Enhanced Cross Z-Complementary Set and Its Application in Generalized Spatial Modulation

Generalized spatial modulation (GSM) is a novel multiple-antenna technique offering flexibility among spectral efficiency, energy efficiency, and the cost of RF chains. In this paper, a novel class of sequence sets, called enhanced cross Z-complementary set (E-CZCS), is proposed for efficient and feasible training sequence design in broadband GSM systems. Specifically, an E-CZCS consists of multiple CZCSs possessing front-end and tail-end zero-correlation zones (ZCZs), whereby any two distinct CZCSs have a tail-end ZCZ when a novel type of cross-channel aperiodic correlation sums is considered. The theoretical upper bound on the ZCZ width is first derived, upon which E-CZCSs with maximum ZCZ width and flexible parameters are constructed. For optimal channel estimation over frequency-selective channels, we introduce and evaluate a novel GSM training framework employing the proposed E-CZCSs. Numerical results demonstrate that the proposed E-CZCS-based training can achieve the minimum channel estimation mean square error (MSE) and outperform other classes of sequences.