Source-linked AI summary
Fast Near-Field Beam Training for Extremely Large-Scale Array
Yunpu Zhang, Xun Wu, Changsheng You
TL;DR
Near-field XL-array beam training must search both angle and distance, making conventional angular-only training insufficient and exhaustive search costly. The paper decomposes this search into angle sweeping followed by distance search, substantially reducing overhead while retaining comparable beamforming performance.
Problem
Near-field XL-array training must search both angular and distance domains under spherical wavefront propagation, unlike conventional far-field direction-only training.
Method
A two-phase method uses far-field codebook sweeping to shortlist candidate angles, then a customized polar-domain codebook to estimate effective distance.
Results
The method significantly reduces exhaustive-search training overhead while achieving comparable beamforming performance for data transmission.
Takeaways & Limitations
Sequential angular and distance sweeping provides high-quality beamforming with lower overhead than two-dimensional exhaustive search.
Abstract
from arXiv · showhide
In this letter, we study efficient near-field beam training design for the extremely large-scale array (XL-array) communication systems. Compared with the conventional far-field beam training method that searches for the best beam direction only, the near-field beam training is more challenging since it requires a beam search over both the angular and distance domains due to the spherical wavefront propagation model. To reduce the near-field beam-training overhead based on the two-dimensional exhaustive search, we propose in this letter a new two-phase beam training method that decomposes the two-dimensional search into two sequential phases. Specifically, in the first phase, the candidate angles of the user is determined by a new method based on the conventional far-field codebook and angle-domain beam sweeping. Then, a customized polar-domain codebook is employed in the second phase to find the best effective distance of the user given the shortlisted candidate angles. Numerical results show that our proposed two-phase beam training method significantly reduces the training overhead of the exhaustive search and yet achieves comparable beamforming performance for data transmission.
I. INTRODUCTION
XL-array users often operate in the near field, where spherical wavefronts make beam training depend on both angle and distance. The paper proposes a two-phase search that reduces exhaustive-search overhead while preserving beamforming performance.
- XL-arrays make near-field operation more likely because enlarged Rayleigh distances and increased antenna number and carrier frequency favor spherical wavefront propagation.
- Near-field beam training must match both the channel angle and distance, unlike far-field training based only on angular codebooks.
- Directly applying far-field beam training to near-field communication causes considerable performance degradation, especially for users very close to the XL-array.
- Prior work uses hierarchical near-field codebooks or polar-domain codebooks with uniform angular and distance-domain sampling.
- The proposed method first selects candidate angles using far-field codebook sweeping, then searches effective distance with a customized polar-domain codebook.
II. SYSTEM MODEL
The system is a narrow-band XL-array downlink with a multi-antenna base station and a single-antenna user. Its near-field channel follows spherical-wave propagation, so the optimal beam depends jointly on spatial angle and distance.
- The considered system has a base station with an N-antenna uniform linear array communicating downlink with a single-antenna user.
- The far-field and near-field regions are separated by the Rayleigh distance Z = 2D^2/λ, determined by array aperture D and wavelength λ.
- For D = 0.4 m and f = 100 GHz, the Rayleigh distance is about 107 m, so users usually lie in the near field.
- The array is placed on the y-axis, with antenna spacing d = λ/2 and the n-th antenna at (0, δ_nd).
- The near-field steering vector depends on spatial angle θ and distance r, with r(n) giving each antenna's user distance under spherical propagation.
- The optimal beamforming vector is vopt = b(θ, r), so a training codeword must align both angle and base-station–user distance.
III. BENCHMARK SCHEMES
The paper introduces benchmark beam-training schemes and notes that near-field operation requires specialized treatment because the channel depends on both angle and distance. The proposed scheme also extends to multiple users, while general multipath remains future work.
- This section introduces two benchmark beam-training schemes and identifies their main issues.
- The proposed two-phase scheme can extend to multiple users by estimating all user angles simultaneously and effective distances sequentially.
- A near-field beam-training scheme for general multipath channels is left for future work because complicated beam patterns make the problem more challenging.
A. Angle-Domain Far-field Beam Training Based on Exhaustive Search
The conventional far-field scheme sweeps an angular codebook and selects the beam with maximum received power. It is inadequate for near-field channels because those channels depend jointly on angle and distance.
