Holographic multiple-input multiple-output (HMIMO) communication systems utilize spatially-constrained massive MIMO arrays containing large numbers of antennas with sub-wavelength spacing, and have emerged as a promising candidate technology for Sixth Generation (6G) networks. In this paper, we consider the downlink of a multi-user HMIMO communication system under a Fourier plane-wave series representation of the stochastic electromagnetic MIMO channel model, and make two important contributions. First, we present a closed-form expression of the ergodic achievable downlink rate under maximum ratio transmission (MRT) precoding at the base station (BS). The derived expression explicitly shows the effect of the side-lengths of the HMIMO surfaces at the BS and each user, and the number of antennas deployed in these surfaces on the user rates. Second, we formulate an energy efficiency (EE) maximization problem with respect to the number of antennas arranged within spatially-constrained HMIMO surfaces at the BS and each user. The resulting implicit solution for this problem is shown to be globally optimal. Numerical results yield useful insights into the EE performance of multi-user HMIMO systems in different operating regimes.

翻译：全息多输入多输出（HMIMO）通信系统利用空间受限的大规模MIMO阵列，其中包含大量亚波长间距的天线，已成为第六代（6G）网络的一种有前景的候选技术。本文考虑在随机电磁MIMO信道模型的傅里叶平面波级数表示下，多用户HMIMO通信系统的下行链路，并做出两项重要贡献。首先，我们给出了基站（BS）采用最大比传输（MRT）预编码下遍历可达下行速率的闭式表达式。该表达式明确显示了BS和每个用户处HMIMO表面的边长、以及这些表面中部署的天线数量对用户速率的影响。其次，我们构建了一个关于BS和每个用户处空间受限HMIMO表面内天线数量的能效（EE）最大化问题。所得问题的隐式解被证明是全局最优的。数值结果揭示了多用户HMIMO系统在不同运行场景下的能效性能。