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

Local mirror symmetry and the sunset Feynman integral

We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time. We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures. Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the motivic cohomology class.Comment: 67 pages. v2: minor typos corrected and now per-section numbering of theorems, lemmas, propositions and remarks. v3: minor typos corrected. Version to appear in Advances in Theoretical and Mathematical Physic

Efficient complementary sequences-based architectures and their application to ranging measurements

Premio Extraordinario de Doctorado de la UAH en 2015En las últimas décadas, los sistemas de medición de distancias se han beneficiado de los avances en el área de las comunicaciones inalámbricas. En los sistemas basados en CDMA (Code-Division Multiple-Access), las propiedades de correlación de las secuencias empleadas juegan un papel fundamental en el desarrollo de dispositivos de medición de altas prestaciones. Debido a las sumas ideales de correlaciones aperiódicas, los conjuntos de secuencias complementarias, CSS (Complementary Sets of Sequences), son ampliamente utilizados en sistemas CDMA. En ellos, es deseable el uso de arquitecturas eficientes que permitan generar y correlar CSS del mayor número de secuencias y longitudes posibles. Por el término eficiente se hace referencia a aquellas arquitecturas que requieren menos operaciones por muestra de entrada que con una arquitectura directa. Esta tesis contribuye al desarrollo de arquitecturas eficientes de generación/correlación de CSS y derivadas, como son las secuencias LS (Loosely Synchronized) y GPC (Generalized Pairwise Complementary), que permitan aumentar el número de longitudes y/o de secuencias disponibles. Las contribuciones de la tesis pueden dividirse en dos bloques: En primer lugar, las arquitecturas eficientes de generación/correlación para CSS binarios, derivadas en trabajos previos, son generalizadas al alfabeto multinivel (secuencias con valores reales) mediante el uso de matrices de Hadamard multinivel. Este planteamiento tiene dos ventajas: por un lado el aumento del número de longitudes que pueden generarse/correlarse y la eliminación de las limitaciones de las arquitecturas previas en el número de secuencias en el conjunto. Por otro lado, bajo ciertas condiciones, los parámetros de las arquitecturas generalizadas pueden ajustarse para generar/correlar eficientemente CSS binarios de mayor número de longitudes que con las arquitecturas eficientes previas. En segundo lugar, las arquitecturas propuestas son usadas para el desarrollo de nuevos algoritmos de generación/correlación de secuencias derivadas de CSS que reducen el número de operaciones por muestra de entrada. Finalmente, se presenta la aplicación de las secuencias estudiadas en un nuevo sistema de posicionamiento local basado en Ultra-Wideband y en un sistema de posicionamiento local basado en ultrasonidos

Low Ambiguity Zone: Theoretical Bounds and Doppler-Resilient Sequence Design in Integrated Sensing and Communication Systems

In radar sensing and communications, designing Doppler resilient sequences (DRSs) with low ambiguity function for delay over the entire signal duration and Doppler shift over the entire signal bandwidth is an extremely difficult task. However, in practice, the Doppler frequency range is normally much smaller than the bandwidth of the transmitted signal, and it is relatively easy to attain quasi-synchronization for delays far less than the entire signal duration. Motivated by this observation, we propose a new concept called low ambiguity zone (LAZ) which is a small area of the corresponding ambiguity function of interest defined by the certain Doppler frequency and delay. Such an LAZ will reduce to a zero ambiguity zone (ZAZ) if the maximum ambiguity values of interest are zero. In this paper, we derive a set of theoretical bounds on periodic LAZ/ZAZ of unimodular DRSs with and without spectral constraints, which include the existing bounds on periodic global ambiguity function as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of sequences against Doppler effect. We then introduce four optimal constructions of DRSs with respect to the derived ambiguity lower bounds based on some algebraic tools such as characters over finite field and cyclic difference sets

Journal of Telecommunications and Information Technology, 2018, nr 3

kwartalni

Thermodynamic formalism for Lorenz maps

For a 2-dimensional map representing an expanding geometric Lorenz at- tractor we prove that the attractor is the closure of a union of as long as possible unstable leaves with ending points. This allows to define the notion of good measures, those giving full measure to the union of these open leaves. Then, for any H\"older continuous potential we prove that there exists at most one relative equilibrium state among the set of good measures. Condition yielding existence are given.Comment: 36 page

Solving Complex Data-Streaming Problems by Applying Economic-Based Principles to Mobile and Wireless Resource Constraint Networks

