Cross Z-Complementary Sets With Flexible Lengths for Optimal Training Design in Spatial Modulation

Cross Z-complementary sets (CZCSs) are useful for optimal training design in spatial modulation (SM) system over frequency-selective channels. Recently, several generic constructions of CZCSs have been proposed based on special sequences. Based on the algebraic tool of generalized Boolean functions, we make the first attempt for two constructions of CZCSs having flexible non-power-of-two lengths and large zero correlation zone properties. It is shown that the proposed CZCSs lead to optimal SM training sequences which can achieve the minimum mean square error of channel estimation performance in frequency-selective channels.