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Cross Z-complementary pairs (CZCPs) are a special kind of Z-complementary pairs (ZCPs) having zero autocorrelation sums around the in-phase position and end-shift position, also having zero cross-correlation sums around the end-shift position. It can be utilized as a key component in designing optimal training sequences for broadband spatial modulation (SM) systems over frequency selective channels. In this paper, we focus on designing new CZCPs with large cross Z-complementary ratio $(mathrm{CZC}_{mathrm{ratio}})$ by exploring two promising approaches. The first one of CZCPs via properly cascading sequences from a Golay complementary pair (GCP). The proposed construction leads to $(28L,13L)-mathrm{CZCPs}$, $(28L,13L+frac{L}{2})-mathrm{CZCPs}$ and $(30L,13L-1)-mathrm{CZCPs}$, where $L$ is the length of a binary GCP. Besides, we emphasize that, our proposed CZCPs have the largest $mathrm{CZC}_{mathrm{ratio}}=frac{27}{28}$, compared with known CZCPs but no-perfect CZCPs in the literature. Specially, we proposed optimal binary CZCPs with $(28,13)-mathrm{CZCP}$ and $(56,27)-mathrm{CZCP}$. The second one of CZCPs based on Boolean functions (BFs), and the construction of CZCPs have the largest $mathrm{CZC}_{mathrm{ratio}}=frac{13}{14}$, compared with known CZCPs but no-perfect CZCPs in the literature.
This paper is devoted to sequences and focuses on designing new two-dimensional (2-D) Z-complementary array pairs (ZCAPs) by exploring two promising approaches. A ZCAP is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value at all tim
The previous constructions of quadrature amplitude modulation (QAM) Golay complementary sequences (GCSs) were generalized as $4^q $-QAM GCSs of length $2^{m}$ by Li textsl{et al.} (the generalized cases I-III for $qge 2$) in 2010 and Liu textsl{et al
Zero correlation zone (ZCZ) sequences and Golay sequences are two kinds of sequences with different preferable correlation properties. It was shown by Gong textit{et al.} and Chen textit{et al.} that some Golay sequences also possess a large ZCZ and
In this paper, a recent method to construct complementary sequence sets and complete complementary codes by Hadamard matrices is deeply studied. By taking the algebraic structure of Hadamard matrices into consideration, our main result determine the
The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matric