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

New Constructions of Zero-Correlation Zone Sequences

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size ($K$) and the ZCZ width ($T$) for a given sequence period ($N$). Our approaches can produce various binary and polyphase ZCZ families with desired parameters $(N,K,T)$ and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor

Design of One-Coincidence Frequency Hopping Sequence Sets for FHMA Systems

Department of Electrical EngineeringIn the thesis, we discuss frequency hopping multiple access (FHMA) systems and construction of optimal frequency hopping sequence and applications. Moreover, FHMA is widely used in modern communication systems such as Bluetooth, ultrawideband (UWB), military, etc. For these systems, it is desirable to employ frequency-hopping sequences (FHSs) having low Hamming correlation in order to reduce the multiple-access interference. In general, optimal FHSs with respect to the Lempel-Greenberger bound do not always exist for all lengths and frequency set sizes. Therefore, it is an important problem to verify whether an optimal FHS with respect to the Lempel-Greenberger bound exists or not for a given length and a given frequency set size. I constructed FHS satisfying optimal with respect to the Lempel-Greenberger bound and Peng-Fan bound for efficiency of available frequency. Parameters of a new OC-FHS set are length p^2-p over Z_(p^2 ) by using a primitive element of Z_p. The new OC-FHS set with H_a (X)=0 and H_c (X)=1 can be applied to several recent applications using ISM band (e.g. IoT) based on BLE and Zigbee. In the construction and theorem, I used these mathematical back grounds in preliminaries (i.e., finite field, primitive element, primitive polynomial, frequency hopping sequence, multiple frequency shift keying, DS/CDMA) in order to prove mathematically. The outline of thesis is as follows. In preliminaries, we explain algorithm for minimal polynomial for sequence, linear complexities, Hamming correlation and bounds for FHSs and some applications are presented. In section ???, algorithm for complexity, correlation and bound for FHSs and some applications are presented. In section ???, using information in section ??? and ???, a new construction of OC-FHS is presented. In order to prove the optimality of FHSs, all cases of Hamming autocorrelation and Hamming cross-correlation are mathematically calculated. Moreover, in order to raise data rate or the number of users, a new method is presented. Using this method, sequences are divided into two times of length and satisfies Lempel-Greenberger bound and Peng-Fan bound.clos

A Direct Construction of Prime-Power-Length Zero-Correlation Zone Sequences for QS-CDMA System

In recent years, zero-correlation zone (ZCZ) sequences are being studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, the lengths of most existing ZCZ sequences are limited, and their parameters are not flexible, which are leading to practical limitations in their use in QS-CDMA and other communication systems. The current study proposes a direct construction of ZCZ sequences of prime-power length with flexible parameters by using multivariable functions. In the proposed construction, we first present a multivariable function to generate a vector with specific properties; this is further used to generate another class of multivariable functions to generate the desired $(p^t,(p-1)p^n,p^{n+t+1})$-ZCZ sequence set, where $p$ is a prime number, $t,n$ are positive integers, and $t\leq n$. The constructed ZCZ sequence set is optimal for the binary case and asymptotically optimal for the non-binary case by the \emph{Tang-Fan-Matsufuji} bound. Moreover, a relation between the second-order cosets of first-order generalized Reed-Muller code and the proposed ZCZ sequences is also established. The proposed construction of ZCZ sequences is compared with existing constructions, and it is observed that the parameters of this ZCZ sequence set are a generalization of that of in some existing works. Finally, the performance of the proposed ZCZ-based QS-CDMA system is compared with the Walsh-Hadamard and Gold code-based QS-CDMA system

Large Zero Autocorrelation Zone of Golay Sequences and 4q4^q-QAM Golay Complementary Sequences

Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single $H$-ary Golay sequence and $4^q$-QAM Golay complementary sequence with a large zero autocorrelation zone, where $H\ge 2$ is an arbitrary even integer and $q\ge 2$ is an arbitrary integer. Those new results on Golay sequences and QAM Golay complementary sequences can be explored during synchronization and detection at the receiver end and thus improve the performance of the communication system

Chip and Signature Interleaving in DS CDMA Systems

Siirretty Doriast