A Novel Construction of Optimal Cross Z-Complementary Sets Based on Generalized Boolean Functions

The cross Z-complementary pair (CZCP) has been employed for training design in spatial modulation (SM). Due to its specific zero correlation zone (ZCZ) for autocorrelation and cross-correlation sums, optimal channel estimation performance in SM over frequency-selective channels can be achieved. However, a disadvantage of the CZCP is that its ZCZ width is theoretically limited by the half sequence length. In this paper, we consider the cross Z-complementary sets (CZCSs) to aim for large ZCZ widths which can be used in SM to combat larger delay spread. A novel construction of CZCSs based on generalized Boolean functions is presented in this paper. The proposed construction leads to the so-called optimal CZCSs with the maximum ZCZ width. The simulation results demonstrate that the proposed CZCS-based training sequences can tolerate larger delay spreads to improve the channel estimation performance in SM.