On the Mates of Cross Z-Complementary Pairs for Training Sequence Design in Generalized Spatial Modulation

Generalized spatial modulation (GSM) as a novel multiple-antenna transmission technique is an extension of spatial modulation (SM). The GSM system provides flexibility in terms of spectral efficiency, energy efficiency, and the cost of radio-frequency (RF) chains. In the literature, cross Z-complementary pair (CZCP) has been proposed for optimal training sequence design in SM, but not for GSM. Due to its specific zero correlation zone (ZCZ) properties for autocorrelation sums and cross-correlation sums, optimal channel estimation performance in SM over frequency-selective channels can be achieved. In this paper, we propose an efficient construction for mutually orthogonal mate of a CZCP and provide a new construction of CZCPs. Based on the proposed CZCP and its mate, a novel training framework of GSM system is presented to achieve the minimum mean square error (MSE) channel estimation performance in frequency-selective channels. Numerical results demonstrate that the proposed CZCP-mate-based training for the GSM system can eliminate inter-symbol interference (ISI) and inter-antenna interference (IAI).