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

Holographic MIMO: How Many Antennas Do We Need for Energy Efficient Transmission?