New Binary Cross Z-Complementary Pairs With Large CZC Ratio

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. CZCPs 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 ) . A construction framework of CZCPs with large ZCZ ratio are proposed by using the Turyn’s method on some seed CZCPs and GCPs. By choosing suitably the seed CZCPs, we obtain 16 classes of new CZCPs with large CZC ratio . Especially, if the GCP is strengthened, our resultant CZCPs have the maximum CZC ratio ≈ M − 1 M for M ∈ { 6 , 12 , 24 , 28 } . We also obtain optimal CZCPs with new parameters (28 , 13) , (48 , 23) and (56 , 27) , which can be extended to (48 N, 23 N ) - CZCPs and (56 N, 27 N ) - CZCPs respectively for any Golay number N .