[Paper Review] How to Differentiate between Near Field and Far Field: Revisiting the Rayleigh Distance

Shu Sun, Renwang Li+4 more|arXiv (Cornell University)|Sep 23, 2023

Electromagnetic Compatibility and Measurements4 citations

TL;DR

This paper proposes an effective degrees of freedom (EDoF)-based near-field (NF) to far-field (FF) demarcation method for massive MIMO systems using extremely large aperture arrays (ELAAs), offering a more accurate boundary than the classical Rayleigh distance by directly linking the NF-FF transition to spectral efficiency. The EDoF-based boundary reduces channel capacity estimation errors by over 35% compared to Rayleigh distance, enabling better system design for 6G mmWave/THz communications.

ABSTRACT

Future wireless systems are likely to adopt extremely large aperture arrays to achieve higher throughput, wider coverage, and higher spatial resolution. Conventional wireless systems predominantly operate in the far field (FF) of the radiation source. However, as the array size increases and the carrier wavelength decreases, the near field (NF) becomes nonnegligible. Since the NF and FF differ in many aspects, it is critical to identify their corresponding regions. In this article, we first provide a comprehensive overview of the existing NF-FF boundaries, then introduce a novel NF-FF demarcation method based on effective degrees of freedom (EDoF) of the channel. Since EDoF is intimately related to channel capacity, the EDoF-based border is able to characterize key channel performance more accurately than the classic Rayleigh distance and other representative benchmarks. Furthermore, we analyze the main features of the EDoF-based NF-FF boundary, provide insights into system design, and outline the associated challenges and research opportunities.

Motivation & Objective

• Address the limitations of the classical Rayleigh distance in defining the NF-FF boundary for modern massive MIMO and ELAA systems.
• Identify the need for a performance-driven NF-FF demarcation criterion that reflects actual system metrics like spectral efficiency.
• Develop and validate a novel EDoF-based boundary that better characterizes channel behavior and system performance.
• Provide design insights for 6G systems by analyzing how the EDoF-based boundary varies with array geometry, orientation, and user location.
• Demonstrate that the EDoF-based boundary outperforms the Rayleigh distance in predicting channel capacity and user separation capability.

Proposed method

• Define the NF-FF boundary based on the effective degrees of freedom (EDoF) of the MIMO channel, which directly relates to spectral efficiency.
• Use the spherical wavefront model (SWM) for accurate channel modeling in the near field and the planar wavefront model (PWM) for the far field.
• Derive the EDoF-based boundary distance by equating the EDoF of the SWM and PWM under the same signal-to-noise ratio (SNR) and array configuration.
• Analyze the boundary for various array configurations, including uniform linear arrays (ULAs), uniform rectangular arrays (URA), and conformal arrays.
• Validate the boundary using simulations across different array geometries, user positions, and orientations, comparing it with the Rayleigh distance.
• Investigate the impact of the boundary on key system performance metrics such as channel capacity, user multiplexing, and beamforming accuracy.

Figure 1: Illustration of wireless communications in the near field and far field.

Experimental results

Research questions

• RQ1 How does the EDoF-based NF-FF boundary compare to the classical Rayleigh distance in terms of accuracy for channel capacity prediction?
• RQ2 What are the key geometric and array configuration factors that influence the EDoF-based NF-FF boundary?
• RQ3 How does the boundary distance vary with user location, orientation, and array aperture size?
• RQ4 In what ways does the EDoF-based boundary improve user multiplexing and beam management in near-field massive MIMO systems?
• RQ5 Can the EDoF-based boundary be generalized across different conformal and planar array structures in 6G wireless systems?

Key findings

• The EDoF-based NF-FF boundary reduces channel capacity estimation errors by over 35% compared to the Rayleigh distance in ULA-to-ULA scenarios, especially at high SNR.
• The EDoF-based boundary is more accurate than the Rayleigh distance because it directly correlates with spectral efficiency, the key performance metric of interest.
• The boundary distance varies significantly with array orientation and geometry: it is minimized when two users are aligned in the same direction from the base station and maximized when they are at maximum angular separation.
• For a URA-to-ULA configuration, the boundary distance increases with the orientation angle θ when the URA’s vertical length is small, but decreases when the vertical length is large, due to the effective aperture dependence.
• The boundary distance reaches its maximum when the line of centers of two ULAs is perpendicular to the arrays and its minimum when aligned with them.
• The EDoF-based boundary enables better user separation in the near field, as spatial channels remain distinguishable even when users are in the same direction, up to a certain distance determined by the boundary.

Figure 2: Antenna array configurations considered in this article. (a) Both the BS and user are equipped with a ULA, where $\alpha$ denotes the angle between the center of the BS ULA and the center of the user ULA, and $\beta$ is the angle of the user ULA with respect to the positive Z-direction wit