Two-Dimensional Sparse Golay Complementary Array Sets for Omnidirectional Transmission in Massive MIMO Systems

Two-dimensional (2D) Golay complementary array sets (GCASs) have been widely used to design omnidirectional precoding matrices for massive multi-input multi-output (MIMO) systems with uniform rectangular arrays (URAs), owing to their favorable 2D autocorrelation properties. However, most existing 2D GCAS constructions are tailored for analog precoding architectures that employ a fully-connected structure (FCS), with limited attention given to the design of precoding schemes for a partially-connected structure (PCS). To address this gap, this letter proposes a new class of 2D sparse GCASs (SGCASs) that incorporate controllable zero elements, enabling efficient precoding design for PCS. The proposed construction is based on 2D restricted generalized Boolean functions (RGBFs) and enables flexible array and set sizes. Moreover, the proposed method is compatible with both PCS and FCS, offering enhanced design flexibility. Simulation results demonstrate that the proposed SGCASs achieve omnidirectional transmission and improved bit error rate (BER) performance.