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

Movable antenna (MA) has emerged as a promising technology for enhancing communication performance over conventional fixed position antenna (FPA) by exploiting spatial channel variations. In this paper, we propose a general energy efficiency (EE) optimization framework for the MA-aided multi-user multiple-input multiple-output (MU-MIMO) downlink communications. We jointly optimize the precoding matrices and the positions of transmit and receive MAs considering two different types of power constraint models, i.e., the sum power constraint (SPC) and multiple weighted power constraints (MWPCs), and various physical constraints on MA positions. In both the SPC case and the MWPCs case, we optimize the MA positions by jointly employing the weighted minimum mean square error (WMMSE) and successive convex approximation (SCA) methodologies. As for the precoding matrices optimization, by exploiting the uplink-downlink duality of MU-MIMO systems, we transform the downlink EE optimization into their virtual uplink EE optimization counterparts. Then, we derive the optimal structures of the precoding matrices, where the involved optimal power allocations take the multi-user water-filling solutions. To compute the parameters of the multi-user water-filling solutions, by taking advantage of the underlying algebraic monotonicity of the problem, we propose three novel design strategies, i.e., the direct Dinkelbach based design, the modified Dinkelbach based design, and the bound-ware penalty based design. In contrast to conventional fractional programming (FP) based EE optimization methods, the proposed algorithms offer significantly lower computational complexities and explicit physical insights. Moreover, the simulation results demonstrate the superior performance and high efficiency of our proposed EE optimization algorithms.