Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasiasynchronous environments. In this paper, we prop...
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Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasiasynchronous environments. In this paper, we propose three new constructions of optimal binary (R2(k+1), 2(k+1), R gamma,gamma )-ZCCS, (R2(k+1), 2(k+1), R2(m2), 2(m2)) -ZCCS and (2(k+1), 2(k+1),3 gamma, 2 gamma)-ZCCS based on generalized boolean functions (GBFs), where gamma = 2(m1-1) + 2(m1-3), m(1) >= 5, k >= 1, m(2) >= 1 and R is any even number. The proposed ZCCSs cover many unreported lengths and a large number of users.
Golay sequences with the zero correlation zone (ZCZ), known as Golay-ZCZ sequences, play a pivotal role in reducing intersymbol interference (ISI) during the process of channel estimation in one dimension. Two-dimensi...
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Golay sequences with the zero correlation zone (ZCZ), known as Golay-ZCZ sequences, play a pivotal role in reducing intersymbol interference (ISI) during the process of channel estimation in one dimension. Two-dimensional (2-D) Golay complementary array set (GCAS) within their ZCZ has the potential application in multiple input multiple output (MIMO) omnidirectional transmission. In this letter, 2-D Golay-ZCZ array set is constructed by using generalized boolean function (GBF) without utilizing any kernels. The proposed construction provides 2-D Golay-ZCZ array set with various array sizes and large ZCZ sizes. Also, we get the one dimensional (1-D) Golay- ZCZ sequence set as a special case of the proposed construction.
In design of secure cryptosystems and CDMA communications, the negabent functions play a significant role. The generalized boolean functions have been extensively studied by Schmidt and established several important r...
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In design of secure cryptosystems and CDMA communications, the negabent functions play a significant role. The generalized boolean functions have been extensively studied by Schmidt and established several important results in this setup. In this paper, several characteristics of the generalized nega-Hadamard transform (GNT) of generalized boolean functions like inverse of GNT, generalized nega-cross correlation, generalized nega-Parseval's identity, relationship between GNT and generalized nega-cross correlation have analyzed. We studied the GNT for the derivative of this setup of functions and established the connection of generalized Walsh-Hadamard transform and GNT of derivatives of these functions. Also, the GNT of composition of vectorial booleanfunction and generalized boolean function is presented. Further, the generalized nega-convolution theorem for generalized boolean function is obtained.
Recently in & Ccedil;e & scedil;melio & gbreve;lu, Meidl (Adv. Math. Commun.,18, 2024), the study of EA-equivalence and CCZ-equivalence for functions from Vn(p)\documentclass[12pt]{minimal} \usepackage{ams...
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Recently in & Ccedil;e & scedil;melio & gbreve;lu, Meidl (Adv. Math. Commun.,18, 2024), the study of EA-equivalence and CCZ-equivalence for functions from Vn(p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {V}}_n<^>{(p)}$$\end{document} to the cyclic group Zpk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_{p<^>k}$$\end{document} has been initiated, where Vn(p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb {V}}_n<^>{(p)}$$\end{document} denotes an n-dimensional vector space over Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {F}}_p$$\end{document}. Amongst others it has been shown that there exist functions from Vn(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {V}}_n<^>{(2)}$$\end{document} to Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}_4$$\end{document} which are CCZ-equivalent but not EA-equivalent. We extend thes
Sequences with low peak-to-average power ratio (PAPR) and desirable lengths are useful and important for orthogonal frequency division multiplexing (OFDM) systems. In this paper, based on the generalizedboolean funct...
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Sequences with low peak-to-average power ratio (PAPR) and desirable lengths are useful and important for orthogonal frequency division multiplexing (OFDM) systems. In this paper, based on the generalized boolean functions (GBFs), a class of q-ary Z-complementary sequence sets (ZCSSs) and a class of complementary sequence sets (CSSs) are constructed. The obtained new ZCSSs and CSSs have low PAPR and non-power-of-two lengths.
In this paper, we present a new family of cross Z-complementary pairs (CZCPs) based on generalized boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set {1, 2, center ...
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ISBN:
(纸本)9781665421607;9781665421591
In this paper, we present a new family of cross Z-complementary pairs (CZCPs) based on generalized boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set {1, 2, center dot center dot center dot, n} with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new q-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.
This paper presents an efficient construction of two-dimensional (2D) complete complementary codes (CCCs) for their modern application as omnidirectional precoding matrices in massive MIMO systems to attain enhanced c...
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ISBN:
(纸本)9781665421607;9781665421591
This paper presents an efficient construction of two-dimensional (2D) complete complementary codes (CCCs) for their modern application as omnidirectional precoding matrices in massive MIMO systems to attain enhanced cell coverage. Unlike the traditional 1D CCCs, little progress has been made on efficient and systematic constructions of the 2D counterpart. In contrast to the existing recursive constructions with the aid of various sequence operations, certain 1D seed sequences or 2D arrays, we propose to use 2D generalized boolean functions for direct synthesis of 2D CCCs. Simulation results show that the proposed 2D CCCs appear to be good candidates for precoding matrices to achieve omnidirectional transmission in massive MIMO systems.
The two-dimensional (2-D) Z-complementary array pair (ZCAP) can be viewed as an extension of the well-known one-dimensional (1-D) Z-complementary pair (ZCP). To date, most constructions of 2-D ZCAPs are indirect and b...
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The two-dimensional (2-D) Z-complementary array pair (ZCAP) can be viewed as an extension of the well-known one-dimensional (1-D) Z-complementary pair (ZCP). To date, most constructions of 2-D ZCAPs are indirect and based on existing 1-D sequences or 2-D arrays. In this letter, a new direct construction of 2-D ZCAPs with flexible array sizes based on 2-D generalized boolean functions is proposed. Compared with the state-of-the-art method, the proposed 2-D ZCAPs have larger 2-D zero correlation zone (ZCZ) sizes and more flexible array sizes. Furthermore, the peak-to-average power ratio of column sequences of the proposed 2-D ZCAPs is analyzed and upper bounded by 2.
Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on gen...
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Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.
In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs)...
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In an OFDM communication system using quadrature amplitude modulation (QAM) signals, peak envelope powers (PEPs) of the transmitted signals can be well controlled by using QAM Golay complementary sequence pairs (CSPs). In this letter, by making use of a new construction, a family of new 16-QAM Golay CSPs of length N = 2(m) (integer m >= 2) with binary inputs is presented, and all the resultant pairs have the PEP upper bound 2N. However, in the existing such pairs from other references their PEP upper bounds can arrive at 3.6N when the worst case happens. In this sense, novel pairs are good candidates for OFDM applications.
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