Near-Field Wideband Beamforming for RIS Based on Fresnel Zone

TL;DR

The paper tackles near-field wideband beam split in RIS-enabled communications by introducing a Fresnel-zone framework that transforms the RIS plane into along/across-Fresnel-zone coordinates. It proves that the RIS channel is the Fourier transform of the Fresnel-zone reflected intensity modulated by a designed phase, enabling a nearly closed-form upper bound on achievable rate via Parseval's theorem. To approach this bound, the authors develop phase designs based on the stationary phase method and the Gerchberg-Saxton algorithm, operating across Fresnel zones to produce a flat in-band gain, validated by simulations. The approach achieves substantial mitigation of near-field beam split without extra hardware and offers practical beamforming strategies for wideband RIS systems in mmWave/THz regimes.

Abstract

Reconfigurable intelligent surface (RIS) has emerged as a promising solution to overcome the challenges of high path loss and easy signal blockage in millimeter-wave (mmWave) and terahertz (THz) communication systems. With the increase of RIS aperture and system bandwidth, the near-field beam split effect emerges, which causes beams at different frequencies to focus on distinct physical locations, leading to a significant gain loss of beamforming. To address this problem, we leverage the property of Fresnel zone that the beam split disappears for RIS elements along a single Fresnel zone and propose beamforming design on the two dimensions of along and across the Fresnel zones. The phase shift of RIS elements along the same Fresnel zone are designed aligned, so that the signal reflected by these element can add up in-phase at the receiver regardless of the frequency. Then the expression of equivalent channel is simplified to the Fourier transform of reflective intensity across Fresnel zones modulated by the designed phase. Based on this relationship, we prove that the uniformly distributed in-band gain with aligned phase along the Fresnel zone leads to the upper bound of achievable rate. Finally, we design phase shifts of RIS to approach this upper bound by adopting the stationary phase method as well as the Gerchberg-Saxton (GS) algorithm. Simulation results validate the effectiveness of our proposed Fresnel zone-based method in mitigating the near-field beam split effect.

Figures (12)

• Figure 1: System model.
• Figure 2: A series of Fresnel zones of the communication system with a BS and a UE. The transmission length $l^\text{B-R}+l^\text{R-U}$ remains the same on each Fresnel zone.
• Figure 3: The intersections of Fresnel zones and the RIS plane are a series of ellipses. A new coordinate system is set on the ellipses with axes of semi-major axis $a$ of Fresnel zone and angular coordinate $\theta$
• Figure 4: The approximation of channel gain $|g_\text{Narr}(f)|^2$. The approximation of $v_t(t)$ is shown in Fig. \ref{['fig:intensity']}. The approximation of channel gain is illustrated in Fig. \ref{['fig:sinc']}. Probability density function of $\Gamma$ as the location of BS and UE chosen randomly is shown in Fig. \ref{['fig_pdfgamma']}.
• Figure 5: Normalized beamforming gain with respect to frequency. With increase of aperture $D$, the effective bandwidth drops significantly.