Constructions of Binary Cross Z-Complementary Pairs With Large CZC Ratio
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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 (CZC_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)-CZCPs, (28L,13L+L/2)-CZCPs and (30L,13L-1)-CZCPs, where L is the length of a binary GCP. Besides, we emphasize that, our proposed CZCPs have the largest CZC_ratio=27/28, compared with known CZCPs but no-perfect CZCPs in the literature. Specially, we proposed optimal binary CZCPs with (28,13)-CZCP and (56,27)-CZCP. The second one of CZCPs based on Boolean functions (BFs), and the construction of CZCPs have the largest CZC_ratio=13/14, compared with known CZCPs but no-perfect CZCPs in the literature.
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