Breaking Near-Field Communication Barriers: Focused, Curved, or Airy Beamforming?

Abstract: To meet the requirements for high data rates and ubiquitous connectivity in 6G networks, higher frequencies and larger array apertures are employed to enhance spatial resolution and spectral efficiency. This evolution leads to an expansion of the near-field region, where spherical-wave focusing can significantly enhance received power. However, the pervasive presence of obstacles in near-field environments makes communication in obstructed scenarios a critical challenge, particularly for sensitive high-frequency links with high penetration losses. In this paper, we propose a new waveform, termed the near-field Airy beam, which is tailored to the amplitude and phase characteristics of obstructed near-field channels. By integrating non-uniform amplitude response with non-linear phase profile, the proposed Airy beam forms specific curved trajectories, energy distributions, and focal points, enabling energy concentration at the user even after circumventing obstacles. An Airy beamforming algorithm is also developed for hybrid beamformer architectures. Considering practical conditions with unknown obstacle and user locations, we design an Airy beam codebook and a low-overhead hierarchical search scheme to identify the optimal user-aligned beam. Simulation results demonstrate that in obstructed environments, the near-field Airy beam achieves a received power gain of over 3 dB compared to conventional waveforms like focused and curved beams, closely approaching the theoretical upper bound. Across the mmWave to THz bands and various obstacle dimensions, the proposed beam training scheme consistently outperforms traditional methods in terms of spectral efficiency while maintaining a comparable training overhead.

• The paper introduces near-field Airy beamforming that jointly optimizes amplitude and phase, achieving over 3 dB improved received power under blockage compared to traditional methods.
• It employs a four-dimensional codebook with a hierarchical search protocol to adapt efficiently to diverse blockage and near-field effects, drastically reducing training overhead.
• The approach delivers enhanced spectral efficiency in mmWave/THz systems, approaching MRT performance while enabling scalable hybrid analog-digital implementations.

Focused, Curved, and Airy Beamforming for Near-Field Obstructed Communications

Problem Context and Motivation

The drive toward 6G wireless systems, characterized by extreme data rate requirements and ubiquitous connectivity, has precipitated an architectural shift toward higher frequency (mmWave/THz) bands and the deployment of massive antenna arrays. This technological evolution markedly extends the near-field (Fresnel) operating regime, altering propagation physics: beyond the traditional plane-wave (far-field) approximation, near-field propagation necessitates non-linear phase (spherical-wave) modeling, enabling spatial focusing of energy.

However, these high-resolution near-field links are exceptionally vulnerable to obstacles. The fine spatial selectivity which boosts spectral efficiency also leads to severe susceptibility: even small blockages can disrupt line-of-sight (LoS), causing substantial received power loss. Traditional focused beamforming, designed for unobstructed channels with maximal constructive superposition at the user, fails under such conditions. While curved and Airy beams have received attention for their unique propagation characteristics—self-bending, self-healing, and trajectory manipulation—existing designs either do not fully exploit the near-field phase properties or lack amplitude adaptation to the complex blockage-induced channel spatial profiles.

Near-Field Airy Beam Design

The paper proposes the near-field Airy beam, a novel waveform synthesis that integrates the amplitude modulation properties of the Airy function with the non-linear, spherical-wave phase control characteristic of near-field beamforming. The key technical insights and design choices are:

• Amplitude Matching (Airy Envelope): The main lobe and suppressed sidelobes of the Airy function are leveraged to spatially modulate the aperture field, effectively matching the highly non-uniform amplitude response encountered when obstacles partially block the array-to-user path.
• Non-linear Phase Focusing: By incorporating the canonical near-field quadratic phase term, the proposed beam retains the spatial focusing ability of conventional near-field schemes, enabling constructive interference at the user.
• Four-Dimensional Codebook: The synthesized waveform is parameterized by angle, focus distance, amplitude decay (Airy parameter), and trajectory curvature (scaling), allowing for flexible adaptation to a wide range of user and blockage geometries.
• Hybrid Beamforming Compatibility: Owing to its spatial sparsity, the Airy beam is efficiently approximated within practical hybrid analog-digital architectures using OMP-based decomposition and quantized phase control.