- The far-field benchmark assumes a planar wavefront and represents the channel primarily through spatial angle.
- It divides the spatial domain [−1, 1] into N equal sectors and constructs one codeword for each sector's central direction.
- The base station sequentially transmits all N codewords, while the user measures received power and feeds back the index producing the maximum value.
- Applying this angular-only method to near-field communication causes significant rate loss because near-field steering depends on both distance and spatial angle.
B. Polar-Domain Near-field Beam Training Based on Exhaustive Search
The polar-domain near-field codebook represents beams across both angle and distance, enabling exhaustive search over candidate direction-and-distance pairs. Its non-uniform distance sampling reduces sampling where distance effects diminish, but the full search can require substantial overhead.
- Codebook construction: Each polar-domain codeword corresponds to a specific direction-and-distance pair, covering N spatial sectors with angle-dependent distance samples.The codebook contains sets F_n, with each codeword f_n,s_n = b(θ_n, r_n,s_n).
- Codebook construction: Distance sampling is non-uniform: intervals become larger as distance increases because distance effects weaken and eventually disappear in the far field.
- Training overhead: Exhaustive near-field training tests all codewords and therefore requires a total of Σ_{n=1}^N S_n training symbols.
- Training overhead: When N is large, this exhaustive-search overhead can leave insufficient time for data transmission.
IV. PROPOSED TWO-PHASE NEAR-FIELD BEAM TRAINING METHOD
The proposed method replaces two-dimensional exhaustive search with sequential candidate-angle and effective-distance estimation. It uses far-field angle sweeping followed by customized polar-domain search, reducing training symbols while preserving beamforming performance and supporting both near- and far-field operation.
- Two-phase design: The method first estimates candidate angles using far-field codebook sweeping, then estimates effective distance with a customized polar-domain codebook.
- First phase: candidate angle estimation: Far-field sweeping identifies a dominant-angle region, and middle-K selection retains K central quantized angles instead of relying on one angle.
- Second phase: effective distance estimation: The second phase sweeps sampled distances for each shortlisted angle and selects the polar-domain codeword with the largest received signal power or SNR.
- Accuracy and scope: Effective-distance estimation is more accurate nearby and can have larger long-distance error, but the error has limited impact on beamforming performance.
- Universal operation: After angle estimation, the method can skip distance estimation when power concentrates in few training symbols, enabling extension to far-field communication.
- Training overhead: For N = 256, f = 100 GHz, S_n = S_k = 6, and K = 3, training requires T^(2P) = 274 symbols versus T^(ex) = 1536.
- Training-performance tradeoff: Increasing K raises training overhead but can improve beamforming gain through more accurate angle estimation.
V. NUMERICAL RESULTS
Numerical results evaluate the proposed two-phase beam training against exhaustive near-field, far-field, perfect-CSI, and LS benchmarks. The method substantially reduces overhead while remaining close to exhaustive near-field performance, particularly with K = 3.
- The evaluation measures beam-training success rate and achievable rate over SNR and user distance, using M = 1000 beam-training realizations.
- 262 versus 1536 training symbols: with K = 1, the proposed method greatly reduces overhead but has a smaller success rate and slightly lower achievable-rate performance.
- 274 versus 1536 training symbols: with K = 3, the proposed method achieves success rate and achievable rate very close to exhaustive near-field training while retaining substantial overhead reduction.
- The proposed method significantly outperforms far-field beam training across different SNRs and performs better than LS channel estimation in the challenging low-SNR regime.The reported explanation is that beam training forms strong beams, whereas LS estimation suffers larger errors at low SNR.
- As user distance increases, success rate generally decreases, achievable rates monotonically decrease, and the proposed method remains very close to exhaustive near-field training across distances.All near- and far-field methods achieve the same rate performance when distance is sufficiently large.
VI. CONCLUSION
The paper concludes that sequential angular and distance-domain beam sweeping reduces near-field training overhead while preserving high-quality beamforming performance. The method is also applicable to both near-field and far-field communication systems.
- The proposed method sequentially performs beam sweeping in the angular domain and then the distance domain.
- The two-phase design significantly reduces the overhead of existing two-dimensional exhaustive-search methods while achieving high-quality beamforming performance.
- The proposed beam training method applies to both far-field and near-field communication systems.