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

This paper considers the optimal training design for broadband generalized spatial modulation systems over frequency-selective channels using a novel class of code sets introduced, 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. Two constructions of (optimal) symmetrical Z-complementary code sets based on generalized Boolean functions are presented. Numerical evaluations indicate that the proposed training sequences for generalized spatial modulation can achieve optimal channel estimation performance and outperform other classes of sequences.