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

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