Near-Field Beam Management

• Near-field beam management is defined by joint angle and range control using spherical wavefront models to focus beams in advanced wireless systems.
• It leverages joint angle-range codebooks and hierarchical beam training to minimize pilot overhead while achieving precise alignment.
• Advanced techniques such as compressive sensing, machine learning, and reinforcement learning enhance beam tracking, scheduling, and multi-user adaptation.

Near-field beam management encompasses the algorithms, architectures, and protocols necessary for precise beam steering, alignment, tracking, and training in wireless systems where the radiative near-field (Fresnel) effects dominate due to large array apertures and/or short ranges. Contrasted with the far-field regime, where planar wavefronts and angle-only beamforming suffice, the near-field exhibits spherical wavefronts, requiring algorithms to simultaneously resolve and control both angle and range (depth). This domain includes channel modeling with spherical-wave physics, codebook design in joint angle-range domains, feedback-efficient training via compressive and machine-learning methods, and robust tracking/scheduling that exploits the high spatial granularity offered by near-field propagation.

1. Physical Principles and Channel Modeling

In the near-field, defined approximately as user-array distances $r \leq 2D^2/\lambda$ (with $D$ the aperture), the array response at position $\mathbf{p}_n$ towards a user at $\mathbf{r}$ is

$$a_n = \exp\!\left(-j\frac{2\pi}{\lambda}\vert \mathbf{r}-\mathbf{p}_n \vert\right)$$

This spherical-wave response (as opposed to the linear phase of far-field beams) underpins key capabilities:

• Focusing at arbitrary ranges: main-lobe can be placed at any polar (angle, range) position, with the ability to spatially separate closely spaced users even if angularly aligned (You et al., 2023).
• Resolution tradeoffs: Spatial (angular) and range resolutions are coupled to both the aperture size and the wavelength. The Rayleigh distance $D_R=2D^2/\lambda$ sets the near-field boundary (Chen et al., 26 Apr 2025).
• Implications for RIS, MIMO, and XL-arrays: Large apertures (RIS, ELAA, DMA) naturally induce near-field conditions across extended indoor/outdoor regions.

2. Near-Field Beamforming and Codebook Design

Unlike the far-field codebooks that discretize angular space only, near-field management utilizes joint angle-range (polar-domain) codebooks. Each codeword is constructed as

$$\mathbf{a}(\theta,r) = \left[e^{-j\frac{2\pi}{\lambda}\left(r_n(\theta,r)-r\right)}\right]_{n}$$

with $r_n$ the distance from element $n$ to $(\theta,r)$ in user-centric coordinates (You et al., 2023, Wang et al., 13 May 2025, Liu et al., 2022). Two main design paradigms emerge:

• Cartesian/polar grid: Sampling over both angle and range yields $N_\theta \times N_r$ codewords, with non-uniform range quantization often used for equal correlation (You et al., 2023, Liu et al., 2022).
• Structured/hierarchical: Multi-resolution, variable-width codebooks exploit beamwidth scaling with range, reducing the number of beams in the initial coarse alignment levels (Alexandropoulos et al., 2022).

RIS and ELAA implementations may additionally exploit variable-width or Fresnel-zone groupings, supporting efficient multi-user focusing and wide angular coverage (Alexandropoulos et al., 2022, Yu et al., 28 Nov 2024).

3. Beam Training, Alignment, and Channel Estimation

Classical exhaustive beam sweeping over $N_\theta \times N_r$ codewords induces prohibitive overhead for extreme-scale arrays. Recent advances address this via:

• Hierarchical and two-stage beam alignment: Multi-level codebook search (coarse-to-fine) reduces pilot consumption by orders of magnitude (e.g., 24 pilots vs 256 for exhaustive alignment in a $Q{=}8649$-element RIS) (Alexandropoulos et al., 2022).
• Sparse and compressive acquisition: By leveraging sparsity of the channel in the joint angle-range dictionary, LASSO-style ($\ell_1$-constrained) recovery extracts the dominant paths with very few pilots and supports off-grid refinement for high accuracy (Wang et al., 13 May 2025).
• Machine learning methods: Deep residual and transformer networks can map partial codeword observations directly to the best near-field codeword, achieving near-optimal gain with 90–95% training overhead reduction (Liu et al., 2022, Zhou et al., 17 Apr 2025).
• Active (ping-pong) learning: Beam alignment framed as alternating optimization in a low-dimensional (wavenumber) subspace, further reducing the pilot cost to 10–20 rounds (Jiang et al., 2023).
• Hashing and multi-arm beams: Polar-domain sparsity bases and random hash functions permit logarithmic-slot overhead, with soft decision voting ensuring $>$96% accuracy (Xu et al., 10 Mar 2024).

A typical protocol integrates sweeping/training (coarse angle/range), feedback of selected beams, sparsity-aware channel estimation (often with LASSO or pursuit), optional refinement, and subsequent data transmission (Wang et al., 13 May 2025, Wang et al., 2023).

