Symmetrical Z-Complementary Code Sets for Optimal Training in Generalized Spatial Modulation

This paper considers the optimal training for generalized spatial modulation systems. First, a training framework for broadband generalized spatial modulation systems is proposed. Then, we introduce a novel class of code sets, called “symmetrical Z-complementary code sets”, whose aperiodic auto- and cross-correlation sums exhibit zero-correlation zones at both the front-end and tail-end of the entire correlation window. A construction of optimal symmetrical Z-complementary code sets based on generalized Boolean functions is presented. Furthermore, we apply symmetrical Z-complementary code sets to design optimal training sequences for broadband generalized spatial modulation systems over frequency-selective channels.