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

Simultaneous ranging and self-positioning in unsynchronized wireless acoustic sensor networks

Automatic ranging and self-positioning is a very desirable property in wireless acoustic sensor networks (WASNs) where nodes have at least one microphone and one loudspeaker. However, due to environmental noise, interference and multipath effects, audio-based ranging is a challenging task. This paper presents a fast ranging and positioning strategy that makes use of the correlation properties of pseudo-noise (PN) sequences for estimating simultaneously relative time-of-arrivals (TOAs) from multiple acoustic nodes. To this end, a proper test signal design adapted to the acoustic node transducers is proposed. In addition, a novel self-interference reduction method and a peak matching algorithm are introduced, allowing for increased accuracy in indoor environments. Synchronization issues are removed by following a BeepBeep strategy, providing range estimates that are converted to absolute node positions by means of multidimensional scaling (MDS). The proposed approach is evaluated both with simulated and real experiments under different acoustical conditions. The results using a real network of smartphones and laptops confirm the validity of the proposed approach, reaching an average ranging accuracy below 1 centimeter.This work was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2015-70202-P, TEC2012-37945-C02-02 and FEDER funds