A Framework for Energy Efficiency Optimization in IRS-Aided Hybrid MU-MIMO Systems

Energy efficiency (EE) optimization has attracted significant research attention for implementing green communications. With cost-effective and low-power advantages, intelligent reflecting surface (IRS) and hybrid analog-digital transceiver have recently emerged as two promising technologies of next-generation green wireless systems. In this paper, we propose a comprehensive framework for EE optimization in four types of IRS-aided hybrid analog-digital multiuser multiple-input multiple-output communication systems, including the uplink (UL) systems under the sum power and box eigenvalue constraints as well as the per-radio-frequency chain power constraints (PRPCs), and the downlink (DL) systems under the sum power constraint and the PRPCs. This framework proposes a unified design methodology to these four considered systems by separating the optimization of analog and digital matrix variables. Specifically, for the UL EE maximization problems, we firstly propose a channel alignment based algorithm to separately optimize the analog precoders at users, the analog combiner at the base station and the IRS reflecting matrix, whose computational complexity is significantly reduced as compared with the traditional alternating optimization algorithm. Then, by introducing the auxiliary variables and exploiting the Karush-Kuhn-Tucker conditions based algorithm, the optimal digital precoders at users are obtained in closed forms. Furthermore, the intractable DL EE optimization can be equivalently transformed into its virtual UL counterpart using the DL-UL duality, leading to the general applicability of the proposed framework. Extensive simulations reveal that the proposed algorithm attains the almost identical EE performance to the traditional benchmarks with a lower computational complexity.