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

## TL;DR

This paper introduces a new framework for optimizing signal transmission in large antenna arrays by accounting for mutual coupling effects, improving power efficiency and performance.

## Contribution

A novel coupling-aware precoding framework using a Neumann series approximation for inverse coupling in extremely large antenna arrays.

## Key findings

- Coupling-aware received power maximization aligns with the dominant eigendirection of the coupling-shaped channel.
- Eigenmode design outperforms coupling-aware MRT in power efficiency under mutual coupling.
- The proposed method is robust in multipath scenarios and achieves the highest received power in simulations.

## Abstract

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.