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ADMM for Hybrid Precoding of Relay in Millimeter-Wave Massive MIMO System

Beamforming with multiple data streams, or named as precoding, plays a significant role in millimeter-wave massive MIMO systems. If properly designed, the precoding can improve spectral efficiency of the system and compensate for the degradation caused by channels. Although the classical full-digital precoding can achieve the optimal performance, it is too expensive for implementation. To reduce cost and power consumption, some hybrid structures of precoding are recently proposed while their precoding schemes have not been extensively studied. In this paper, the mathematical model of the precoding for relay assisted system is reconstructed. The objective function is highly non-convex and has some complex constraints. Especially the block-diagonal constraint and constant-modulus constraint make the classical precoding methods based on singular value decomposition not applicable. We design an algorithm based on alternating direction method of multipliers to optimize the objective function. By deliberating over the iteration order of the variables, we give the convergent condition of the proposed algorithm. This paper focused on sub-connected precoding structures since they have more constraints. Meanwhile, the proposed algorithm can be applied to full-connected structures simply. We present the simulation results which indicate that the proposed algorithm can provide a near optimal solution to the original precoding problem.