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 have many applications in modern wireless communications, such as multi-carrier code division multiple access (MC-CDMA), massive multiple input multiple output (mMIMO), etc. The main theoretical problem for sequences and 2-D arrays for application in MC-CDMA lies in the efficient construction of such sequences and arrays, which have low peak-to-mean envelope power ratio (PMEPR) and flexible parameter values. The PMEPR measures the power efficiency of the concerned system and hence has been an important research topic for past several years. The proposed construction produces a better PMEPR upper bound than the existing constructions. We also propose a tighter upper bound for the set size which translates more number of supported users in the communication system. We show that for some special cases, the proposed code set is optimal with respect to that bound. Finally, We derive 2-D Golay complementary array set (GCAS) and Golay complementary set (GCS) from the proposed construction, which has significant 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 arrays. In essence, we show that the flexibility of the parameters of the proposed 2-D ZCACS makes it a good candidate for practical use cases, both in theory and simulation.