Symmetric Hadamard matrices of orders 268, 412, 436 and 604

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is that we have constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604.Comment: 12 page

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.

The design and optimization of synchronization sequence for Ultraviolet communication

In the ultraviolet (UV) scattering communication, the received signals exhibit the characteristics of discrete photoelectrons due to path loss. The synchronization is based on maximum Pulse Number-Sequence correlation problem. First of all, the accuracy of synchronization is vital to channel estimation and decoding. This article focuses on improving synchronization accuracy by designing and optimizing synchronization sequences. As for the maximum Pulse Number-Sequence correlation problem, it is assumed that the correlation values satisfy the Gaussian distribution and their mathematical expectation, variance and covariance are derived to express the upper bound of synchronization offset. The synchronization sequence we designed has two equilong RANDOM parts (Symbols meet Bernoulli distribution with equal probability.) and a $\{1,0,1,0,1,0,...,1,0,1,0\}$ part between them with $\alpha$ as its proportion of entire sequence. On the premise of ensuring the synchronization reliability, the synchronization deviation can be reduced by optimizing $\alpha$. There are simulation experiments to verify correctness of the derivation, reasonableness of the hypothesis and reliability of optimization. Compared with equilong random sequence, the synchronization accuracy of the optimized synchronization sequence is significantly improved

Partial geometric designs and difference families

We examine the designs produced by different types of difference families. Difference families have long been known to produce designs with well behaved automorphism groups. These designs provide the elegant solutions desired for applications. In this work, we explore the following question: Does every (named) design have a difference family analogue? We answer this question in the affirmative for partial geometric designs

Design of sequences with good correlation properties

This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems. Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays. Paper III-VI and a part of Paper II are devoted to ZCZ sequences. Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin