This paper presents an innovative movable antenna (MA)-enhanced multi-user multiple-input multiple-output (MIMO) downlink system. We aim to maximize the energy efficiency (EE) under statistical channel state information (S-CSI) through a joint optimization of the precoding matrix and the antenna position vectors (APVs). To solve the resulting stochastic problem, we first resort to deterministic equivalent (DE) tecnology to formulate the deterministic minorizing function of the system EE and the deterministic function of each user terminal (UT)'s average achievable rate w.r.t. the transmit variables (i.e., the precoding matrix and the transmit APV) and the corresponding receive APV, respectively. Then, we propose an alternating optimization (AO) algorithm to alternatively optimize the transmit variables and the receive APVs to maximize the formulated deterministic objective functions, respectively. Finally, the above AO algorithm is tailored for the single-user scenario. Our numerical results reveal that, the proposed MA-enhanced system can significantly improve the system EE compared to several benchmark schemes based on the S-CSI and the optimal performance can be achieved with a finite size of movement regions for MAs.
Chen et al. (Mon,) studied this question.