Continuous Wavefront Design via Virtual Point Sources: A Holographic Paradigm for Near-Field XL-MIMO

TL;DR

This paper introduces a holographic beamforming paradigm for XL-MIMO systems that shapes a continuous wave function over the array, reducing complexity and effectively addressing near-field challenges.

Contribution

It proposes a Virtual Point Source method for non-iterative wave function approximation, improving near-field XL-MIMO beamforming design.

Findings

Non-iterative VPS approach achieves comparable performance to iterative algorithms.

The method significantly reduces computational complexity.

The framework is demonstrated in IRS-assisted systems.

Abstract

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.