Omnidirectional Precoding Designs Based on 2-D Golay Complementary Array Pairs for Massive MIMO Systems With Fully-Connected and Partially-Connected Structures

Recently, the design of omnidirectional precoding has been widely studied for massive multiple-input multiple-output (MIMO) systems. For the base station (BS) equipped with a uniform rectangular array (URA), the current state-of-the-art scheme uses two-dimensional (2-D) Golay complementary array pairs (GCAPs)/Golay complementary array sets (GCASs) as precoding matrices to achieve omnidirectional transmission. However, the existing constructions of 2-D GCAP/GCAS-based precoding can just be implemented using the analog phase shifter network with fully-connected structure (FCS), and the existing parameters of 2-D GCAPs constructed from function-based methods are limited. More specifically, the array sizes are in the form of a power-of-two. In this paper, utilizing the truncation technique, we presented three constructions of new 2-D GCAPs with non-power-of-two array sizes from 2-D generalized Boolean functions (GBFs), which have never been reported in the literature. The proposed constructions include 2-D GCAPs with power-of-two array sizes as a special case, with flexible parameters. Moreover, we further provide a theoretical connection between 2-D GBFs and precoding matrices, such that the omnidirectional precoding scheme based on the proposed 2-D GCAPs is applicable to both FCS and partially-connected structure (PCS). Finally, simulation results demonstrate that the precoding scheme is useful in massive MIMO omnidirectional transmission systems.