Cross Z-Complementary Pairs for Optimal Training in Spatial Modulation Over Frequency Selective Channels

The contributions of this article are twofold: Firstly, we introduce a novel class of sequence pairs, called “cross Z-complementary pairs (CZCPs),” each displaying zero-correlation zone (ZCZ) properties for both their aperiodic autocorrelation sums and crosscorrelation sums. Systematic constructions of perfect CZCPs based on selected Golay complementary pairs (GCPs) are presented. Secondly, we point out that CZCPs can be utilized as a key component in designing training sequences for broadband spatial modulation (SM) systems. We show that our proposed SM training sequences derived from CZCPs lead to optimal channel estimation performance over frequency-selective channels.