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.

Controlling the peak-to-mean envelope power ratio (PMEPR) of multi-carrier code division multiple access (MC-CDMA) transmissions is a notoriously important problem. In this letter, a direct construction of multiple complete complementary codes (CCCs) with inter-set zero cross-correlation zone (ZCCZ) is proposed based on multivariable functions. The presented construction has an advantage over the previous works with regard to the new flexible parameters and low column sequence PMEPR, which may give an extra benefit in fulfilling different requirements and managing PMEPR in MC-CDMA systems with multiple cells. In addition, it turns out that the combination of the constructed CCCs results in a new optimal Z-complementary code set (ZCCS).