radars), as well as its high velocity unambiguity and multiple-input multiple-output operation capability, all of which are characteristic of digital radars. For appropriate operation of a PMCW radar, choosing a PRBS whose periodic autocorrelation function (PACF) has low sidelobes and high robustness to Doppler shifts is paramount. In this sense, this article performs an analysis of Doppler shift tolerance of the PACFs of typically adopted PRBSs in PMCW radar systems supported by simulation and measurement results. To accurately measure the Doppler-shift-induced degradation of PACFs, peak power loss ratio (PPLR), peak sidelobe level ratio (PSLR), and integrated-sidelobe level ratio (ISLR) were used as metrics. Furthermore, to account for effects on targets whose ranges are not multiples of the range resolution, oversampled PACFs are analyzed