New Constructions of Z-Complementary Code Sets Based on Generalized Column Orthogonal Matrices

Z-complementary code sets (ZCCSs) are widely employed in multi-carrier spread spectrum and MIMO communication systems. This study introduces the concept and construction of generalized column orthogonal (GCO) matrices to develop new classes of Z-paraunitary (ZPU) matrices. Utilizing the equivalence between ZCCSs and ZPU matrices, novel polyphase ZCCSs are constructed. The flexible sizing of GCO matrices allows for a wide range of parameter configurations. The proposed method enables the derivation of optimal ZCCS parameters that are unattainable in existing literature. Furthermore, by designing GCO matrices whose column vectors exhibit low peak-to-mean envelope power ratio (PMEPR), ZCCSs with column sequence PMEPR no greater than 2 are achieved. This work expands the repertoire of code options for various communication scenarios.