Construction of 2-D Z-Complementary Array Code Sets with Flexible Lengths for Different System Requirements

Abstract: In this paper, we propose a new and optimal construction of two-dimensional (2-D) Z-complementary array code set (ZCACS) using multivariable extended Boolean functions (EBFs). The proposed 2-D arrays can be used in multi-carrier code division multiple access (MC-CDMA) systems. The proposed construction produces a better PMEPR upper bound than the existing constructions for such use cases. We also propose a tighter upper bound for the set size and showed that the proposed code set is optimal in special cases. Finally, We derive 2-D Golay complementary array set (GCAS) and Golay complementary set (GCS) from the proposed construction, which has application in uniform rectangular array (URA)-based massive multiple-input multiple-output (mMIMO) system to achieve omnidirectional transmission. The simulation result shows the performance benefits of the derived codes. In essence, we show that the flexibility of the parameters of the proposed 2-D ZCACS makes it a good candidate for a wide range of use cases in wireless communication.