Hybrid Precoding Design for Two-Way Relay-Assisted Terahertz Massive MIMO Systems

Hybrid precoding has emerged as a promising technique to reduce the hardware cost and complexity in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, due to the drastic increase in the number of user devices and higher data rate demand, new frequency bands (i.e., terahertz (THz) communications) are needed to explore. At THz frequencies, the precoding technique can provide a large beamforming gain, but still, the blockage and high path-loss remain a significant problem. To overcome the blockage problem, in this paper, we introduce the two-way relay design where the well-known two-way amplify-and-forward (AF) relay in THz-MIMO orthogonal frequency-division multiplexing (OFDM) systems is employed. The optimal two-way relay hybrid precoding problem is non-convex due to the practical hardware constraints (i.e., unit-modulus and block-diagonal constraints). To solve this problem, we first propose to use mathematical manipulations to remove the block-diagonal constraints from its analog part and then reformulate the original two-way relay hybrid precoding problem into a quadratic-convex problem with only power constraint. Finally, we obtain the closed-form solution for the two-way relay hybrid precoding problem. Simulation results reveal that our proposed solution can achieve better sum-rate and energy efficiency than existing hybrid schemes.