New Design of Sparse Zero-Correlation-Zone Sequence Sets for Optimal Channel Estimation in (Generalized) Spatial Modulation Systems

Within the zero-correlation-zone (ZCZ), ZCZ sequence sets exhibit ideal correlation properties, which is highly advantageous for both wireless communications and radar sensing applications. Recently, to achieve optimal training for spatial modulation (SM), Pai et al. introduced the concept of sparse ZCZ (SZCZ) sequence sets, where each column contains only one non-zero element. In this paper, we first extend the SZCZ sequence set concept by permitting multiple non-zero elements per column, thereby accommodating training design requirements for generalized SM (GSM) systems. Then, we propose a direct construction of SZCZ sequence sets with parameter (qn+k, qm+n+k, (q−1)qπ(2)−1+(q−2)qπ(3)−1, (qn, qm+n)) based on restricted extended Boolean functions. Compared to existing works, the proposed SZCZ sequence sets exhibit a greater ZCZ width and can be applied to both SM and GSM training designs simultaneously. Simulation results show that compared with other training sequences, the channel estimation performance is significantly improved when the proposed SZCZ sequence set is used as the training sequences.