期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 67, 期 6, 页码 3892-3904出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3052920
关键词
Correlation; Upper bound; Peak to average power ratio; Delays; Zero correlation zone; Two dimensional displays; Synchronization; Golay complementary pair (GCP); Golay complementary array pair (GCAP); Z-complementary pair (ZCP); Z-complementary array pair (ZCAP); zero correlation zone (ZCZ)
资金
- Ministry of Science and Technology, Taiwan [MOST 107-2221-E-006-065-MY2, MOST 109-2628-E-006-008-MY3]
The concept of Golay complementary pairs has been extended to two-dimensional arrays with the introduction of zero correlation zone property. Various constructions of Z-complementary array pairs are proposed in the article, along with a discussion on their existence for all sizes. Additionally, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived for odd dimensions, with proposed constructions achieving this upper bound.
One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.
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