A Construction of Binary Cross Z-Complementary Pairs with Large CZC Ratio

Abstract

Cross Z-complementary pairs (CZCPs), characterized by two symmetric zero autocorrelation zones (ZACZs) and one tail-end zero cross-correlation zone (ZCCZ), play an instrumental role in the design of training sequences for broadband spatial modulation systems. In this letter, we propose a systematic construction of CZCPs with large cross Z-complementary ratio (CZCR) by employing Turyn's method to some seed CZCPs and Golay complementary pairs (GCPs). By appropriately selecting the seed CZCPs, we can extend the CZCPs with parameters (18,7) and (22,9) to new (18N, 8N - 1)-CZCPs and (22N, 9N + Z₁)-CZCPs, where Z₁ signifies the zero correlation zone width achievable by a binary GCP. Additionally, we introduce new CZCPs with parameters (34,14) and (38,14), which were not previously reported in the literature, and extend them to (34N, 14N + Z₁)-CZCPs and (38N, 15N - 1)-CZCPs.