Beam Training and Codebook Construction

Channel state information (CSI) is typically unavailable in realistic deployments, especially with dynamic or unknown obstruction profiles. The authors design a dedicated hierarchical codebook and search protocol:

• Parameter Sampling: Steering angle and focusing distance follow non-uniform polar sampling (to resolve distance-dependent near-field effects), while the Airy amplitude and curvature parameters are sampled to maximize mutual orthogonality and coverage.
• Hierarchical Search: Training overhead is contained by a multi-stage search—first, the best angle-distance pair is located (phase focusing), then curvature (spatial scaling), and finally amplitude decay (main lobe width) are refined. This additive search structure ($N_\theta N_r + N_s + N_a$ complexity) sharply contrasts the combinatorial explosion of brute-force multi-dimensional search.
• Blockage-Aware Adaptation: The amplitude profile of each candidate is explicitly designed to align with the empirically or statistically observed spatial channel responses, significantly outperforming codebooks constructed under uniform or phase-only assumptions.

Numerical Results and Performance Analysis

Comprehensive EM-based simulations and codebook evaluations yield several strong numerical findings:

• Received Power Gain: In scenarios with substantial blockage (e.g., user isolated by a rectangular obstacle occluding a central portion of the aperture), the Airy beam yields average improvements exceeding 3 dB over both focused and curved beams, closely approaching the theoretical Maximum Ratio Transmission (MRT) bound with perfect CSI.
• Spectral Efficiency: Across the mmWave–THz frequency range, the hierarchical Airy beam search consistently produces higher spectral efficiency than existing near-field (polar, curved) and far-field (DFT) schemes, with only a marginal gap from exhaustive search results.
• Overhead–Performance Tradeoff: The hierarchical search protocol reduces codebook search overhead by orders of magnitude while retaining nearly all the performance, and is robust across a wide range of blockage ratios and obstacle aspect ratios.
• Amplitude and Phase Alignment: Detailed investigations into the magnitude and phase responses of the synthesized waveforms demonstrate that only the near-field Airy beam achieves joint spatial phase coherence and amplitude adaptation to the underlying (non-uniform) channel, unlike the fixed-amplitude focused and curved beams.

Theoretical and Practical Implications

The synthesis and deployment of the near-field Airy beam deliver new theoretical understanding and practical strategies for overcoming the near-field blockage problem:

• Decoupling Phase and Amplitude Design: The approach shows that optimal near-field beamforming under blockage necessitates joint control of both amplitude and phase at the aperture—a significant departure from the phase-only paradigm dominant in MIMO literature.
• Scalability to Hybrid Architectures: The sparsity of Airy beams enables realizable, low-cost hybrid beamformers to approximate the ideal fully digital solution with minimal performance loss, facilitating practical implementation for large-scale THz and mmWave arrays.
• Resilience Across Environments: The scheme's adaptability, validated across obstacle dimension, blockage ratio, and frequency, points toward its suitability for deployment in complex indoor/outdoor environments anticipated in 6G and beyond.

Future Directions

This work lays the groundwork for future multi-user extensions, integration with machine learning-based channel inference, and adaptive real-time codebook updates in mobile or fast-fading near-field scenarios. Exploration of metamaterial or holographic surfaces for direct physical synthesis of amplitude/phase-engineered Airy wavefronts is a promising hardware direction.

Conclusion

This paper introduces and rigorously demonstrates the efficacy of the near-field Airy beam, a new waveform that realizes significant, robust improvements in received power and spectral efficiency for obstructed near-field communications by integrating non-uniform amplitude and non-linear phase control. The hierarchical codebook and training protocol make this approach feasible at scale, and strong numerical evidence is provided for its superiority over existing focused and curved beam methods. The results have broad implications for the design of future high-frequency, high-capacity wireless networks under realistic, dynamic blockage conditions.

Reference: "Breaking Near-Field Communication Barriers: Focused, Curved, or Airy Beamforming?" (2604.01704)