Coupling Effects and Analysis in Extremely Large-Scale Planar Array Antennas

This paper develops a physically consistent precoding framework for extremely large antenna arrays (ELAAs), incorporating structural mutual coupling through a two-dimensional impedance network. To maintain scalability, we introduce a Neumann series approximation for the inverse coupling operator. Our analysis reveals that coupling-aware received power maximization reduces to a Hermitian rank-one quadratic form, whose optimum aligns with the dominant eigendirection of the effective coupling-shaped channel. This result indicates that both eigen-decomposition-based optimization and coupling-aware maximum ratio transmission (MRT) enhance power efficiency under mutual coupling, with the eigenmode design achieving superior performance. In addition, we further extend the analysis from the free-space path to the multipath scenario, demonstrating the robustness and adaptability of the proposed method under practical propagation conditions. Simulations confirm that structural coupling severely degrades conventional MRT, whereas the proposed eigenmode method with Neumann approximated coupling attains the highest received power among all considered schemes. The framework is interpretable, numerically stable, and readily implementable, offering practical guidance for energy-efficient near-field beamforming on ultra-large apertures.