4 research outputs found

    Design of sequences with good correlation properties

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    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

    Asymmetric ZCZ Sequence Sets with Inter-Subset Uncorrelated Sequences via Interleaved Technique

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    Nowe metody przetwarzania losowo pr贸bkowanych wielowymiarowych eksperyment贸w NMR

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    The topic of this dissertation is a new algorithm for processing of sparsely sampled data sets from multidimensional nuclear magnetic resonance (NMR) experiments. NMR remains one of the major experimental technique for studying biological macromolecules. However, increasing size of investigated objects poses a challenge for NMR due to rapidly decreasing sensitivity and increasing signal crowding. The first chapter focuses on recent advances in sensitivity enhancements and summarises a few solutions for resolution of spectral overlap. Subsequently, one describes the crucial and limiting problem of signal sampling in multidimensional NMR, which, up to recently, has impeded the widespread use of high-dimensional NMR methods. Major fast acquisition and non-uniform sampling (NUS) approaches are presented. The particular emphasis was put on detailed discussion of competetive approaches to processing of data from NUS experiments. In chapter 3 the new iterative algorithm is proposed for artefact suppression in high-resolution NMR spectra. The detailed description of its design and implementation is given, and followed by comparison with selected processing methods. The efficacy of the algorithm is demonstrated on model synthetic and experimental data. The last chapter of the thesis shows various applications of the proposed method to existing and new four- and five-dimensional NMR experiments. The algorithm is proven most beneficial in challenging applications including spectra for assignment of sidechain resonances in protein and nucleic acids, NOESY spectra for structural analysis, and cross-correlated relaxation measurements for proteins. // Niniejsza praca jest po艣wiecona nowej metodzie przetwarzania danych pochodz膮cych z oszcz臋dnie pr贸bkowanych wielowymiarowych eksperyment贸w j膮drowego rezonansu magnetycznego (ang. Nuclear Magnetic Resonance, NMR). Technika ta jest, obok krystalografii rentgenowskiej, g艂贸wn膮 eksperymentaln膮 metod膮 badawcz膮 pozwalaj膮c膮 na okre艣lenie struktury i dynamiki makromoleku艂 o znaczeniu biologicznym. Jednak偶e NMR napotyka dwie istotne przeszkody w odniesieniu do du偶ych biomoleku艂, a mianowicie gwa艂townie pogarszaj膮c膮 si臋 czu艂o艣膰 oraz krytyczne zat艂oczenie sygna艂贸w w widmach. W rozdziale pierwszym przedstawiono ostatnie osiagni臋cia w poprawie czu艂o艣ci technik NMR oraz rozwi膮zania s艂u偶膮ce podniesieniu rozdzielczo艣ci widm. Nast臋pnie opisano kluczowy problem pr贸bkowania wielowymiarowych sygna艂贸w NMR, kt贸ry do niedawna uniemo偶liwia艂 wykorzystanie pe艂nego potencja艂u tych technik do rozdzielenia sygna艂贸w. Om贸wiono pokr贸tce wsp贸艂czesne podej艣cia do szybkiej akwizycji i oszcz臋dnego pr贸bkowania sygna艂贸w NMR (ang. non-uniform sampling, NUS). Szczeg贸lny nacisk po艂o偶ono na por贸wnanie i dyskusje wad i zalet stosowanych obecnie metod przetwarzania sygna艂贸w niejednorodnie pr贸bkowanych. W rozdziale 3-cim opisano nowy iteracyjny algorytm oparty o transformacje Fouriera, usuwaj膮cy artefakty oszcz臋dnego pr贸bkowania w wysokorozdzielczych widmach NMR. Szczeg贸艂owo om贸wiono schemat algorytmu oraz jego programow膮 implementacj臋. Rozdzia艂 uzupe艂nia por贸wnanie wynik贸w algorytmu oraz wybranych metod przetwarzania na wysymulowanych oraz modelowych danych eksperymentalnych. W ostatnim rozdziale pracy zademonstrowano u偶yteczno艣膰 nowej metody do literaturowych oraz nowych cztero- i pieciowymiarowych eksperyment贸w NMR. W艣r贸d proponowanych zastosowa艅 wymieni膰 mo偶na widma do przypisania sygna艂贸w w 艂a艅cuchach bocznych aminokwas贸w (w bia艂kach) i pier艣cieniach rybozy (w kwasach rybonukleinowych), widma NOESY s艂u偶膮ce okre艣leniu struktury tr贸jwymiarowej biomoleku艂, oraz pomiary szybko艣ci relaksacji skorelowanej w 艂a艅cuchach g艂贸wnych bia艂ek
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