Beamforming design for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging due to prohibitive computational complexity and complex near-field propagation effects. To address this, this paper introduces a holographic beamforming paradigm that reformulates the design from optimizing variables at spatially discrete antenna locations to shaping a continuous electromagnetic wave function over the array aperture, effectively mitigating the growth of algorithmic complexity as the array scale increases. We apply this paradigm to the challenging dual near-field (DNF) scenario, where strong transceiver coupling severely degrades conventional iterative algorithms. In this case, we propose a novel Virtual Point Source (VPS) method, which approximates the ideal wave function with a single and analytically tractable spherical-wave. A rigorous geometric-optical analysis is provided to show that the optimal VPS location can be determined in a fully non-iterative manner, thus decoupling the coupled DNF problem. The proposed method is demonstrated in an intelligent reflecting surfaces (IRS)-assisted system, where simulation results show that our non-iterative approach achieves performance comparable to converged alternating-optimization (AO) algorithms, while incurring significantly lower complexity and avoiding convergence uncertainty. This work offers a new theoretical framework for holographic beamforming design in XL-MIMO systems.

翻译：针对超大规模多输入多输出（XL-MIMO）系统的波束成形设计，因其计算复杂度过高且需处理复杂的近场传播效应而面临严峻挑战。为此，本文提出一种全息波束成形范式，将设计从优化空间离散天线位置的变量，重构为在阵列孔径上塑造连续电磁波函数，从而有效缓解算法复杂度随阵列规模增长的问题。我们将该范式应用于具有挑战性的双近场（DNF）场景——在该场景中，收发端强耦合会严重劣化传统迭代算法性能。针对该问题，我们提出新颖的虚拟点源（VPS）方法，利用单一且解析可处理的球面波来逼近理想波函数。通过严格的几何光学分析证明，最优VPS位置可通过完全非迭代方式确定，从而解耦DNF耦合问题。所提方法在智能反射面（IRS）辅助系统上得到验证：仿真结果表明，这种非迭代方法在实现与交替优化（AO）算法可比性能的同时，显著降低计算复杂度且避免了收敛不确定性。本研究为XL-MIMO系统的全息波束成形设计提供了新的理论框架。