Construction of complementary arrays

Matsufuji, Shinya; Shigemitsu, R.; Tanada, Yoshihiro; Kuroyanagi, Noriyoshi

doi:10.1109/tic.2004.1409503

Cited by 16 publications

(5 citation statements)

References 6 publications

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“…Later in [13], Fiedler et al applied the method given in [10] recursively to construct multi-dimensional GCAPs and then 2-D GCAPs can be obtained via projection. In [11], via concatenating existing 1-D GCPs or interleaving existing 2-D GCAPs, 2-D GCAPs can be constructed. In [14], Zeng and Zhang proposed a construction of 2-D GCASs based on 2-D perfect arrays and only periodic GCASs were considered.…”

Section: Introductionmentioning

confidence: 99%

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Pai

Chen

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in engineering. The concept of 1-D GCS can be extended to the twodimensional (2-D) Golay complementary array set (GCAS) where the 2-D aperiodic autocorrelations of constituent arrays sum to zero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay complementary array pair (GCAP) as a special case when the set size is 2. In this paper, 2-D generalized Boolean functions are introduced and novel constructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates based on generalized Boolean functions are proposed. Explicit expressions of 2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they are all direct constructions without the aid of other existing 1-D or 2-D sequences. Moreover, for the column sequences and row sequences of the constructed 2-D GCAPs, their peak-to-average power ratio (PAPR) properties are also investigated. Index Terms Golay complementary pair (GCP), Golay complementary array pair (GCAP), Golay complementary array mate, Golay complementary array set (GCAS), peak-to-average power ratio (PAPR). * In our previous conference paper [40], we provided constructions of 2-D GCAPs and 2-D Golay complementary array mates from Boolean functions which can be found in [40, Th.6] and [40, Th.7], respectively. The result from [40, Th.6] will be described in Theorem 9 in this paper. Then, we provide more general constructions of 2-D GCAPs and Golay complementary array mates in Theorem 12 and Theorem 16, respectively.

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Section: Introductionmentioning

confidence: 99%

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Pai

Chen

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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“…It follows that the enumeration for IH strings with a rightmost H is identical to that for IH strings with a rightmost I. (16) and (17).…”

Section: Theoremmentioning

confidence: 94%

“…where |s| = 0. Although [8] only viewed their objects as complementary sequences they are, more generally, complementary arrays over (C 2 ) ⊗n [19,20,17,15,10,21]. As n gets large, |B n | approaches 6 n , whereas the size of the construction of [8] approaches 4 n .…”

Section: Number Of Arrays In B Nmentioning

confidence: 99%

“…The work was subsequently extended by [22,26,27] and by numerous other authors [31]. [19,20,17,10,15,21] show that the complementary set construction is primarily an array construction, where sequence sets are obtained by considering suitable projections of the arrays. It is desirable to propose complementary constructions that significantly improve set size without greatly compromising the upper bound on PAPR or the pairwise distinguishability.…”

Section: Introductionmentioning

confidence: 99%

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A complementary construction using mutually unbiased bases

Parker

2013

Cryptogr. Commun.

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We propose a construction for complementary sets of arrays that exploits a set of mutually-unbiased bases (a MUB). In particular we present, in detail, the construction for complementary pairs that is seeded by a MUB of dimension 2, where we enumerate the arrays and the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be 1 2 . Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves 3 2 times the Welch bound.

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“…In [20], [21], [23], [24], 2D GCASs were employed for precoding matrices in URAs by applying interleaving and Kronecker-product to existing 1D sequences or 2D arrays. As a result, the array sizes of 2D GCASs are only feasible for certain lengths.…”

mentioning

confidence: 99%

Two-Dimensional Golay Complementary Array Sets With Arbitrary Lengths for Omnidirectional MIMO Transmission

Zhao,

Pai,

Huang

et al. 2024

IEEE Trans. Commun.

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This paper presents a coding approach for achieving omnidirectional transmission of certain common signals in massive multi-input multi-output (MIMO) networks such that the received power at any direction in a cell remains constant for any given distance. Specifically, two-dimensional (2D) Golay complementary array set (GCAS) can be used to design the massive MIMO precoding matrix so as to achieve omnidirectional transmission due to its complementary autocorrelation property. In this paper, novel constructions of new 2D GCASs with arbitrary array lengths are proposed. Our key idea is to carefully truncate the columns of certain larger arrays generated by 2D generalized Boolean functions. Finally, the power radiation patterns and numerical results are provided to verify the omnidirectional property of the GCAS-based precoding. The error performances of the proposed precoding scheme are presented to validate its superiority over the existing alternatives.

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Construction of complementary arrays

Cited by 16 publications

References 6 publications

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

A complementary construction using mutually unbiased bases

Two-Dimensional Golay Complementary Array Sets With Arbitrary Lengths for Omnidirectional MIMO Transmission

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