Two-Dimensional Golay Complementary Array Pairs/Sets With Bounded Row and Column Sequence PAPRs

Cheng Yu Pai, Chao Yu Chen

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in communications engineering. The concept of 1-D GCS can be extended to the two-dimensional (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 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, the peak-to-average power ratio (PAPR) properties of the column sequences and row sequences of the constructed 2-D GCAPs and 2-D GCASs are investigated and the PAPRs are proved to be upper bounded.

Original languageEnglish
Pages (from-to)3695-3707
Number of pages13
JournalIEEE Transactions on Communications
Issue number6
Publication statusPublished - 2022 Jun 1

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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