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

2026-04-10

AI Summary

This work addresses the performance degradation and high computational complexity of conventional beamforming algorithms in extremely large-scale MIMO systems operating in dual near-field scenarios, where strong transceiver coupling poses significant challenges. To overcome these limitations, the paper introduces a novel holographic beamforming paradigm that reformulates discrete antenna optimization as a continuous electromagnetic wavefront design problem. A key innovation is the proposed virtual point source method, which leverages geometric optics to non-iteratively determine the optimal equivalent source location, enabling a single spherical wave to accurately approximate the ideal wavefront and effectively decouple the dual near-field interactions. This approach achieves performance comparable to convergent alternating optimization algorithms in intelligent reflecting surface (IRS)-assisted systems, yet with substantially reduced computational complexity and without requiring iterative procedures, thereby overcoming the longstanding trade-off between convergence reliability and computational overhead in traditional schemes.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• XL-MIMO
• beamforming
• near-field
• computational complexity
• dual near-field

Innovation

• Holographic Beamforming
• Virtual Point Source
• Near-Field XL-MIMO
• Non-Iterative Design
• Continuous Wavefront