Deterministic and Statistical Analysis of the DoF of Continuous Linear Arrays in the Near Field

2025-03-12

AI Summary

This work addresses the modeling and analysis of degrees of freedom (DoF) for communication between large, linear, intelligent antenna arrays in the near-field regime—breaking away from conventional far-field assumptions and co-axial/axial approximations. We propose a unified deterministic DoF analytical framework for non-co-axial near-field configurations, integrating integral-equation-based channel modeling, asymptotic singular-value analysis, and stochastic geometry. This framework yields, for the first time, a statistical DoF model accommodating arbitrary two-dimensional distributions of relative position and mutual orientation between the two arrays. Key findings reveal that near-field DoF substantially exceed classical far-field limits; DoF exhibits high sensitivity to both relative position and array orientation; and the proposed model provides a quantifiable, generalizable theoretical foundation for capacity assessment and system design in millimeter-wave near-field networking.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

This paper examines the number of communication modes, that is, the degrees of freedom (DoF), in a wireless setup comprising a small continuous linear intelligent antenna array in the near field of a large one. The framework allows for any orientations between the arrays and any positions in a two-dimensional space assuming that the transmitting array is placed at the origin. Therefore, apart from the length of the two continuous arrays, four key parameters determine the DoF and are hence considered in the analysis: the Cartesian coordinates of the center of the receiving array and two angles that model the rotation of each array around its center. The paper starts with the calculation of the deterministic DoF for a generic geometric setting, which extends beyond the widely studied paraxial case. Subsequently, a stochastic geometry framework is proposed to study the statistical DoF, as a first step towards the investigation of the system-level performance in near field networks. Numerical results applied to millimeter wave networks reveal the large number of DoF provided by near-field communications and unveiled key system-level insights.

Problem

• Analyzes degrees of freedom in near-field wireless communication.
• Considers array orientations and positions in 2D space.
• Investigates system-level performance in millimeter wave networks.

Innovation

• Analyzes DoF in near-field wireless communication setups
• Uses deterministic and stochastic geometry frameworks
• Focuses on millimeter wave network applications