The applications that employ mobile networks depend on the continuous input of reliable data collected by sensing devices. A common application is in military systems, where as an example, drones that are sent on a mission can communicate with each other, exchange sensed data, and autonomously make decisions. Although the mobility of nodes enhances the network coverage, connectivity, and scalability, it introduces pressing issues in data reliability compounded by restrictions in sensor energy resources, as well as limitations in available memory, and computational capacity. This dissertation investigates the issues that mobile networks encounter in providing reliable data. Our research goal is to develop a diverse set of novel data handling solutions for mobile sensor systems providing reliable data by considering the dynamic trajectory behavior relationships among nodes, and the constraints inherent to mobile nodes. We study the applicability of economic models, which are simplified versions of real-world situations that let us observe and make predictions about economic behavior, to our domain. First, we develop a data cleaning method by introducing the notion of “beta,” a measure that quantifies the risk associated with trusting the accuracy of the data provided by a node based on trajectory behavior similarity. Next, we study the reconstruction of highly incomplete data streams. Our method determines the level of trust in data accuracy by assigning variable “weights” considering the quality and the origin of data. Thirdly, we design a behavior-based data reduction and trend prediction technique using Japanese candlesticks. This method reduces the dataset to 5% of its original size while preserving the behavioral patterns. Finally, we develop a data cleaning distribution method for energy-harvesting networks. Based on the Leontief Input-Output model, this method increases the data that is run through cleaning and the network uptime

2012 program of study : coherent structures

The 2012 GFD Program theme was Coherent structures with Professors Jeffrey Weiss of the University of Colorado at Boulder and Edgar Knobloch of the University of California at Berkeley serving as principal lecturers. Together they introduced the audience in the cottage and on the porch to a fascinating mixture of models, mathematics and applications. Deep insights snaked through the whole summer, as the principal lecturers stayed on to participate in the traditional debates and contributed stoutly to the supervision of the fellows. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer's GFD fellows. Following the principal lecture notes are the written reports of the fellows' own research projects. In 2012, the Sears Public Lecture was delivered by Professor Howard Bluestein, of the University of Oklahoma on the topic of "Probing tornadoes with mobile doppler radars". The topic was particularly suitable for the summer's theme: a tornado is a special examples of a vortex, perhaps the mother of all coherent structures in fluid dynamics. Howie "Cb" showed how modern and innovative measurement techniques can yield valuable information about the formation and evolution of tornadoes, as well as truly amazing images.Funding was provided by the Office of Naval Research under Grant No. N00014-09-10844 and the National Science Foundation under Contract No. OCE-0824636

Use of RNS Based Pseudo Noise Sequence in DS-CDMA and 3G WCDMA

Code Division Multiple Access (CDMA) based on Spread Signal (SS) has emerged as one of the most important multiple access technologies for Second Generation (2G) and Third Generation (3G) wireless communication systems by its wide applications in many important mobile cellular standards. CDMA technique relies on spreading codes to separate dierent users or channels and its properties will govern the performance of the system. So many of the problems of communication systems based on CDMA technology stem from the spreading codes/sequences, which includes two sub-categories, one being the orthogonal codes, such as Walsh Hadamard (WH) codes and Orthogonal Variable Spreading Factor (OVSF) codes, and the other being pseudo-noise or Pseudo Random (PN) sequences, such as Gold sequences, Kasami sequences, m-sequences, etc. In this thesis a PN sequence generation based on Residue Arithmetic is investigated with an eort to improve the performance of existing interference-limited CDMA technology for mobile cellular systems. This interference-limited performance is due to the fact that all the existing CDMA codes used in mobile cellular standards does not consider external interferences, multipath propagation, Doppler eect etc. So the non-ideal correlation properties of the pseudo-random CDMA codes results in MAI when used in a multi-user system. The PN codes appear random yet they are completely deterministic in nature with a small set of initial conditions. Consequently this work focuses on CDMA code design approach based on Residue Number System (RNS) which should take into account as many real operational conditions as possible and to maintain a suciently large code set size.First, the thesis reviews RNS, DS-CDMA and CDMA codes that are already implemented in various mobile cellular standards. Then the new PN Sequencegenerator design based on RNS is discussed. Comparison of the generated PN sequence with respect to other standard sequence is done in terms of number of codes and correlation properties. Monte-Carlo simulations with the generated sequence are carried out for performance analysis under multi-path environment. The system has been evaluated in AWGN, Rayleigh Fading channel and dierent Stationary Multipath Channels for dierent cross-correlation threshold. It is known that orthogonal Codes are used to multiplex more than one signal for downlink transmission over cellular networks. This downlink transmission is prone to self interference caused by the loss of orthogonality between spreading codes due to multipath propagation. This issue is investigated in detail with respect to WCDMA standards, which is very good representative for CDMA based 3G mobile cellular systems where the channelization code is OVSF code. The code assignment blocking (CAB) (If a particular code in the tree is used in a cell, then all its parent codes and child codes should not be used in the same cell to maintain orthogonality among the users) problem of OVSF codes restricts the number of available codes for a given cell. Since the 3rd generation WCDMA mobile communication systems apply the same multiple access technique, the generated sequence can also be the channelization code for downlink WCDMA system to mitigate the the same. The performance of the system is compared with Walsh Hadamard code over multipath AWGN and dierent Fading channels. This thesis work shows that RNS based PN sequence has enhanced performance to that of other CDMA codes by comparing the bit error probability in multi- user and multipath environment thus contributing a little towards the evolution of next generation CDMA technology