Novel Constructions of Cross Z-Complementary Pairs with New Lengths

Spatial modulation (SM) is a type of multiple-input multiple-output (MIMO) technology that provides several benefits over traditional MIMO systems. SM-MIMO is characterized by its unique transmission principle, which results in lower costs, enhanced spectrum utilization, and reduced inter-channel interference. To optimize channel estimation performance over frequency-selective channels in the spatial modulation system, cross Z-complementary pairs (CZCPs) have been proposed as training sequences. The zero correlation zone (ZCZ) properties of CZCPs for auto-correlation sums and cross-correlation sums enable them to achieve optimal channel estimation performance. In this paper, we systematically construct CZCPs based on binary Golay complementary pairs and binary Golay complementary pairs via Turyn's method. We employ a special matrix operation and concatenation method to obtain CZCPs with new lengths 2M + N and 2(M + L), where M and L are the lengths of binary GCP, and N is the length of binary GCP via Turyn's method. Further, we obtain the perfect CZCP with new length 4N and extend the lengths of CZCPs.