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.
翻译:跨Z补充配对 (CZCP) 是一种特殊的 Z-补充配对 {CZCP$}, 其在中阶段位置和末班位置周围的自动反热值为零, 其在末班位置周围的交叉反热值为零。 它可以用作设计宽带空间调制(SM)系统在频率选择性频道上的最佳培训序列的关键组成部分。 在本文中, 我们侧重于设计具有大跨Z补充比率的新的CZCP$ {CM{C- CP$ 。 通过探索两种有希望的方法 。 首个CZCP在Golay 补充配对(GCP) 上进行适当的剖析序列 。 提议的构造可以达到$( 28, 13L)\ 美元空间调制系统在频率选择频道上进行最佳培训序列 。 $( 28L) 美元在Z- 美元, 在 C- c- COM 中, 以 $( 30, 13- CCP) 特殊 {C} 。 与已知的硬 磁盘 。