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）通信系统利用带有亚波长间距的大量天线的空间限制的大规模MIMO阵列，并已成为第六代（6G）网络的一种有前途的候选技术。在本文中，我们考虑多用户HMIMO通信系统的下行链路，在随机电磁MIMO信道模型的傅里叶平面波级数表示下，做出了两个重要贡献。首先，我们在基站（BS）的最大比传输（MRT）预编码下，提出了一个可达的下行速率的封闭形式表达式。所得的表达式明确显示在用户速率上， HMIMO表面的边长和每个用户部署的天线数量的影响。其次，我们针对在空间限制的HMIMO表面上部署的天线数量，制定了一个能源效率（EE）最大化问题。所得到的这个问题的隐式解被证明是全局最优的。数值结果为不同操作区域的多用户HMIMO系统的EE性能提供了有用的见解。