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.
Has partsPaper I: Dan Zhang and Tor Helleseth, New optimal sets of perfect polyphase sequences based on circular Florentine arrays, IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, pp. 2921-2925 (2020). The article is available in the thesis. The article is also available at: https://doi.org/10.1109/ISIT44484.2020.9174001
Paper II: Dan Zhang and Tor Helleseth, Sequences with good correlations based on circular Florentine arrays, IEEE Transactions on Information Theory. Not available in BORA
Paper III: Dan Zhang, Zero correlation zone sequences from a unified construction of perfect polyphase sequences, IEEE International Symposium on Information Theory (ISIT), Paris, France, pp. 2269-2273 (2019). The article is available in the thesis. The article is also available at: https://doi.org/10.1109/ISIT.2019.8849376
Paper IV: Dan Zhang, Chunlei Li and Matthew Geoffrey Parker, New optimal zerocorrelation zone sequences based on IF-ZAZ sequences and interleaving technique, partly presented at the conference SETA (2020). Not available in BORA.
Paper V: Zhengchun Zhou, Dan Zhang, Tor Helleseth, and JinmingWen, A construction of multiple optimal ZCZ sequences with good cross correlation, IEEE Transactions on Information Theory, vol. 64, no. 2, pp. 1340-1346 (2018). The article is available in the thesis. The article is also available at: https://doi.org/10.1109/TIT.2017.2756845
Paper VI: Dan Zhang, Matthew Geoffrey Parker, and Tor Helleseth, Polyphase zero correlation zone sequences from generalised bent functions, Cryptography and Communications, 12, pp. 325-335 (2020). The article is available in the thesis. The article is also available at: https://doi.org/10.1007/s12095-019-00413-2