RIS-Aided Millimeter Wave Cell-Free Massive MIMO Systems: Joint Beamforming and SE–EE Trade-Off

When millimeter wave (mmWave) frequencies and reconfigurable intelligent surfaces (RISs) are used in cell-free (CF) massive multiple-input multiple-output (MIMO) systems to enhance the data rate, the energy efficiency (EE) may decrease due to the high power consumption of more antennas and RIS elements. In this paper, we aim to design a hybrid beamforming scheme to strike the balance between the spectral efficiency (SE) and EE of the RIS-aided mmWave CF massive MIMO system. To achieve this goal, we formulate the resource efficiency (RE) maximization problem to jointly design the analog and digital beamformings at access points (APs) and the reflect beamforming at RISs. Since the original problem is non-convex, we propose a golden-search-based alternating optimization algorithm to solve it in an iterative manner. The closed-form solutions of three beamformings are also derived. Numerical results demonstrate that the proposed hybrid beamforming scheme is effective in realizing the trade-off among the SE and EE in RIS-aided mmWave CF massive MIMO systems. Moreover, the proposed algorithm exhibits the fast convergence behavior.