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 and end-shift positions and zero cross-correlation sums around the end-shift positions. CZCPs can be crucial 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 (CZCR). A construction framework of CZCPs with a large ZCZ ratio is proposed using Turyn’s method on some seed CZCPs and GCPs. By choosing suitably the seed CZCPs, we obtain 24 classes of new CZCPs with large CZCR. Especially, if the GCP is strengthened, our resultant CZCPs have the maximum
$\mathrm {\mathbf{CZCR}}\approx \frac {M-1}{M}$
for
$M\in \{6,12,24,28,48,56\}$
. We also obtain optimal CZCPs with new parameters (28, 13), (48, 23), (56, 27), (96, 47) and (112, 55), which can be extended to
$(96N,47N)$
-CZCPs and
$(112N,55N)$
-CZCPs respectively for any Golay number
$N$
.