Wideband Beamforming for Near-Field Communications with Circular Arrays

TL;DR

This work addresses wideband near-field beamforming with uniform circular arrays (UCA) in XL-MIMO settings, where beam squint degrades conventional frequency-independent PS-based beams. It develops a two-pronged approach: an analytical TTD-based beamforming design and a joint-delay/phase optimization under practical delay constraints, both leveraging the near-field array response and Bessel-function approximations (e.g., $G_m \approx |J_0(\eta)|$) to characterize performance in angular and distance domains. The proposed methods mitigate squint, quantify the required number of TTD units, and demonstrate superior spectral efficiency relative to PS-based and fully digital benchmarks, with joint optimization offering the best performance across bandwidths and hardware limits. The findings highlight the practical viability of TTD-enabled wideband near-field UCA systems for achieving high data rates in 6G-era XL-MIMO deployments, while pointing to future work in channel estimation and efficient beam training for such architectures.

Abstract

The beamforming performance of the uniform circular array (UCA) in near-field wideband communication systems is investigated. Compared to uniform linear array (ULA), UCA exhibits uniform effective array aperture in all directions, thus enabling more users to benefit from near-field communications. In this paper, the unique beam squint effect in near-field wideband UCA systems is comprehensively analyzed in both the distance and angular domains. It is rigorously demonstrated that the beam focal point only exists at a specific frequency in wideband UCA systems, resulting in significant beamforming loss. To alleviate this unique beam squint effect, the true-time delay (TTD)-based beamforming architecture is exploited. In particular, two wideband beamforming optimization approaches leveraging TTD units are proposed. 1) Analytical approach: In this approach, the phase shifters (PSs) and the time delay of TTD units are designed based on the analytical formula for beamforming gain. Following this design, the minimum number of TTD units required to achieve a predetermined beamforming gain is quantified. 2) Joint-optimization approach: In this method, the PSs and the TTD units are jointly optimized under practical maximum delay constraints to approximate the optimal unconstrained analog beamformer. Specifically, an efficient alternating optimization algorithm is proposed, where the PSs and the TTD units are alternately updated using either the closed-form solution or the low-complexity linear search approach. Extensive numerical results demonstrate that 1) the proposed beamforming schemes effectively mitigate the beam squint effect, and 2) the joint-optimization approach outperforms the analytical approach in terms of array gain and achievable spectral efficiency.

Figures (9)

• Figure 1: Illustration of the near-field channel model.
• Figure 2: Illustration of TTD-based hybrid beamforming structure for alleviating near-field beam squint effect in wideband UCA systems.
• Figure 3: Illustration of beamforming gain in the angular domain. The beams are generated towards $\phi = {30^ \circ }$ at the central frequency $f_c$ = 28 GHz. Moreover, $f_l$ = 26.5 GHz and ${f_m} = \frac{{{f_c} + {f_l}}}{2}$ denote the lowest and the middle frequency.
• Figure 4: Illustration of beamforming gain in the distance domain.
• Figure 5: The beamforming gain comparison between conventional PS-based beamforming scheme and TTD-based beamforming schemes.

Theorems & Definitions (9)

• Remark 1
• Remark 2
• Lemma 1
• proof
• Remark 3
• Lemma 2
• proof
• Lemma 3
• proof