4. Beam Steering, Shaping, and Bending in the Near Field

Near-field steering is not restricted to simple focal points along straight lines. Key methodologies include:

• Wavefront rotation and surface parametrization: Arbitrary (e.g., Bessel, Gaussian) beams can be rigorously steered via shape-preserving rotation of the phase manifold, with per-element phases computed by minimizing the propagation path difference to the target wavefront (Simončič et al., 25 Mar 2024).
• Bending and caustic design (Airy, Bessel, OAM beams): By synthesizing the input aperture phase according to the desired beam caustic, self-accelerating or abruptly autofocusing beams follow parabolic or custom convex trajectories for blockage avoidance or distributed power transfer (Droulias et al., 10 Oct 2024). The required phase profile for a generic caustic $x_c=f(z)$ is

$$\frac{d\varphi(x)}{dx} = k f'(z_c) / \sqrt{1 + f'(z_c)^2}$$

• Array and hardware considerations: Phase quantization at 3–4 bits, random element deactivation, and aperture scaling impact main-lobe power and beam efficiency, with high performance retained for moderate hardware constraints (Droulias et al., 10 Oct 2024).

5. Tracking, Scheduling, and Cross-Layer Beam Management

Owing to high spatial selectivity, tracking and scheduling in the near-field is sensitive to both angular and range motion. Advanced strategies include:

• EKF/UKF/particle filtering: State-space estimation on $(\theta,r)$ and their rates achieves robust beam tracking under user mobility, with performance scaling with both aperture and SNR (You et al., 2023).
• Beam gain decay and renewal: Analytical bounds on the correlation between focusing vectors under small positional shifts enable threshold-based tracking, with the “beam coherence time” directly informing retraining intervals (Gavriilidis et al., 3 Jun 2024).
• Location Division Multiple Access (LDMA): Joint angle-range scheduling enables high-density user multiplexing, with cross-interference minimized by spatial separation in the polar domain (You et al., 2023).
• Cross-layer POMDP and RL: Coverage, energy, and latency are balanced via deep RL, which jointly optimizes pilot count, retraining intervals, and transmit power, yielding up to 85% throughput gains over DFT-based sweeping and 78% drops in buffer overflows (Wang et al., 16 Nov 2025).

6. Wideband Effects, RIS/Fresnel Architectures, and Multibeam Control

Wideband and RIS/ELAA designs present unique challenges and solutions:

• Beam squint and spectral wideband effect: Frequency-dependent focus points lead to “beam split,” deteriorating array gain at band edges. RIS elements grouped by Fresnel zone—with phase aligned per zone—eliminate intra-zone beam split, and equivalent channel design reduces the 2D shaping to a 1D spectral optimization (Yu et al., 28 Nov 2024, Luo et al., 2022).
• Hybrid analog/digital/TDD beamforming: True-time-delay or frequency-scaled digital baseband compensation is necessary for spatial alignment across wideband, with algorithms optimizing analog PS and TDD jointly to remove both angular and range squint (Wang et al., 2023, Elbir et al., 2023).
• RIS eigenmode feeding and XL-RIS: Eigenmode decomposition of the active feeder-to-RIS near-field channel allows RISs to synthesize beams with highly flexible angular selectivity or composite patterns (e.g., monopulse, flat-top) using minimal active hardware, with the AMAF-RIS spacing optimized according to RIS size (Tiwari et al., 2022).

Method/Architecture	Key Feature	Overhead/Complexity
Hierarchical Codebook	Coarse-to-fine beam refinement	$O(\log N_\theta + \log N_r)$
LASSO/Compressive Training	Sparse path selection, off-grid	$O(K^3)$, $K\ll N$
Deep Learning/Transformers	Nonlinear regression, learned scanning	$O(\text{network size})$, offline training
Fresnel-zone RIS Design	Intra-zone phase alignment, Fourier spectral shaping	$O(N)$ or $O(N_t^3)$
Analytical Beam Bending	Arbitrary caustic/trajectory design	$O(N)$ phase precomputation
RL/POMDP Scheduling	Cross-layer, queue-aware decisions	$O(\text{policy network size})$

7. Open Challenges and Research Directions

Several open problems remain for near-field beam management:

• Unified cross-field management: Algorithms and codebooks that seamlessly span both near- and far-field (cross-field) scenarios, avoiding mode switch discontinuities (Chen et al., 26 Apr 2025).
• Low-overhead, wideband, and hardware-efficient designs: Practical designs accounting for finite PS/TDD quantization, phase errors, and hybrid analog-digital constraints.
• Joint communication, localization, and sensing: ISAC paradigms exploiting the polar-domain spatial focus for fused connectivity and spatial inference (Elbir et al., 2023, Luo et al., 2022).
• Robust multi-user adaptation, mobility tracking, and blockage avoidance: Adaptive algorithms that respond to non-stationary channels, intermittent feedback, and device density.
• Channel, hardware, and ML-aid calibration: Accurate calibration for Fresnel-phase models, bias/offset correction in large RISs, and auto-tuning of learned inference in deployment (Liu et al., 2022, Zhou et al., 17 Apr 2025).
• Physical-layer security and interference management: Leveraging spatial focusing for heightened privacy and controlled energy delivery, potentially using non-Gaussian beamforms (e.g., Bessel, OAM, Airy) (Droulias et al., 10 Oct 2024, Chen et al., 26 Apr 2025).

Near-field beam management stands as an essential enabler for next-generation mmWave/THz systems, extreme multi-antenna deployments, and high-density environments, with ongoing research focusing on the interplay of physical-layer innovation, algorithmic efficiency, and hardware reality (Simončič et al., 25 Mar 2024, Wang et al., 13 May 2025, You et al., 2023, Yu et al., 28 Nov 2024, Wang et al., 16 Nov 2025).