Two-Dimensional Z-Complementary Array Quads with Low Column Sequence PMEPRs

In this paper, we first propose a new design strategy of 2D $Z$-complementary array quads (2D-ZCAQs) with feasible array sizes. A 2D-ZCAQ consists of four distinct unimodular arrays satisfying zero 2D auto-correlation sums for non-trivial 2D time-shifts within certain zone. Then, we obtain the upper bounds on the column sequence peak-to-mean envelope power ratio (PMEPR) of the constructed 2D-ZCAQs by using specific auto-correlation properties of some seed sequences. The constructed 2D-ZCAQs with bounded column sequence PMEPR can be used as a potential alternative to 2D Golay complementary array sets for practical applicationsComment: This work has been presented in 2023 IEEE International Symposium on Information Theory (ISIT), Taipei, Taiwa

Sequences design for OFDM and CDMA systems

With the emergence of multi-carrier (MC) orthogonal frequency division multiplexing (OFDM) scheme in the current WLAN standards and next generation wireless broadband standards, the necessitation to acquire a method for combating high peak to average power ratio (PMEPR) becomes imminent. In this thesis, we will explore various sequences to determine their PMEPR behaviours, in hopes to find some sequences which could potentially be suitable for PMEPR reduction control under MC system settings. These sequences include $m$ sequences, Sidelnikov sequences, new sequences, Golay sequences, FZC sequences and Legendre sequences. We will also examine the merit factor properties of these sequences, and then we will derive a bound between PMEPR and merit factor. Moreover, in the design of code division multiple access (CDMA) spreading sequence sets, it is critical that each sequence in the set has low autocorrelations and low cross-correlation with other sequences in the same set. In the thesis, we will present a class of GDJ Golay sequences which contains a large zero autocorrelation zone (ZACZ), which could satisfy the low autocorrelation requirement. This class of Golay sequences could potentially be used to construct new CDMA spreading sequence sets

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

Large Families of Ternary Sequences with Aperiodic Zero Correlation Zone Sequences for a Multi-Carrier DS-CDMA System

A new method for generating families of ternary spreading sequences is presented. The sequences have aperiodic zero correlation zones and large families are created for a specific sequence length. The sequences are proposed as spreading sequences to provide high capacity and cancel multipath and multiple access interference (MAI) in a single carrier (SC) or multi-carrier (MC) direct-spread code division multiple access (DS-CDMA) system. A Multi-carrier DS-CDMA system is simulated that employs the new sequences as spreading sequences in a multipath channel. Bit error rates (BER) and frame error rates (FER) for a range of Eb/No values are presented and it is demonstrated that the proposed sequences improve the BER and FER performance when used in place of masked Walsh Codes for the frequency selective fading channel evaluated, when a single correlator receiver is used on each sub-carrier

Generalized pairwise z-complementary codes

An approach to generate generalized pairwise Z-complementary (GPZ) codes, which works in pairs in order to offer a zero correlation zone (ZCZ) in the vicinity of zero phase shift and fit extremely well in power efficient quadrature carrier modems, is introduced in this letter. Each GPZ code has MK sequences, each of length 4NK, whereMis the number of Z-complementary mates, K is a factor to perform Walsh–Hadamard expansions, and N is the sequence length of the Z-complementary code. The proposed GPZ codes include the generalized pairwise complementary (GPC)codes as special cases

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

A Systematic Framework for the Construction of Optimal Complete Complementary Codes

The complete complementary code (CCC) is a sequence family with ideal correlation sums which was proposed by Suehiro and Hatori. Numerous literatures show its applications to direct-spread code-division multiple access (DS-CDMA) systems for inter-channel interference (ICI)-free communication with improved spectral efficiency. In this paper, we propose a systematic framework for the construction of CCCs based on $N$-shift cross-orthogonal sequence families ($N$-CO-SFs). We show theoretical bounds on the size of $N$-CO-SFs and CCCs, and give a set of four algorithms for their generation and extension. The algorithms are optimal in the sense that the size of resulted sequence families achieves theoretical bounds and, with the algorithms, we can construct an optimal CCC consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence families. We also discuss the family size, alphabet size, and lengths of constructible CCCs based on the proposed algorithms