Electromagnetic Normalization of Channel Matrix for Holographic MIMO Communications

Holographic multiple-input and multiple-output (MIMO) communications introduce innovative antenna array configurations, such as dense arrays and volumetric arrays, which offer notable advantages over conventional planar arrays with half-wavelength element spacing. However, accurately assessing the performance of these new holographic MIMO systems necessitates careful consideration of channel matrix normalization, as it is influenced by array gain, which, in turn, depends on the array topology. Traditional normalization methods may be insufficient for assessing these advanced array topologies, potentially resulting in misleading or inaccurate evaluations. In this study, we propose electromagnetic normalization approaches for the channel matrix that accommodate arbitrary array topologies, drawing on the array gains from analytical, physical, and full-wave methods. Additionally, we introduce a normalization method for near-field MIMO channels based on a rigorous dyadic Green's function approach, which accounts for potential losses of gain at near field. Finally, we perform capacity analyses under quasi-static, ergodic, and near-field conditions, through adopting the proposed normalization techniques. Our findings indicate that channel matrix normalization should reflect the realized gains of the antenna array in target directions. Failing to accurately normalize the channel matrix can result in errors when evaluating the performance limits and benefits of unconventional holographic array topologies, potentially compromising the optimal design of holographic MIMO systems.