Wideband Beamforming with RIS: A Unified Framework via Space-Frequency Transformation

TL;DR

This work tackles wideband RIS beamforming when RIS phase shifts are frequency-invariant and beam squint degrades performance across the band. It introduces a unified space-frequency framework based on space-frequency Fourier transform (SFFT) and stationary phase method (SPM) to derive an approximate closed-form RIS phase profile that yields a large, flat beampattern over the desired band without adding time-delay hardware. The approach handles both boresight and arbitrary target locations by transitioning from discrete to continuous RIS models and then to frequency-domain design, employing polar and prolate spheroidal coordinates as needed and using an LFM-CW–inspired modulation strategy aligned with an amplitude function. Simulations show substantial gains in spectral efficiency (over 10%) and a significant enhancement in distance resolution (over 2x) for sensing, with robustness to RIS size and bandwidth, indicating strong practical impact for wideband RIS-enabled ISAC and communication systems.

Abstract

The spectrum shift from the sub-6G band to the high-frequency band has posed an ever-increasing demand on the paradigm shift from narrowband beamforming to wideband beamforming. Despite recent research efforts, the problem of wideband beamforming design is particularly challenging in reconfigurable intelligent surface (RIS)-assisted systems, due to that RIS is not capable of performing frequency-dependent phase shift, therefore inducing high signal processing complexity. In this paper, we propose a simple-yet-efficient wideband beamforming design for RIS-assisted systems, in which a transmitter sends wideband signals to a desired target, through the aid of the RIS. In our proposed design, we exploit space-frequency Fourier transformation and stationary phase method to yield an approximate closed-form solution of the RIS phase shifts which significantly reduces the signal processing complexity, compared to the existing approaches. The obtained solution is then used to generate a large and flat beampattern over the desired frequency band. Through numerical results, we validate the effectiveness of our proposed beamforming design and demonstrate how it can improve system performances in terms of communication rate and sensing resolution. Beyond generating the flat beampattern, we highlight that our proposed design is capable of mimicking any desired beampattern by matching the RIS phase shift with the amplitude modulation function, thus providing valuable insights into the design of novel wideband beamforming for RIS-assisted systems.

Figures (16)

• Figure 1: System model.
• Figure 2: The ideal RIS wideband beampattern and the standard narrowband beampattern ($f_{\mathrm{c}}=30$ GHz, $B=4$ GHz, $R=1$ m, $l_{\mathrm{TX}}=0.5$ m, $l_{\mathrm{DT}}=10$ m).
• Figure 3: The scenario when the DT is along the boresight.
• Figure 4: Results of SPM in the boresight scenario.
• Figure 5: Boresight phase shifts.