New Constructions of Optimal Symmetrical Z-Complementary Code Sets

Symmetrical Z-complementary code sets (SZCCSs), as a novel type of training sequences, have demonstrated exceptional channel estimation performance when applied to generalized spatial modulation (GSM) systems. This paper addresses the current limitations in the design methods and parameter range of SZCCSs by proposing three schemes. Initially, by analyzing the complementary properties of Discrete Fourier Transform (DFT) matrix elements, we construct a class of optimal SZCCSs using the Kronecker product of unit modulus sequences and DFT matrices. Subsequently, to diversify the parameter of code quantity, we perform the Kronecker product with complete complementary codes (CCCs) and orthogonal matrices, resulting in a class of optimal SZCCSs. Also, if a sequence with low autocorrelation replace the orthogonal matrix, the resulting SZCCS exhibits low autocorrelation sidelobes outside the zero correlation zone and complete complementary cross correlation characteristics. The study offer a broad range of parameters not previously identified in the literature, significantly enriching the parameter space of SZCCSs. Simulation results validate that the proposed SZCCSs show superior resistance to multipath interference in GSM systems compared to traditional sequences, highlighting their potential advantages in channel estimation.