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Codebook Design and Beam Training for Extremely Large-Scale RIS: Far-Field or Near-Field?
Xiuhong Wei, Linglong Dai, Yajun Zhao, Guanghui Yu, Xiangyang Duan
TL;DR
XL-RIS makes near-field propagation likely, but existing far-field codebooks mismatch the near-field channel model, motivating improved CSI acquisition. The paper designs near-field and hierarchical near-field codebooks and evaluates their beam-training schemes. Both outperform the existing far-field scheme, while the hierarchical scheme reduces overhead by about 90% with about 92% achievable-rate performance.
Problem
Large XL-RIS apertures make near-field propagation more likely, while existing far-field beam-training codebooks mismatch the near-field channel model.
Method
The paper designs a near-field codebook from the XL-RIS near-field cascaded array steering vector and adds a hierarchical codebook searched through progressively smaller sub-codebooks.
Results
Both proposed near-field beam-training schemes outperform the existing far-field scheme; the hierarchical scheme reduces beam-training overhead by about 90% with about 92% achievable-rate performance.
Takeaways & Limitations
Near-field codebook design is effective for XL-RIS beam training, and hierarchical search substantially lowers overhead with acceptable performance loss.
Abstract
from arXiv · showhide
Reconfigurable intelligent surface (RIS) can improve the capacity of the wireless communication system by providing the extra link between the base station (BS) and the user. In order to resist the "multiplicative fading" effect, RIS is more likely to develop into extremely large-scale RIS (XL-RIS) for future 6G communications. Beam training is an effective way to acquire channel state information (CSI) for the XL-RIS assisted system. Existing beam training schemes rely on the far-field codebook, which is designed based on the far-field channel model. However, due to the large aperture of XL-RIS, the user is more likely to be in the near-field region of XL-RIS. The far-field codebook mismatches the near-field channel model. Thus, the existing far-field beam training scheme will cause severe performance loss in the XL-RIS assisted near-field communications. To solve this problem, we propose the efficient near-field beam training schemes by designing the near-field codebook to match the near-field channel model. Specifically, we firstly design the near-field codebook by considering the near-field cascaded array steering vector of XL-RIS. Then, the optimal codeword for XL-RIS is obtained by the exhausted training procedure between the XL-RIS and the user. In order to reduce the beam training overhead, we further design a hierarchical near-field codebook and propose the corresponding hierarchical near-field beam training scheme, where different levels of sub-codebooks are searched in turn with reduced codebook size. Simulation results show the two proposed near-field beam training schemes both perform better than the existing far-field beam training scheme. Particulary, the hierarchical near-field beam training scheme can greatly reduce the beam training overhead with acceptable performance loss.
I. INTRODUCTION
The paper addresses CSI acquisition for XL-RIS, where large apertures make near-field propagation likely and expose a mismatch between existing far-field codebooks and the near-field channel model. It proposes near-field and hierarchical near-field beam training schemes to improve performance while reducing training overhead.
- CSI acquisition: High-dimensional cascaded-channel estimation creates unaffordable pilot overhead, while low-SNR reception limits its achievable estimation accuracy.Only the cascaded channel can be estimated for passive RIS elements, and the received SNR is usually low before reliable reflecting beamforming.
- CSI acquisition: RIS beam training estimates physical channel-path directions through predefined directional codewords, avoiding full-channel estimation under low received SNR.The RIS-user procedure searches for the optimal RIS directional beam using a codebook based on the cascaded array steering vector.
- XL-RIS near-field challenge: XL-RIS increases the array aperture and Rayleigh distance, making scatters more likely to lie in the near-field region.The paper motivates XL-RIS development for future 6G communications and states that the near-field channel model should therefore be considered.
- XL-RIS near-field challenge: Existing far-field codebooks mismatch the XL-RIS near-field channel model and cause severe performance loss in near-field communications.The far-field codebook was designed for the far-field channel model used in earlier RIS beam-training schemes.
- Proposed schemes: The proposed near-field codebook uses near-field cascaded array steering vectors, with codewords determined by sampled points in x-y-z coordinates.The optimal codeword is obtained through exhaustive training between the XL-RIS and the user.
II. SYSTEM MODEL
This section introduces the XL-RIS-assisted communication signal model, reviews the existing far-field channel model and codebook, and presents the near-field channel model for XL-RIS.
- Signal model: The section first introduces the signal model for the XL-RIS-assisted communication system.
- Far-field model: It reviews the existing far-field channel model and far-field beam-training codebook.
- Near-field model: It then presents the near-field channel model for the XL-RIS-assisted system.
A. Signal Model
The XL-RIS system places a reflecting surface between the BS and user, and beam training acquires CSI by searching directional beams at the XL-RIS. The model focuses on XL-RIS beam training while assuming the BS beam is aligned with the BS–XL-RIS main path.
- The XL-RIS is deployed between an M-element BS antenna array and a single-antenna user to provide a reflecting communication link.
- The received signal depends on the BS beamforming vector, RIS reflecting coefficients, transmitted symbol, and receiver noise.
- Accurate CSI is needed to design the BS and RIS beamforming vectors, but conventional channel estimation requires excessive pilot overhead with extremely many RIS elements.
- Beam training instead searches the main-path physical direction rather than explicitly estimating the entire channel, reducing the CSI acquisition task.
- The paper focuses on XL-RIS beam training, assuming the BS beam is aligned with the BS–XL-RIS main path because that link has longer channel coherence than the user link.
B. Far-Field Channel Model and Far-Filed Codebook
The conventional scheme models the RIS channels with far-field planar-wave steering vectors and trains by testing codewords from an angle-based codebook. As XL-RIS aperture increases, this far-field codebook may no longer apply.
- The far-field model represents the BS–XL-RIS and XL-RIS–user channels using far-field array steering vectors associated with spatial angles.
- The steering-vector spatial variables are determined by physical azimuth and elevation angles, carrier wavelength, and half-wavelength element spacing.
- With the BS beam designed, the cascaded far-field channel combines the two path gains and the RIS spatial-angle response.
- Far-field beam training tests different RIS codewords across time slots, and the user feeds back the codeword producing the strongest received signal.
- The existing codebook forms codewords from sampled spatial angles, but its applicability to XL-RIS can fail as the RIS aperture grows.
C. Near-Field Channel Model
XL-RIS apertures enlarge the Rayleigh distance, making near-field spherical-wave modeling more relevant than conventional far-field modeling. The resulting cascaded steering vector depends on source and user coordinates, so angle-only codebooks mismatch it.
- Increasing the RIS aperture increases the Rayleigh distance, making XL-RIS scatterers more likely to lie in the near-field region.For D = 0.1 meters the Rayleigh distance is 2 meters, whereas D = 1 meter gives 200 meters.
- Near-field XL-RIS channels should use a spherical-wave assumption rather than the planar-wave model used for conventional RIS.
- The near-field XL-RIS channel uses a steering vector whose phase depends on the distance from each RIS element to the main-path scatterer.
- For the cascaded BS–XL-RIS–user channel, the effective distance combines the distances associated with both propagation paths.
- Unlike the far-field steering vector, the near-field cascaded steering vector is determined by a pair of 3D points rather than angles alone.
- Because the far-field codebook mismatches the near-field model, far-field beam training can cause severe performance loss in XL-RIS near-field communications.
III. PROPOSED NEAR-FIELD CODEBOOK DESIGN AND BEAM TRAINING SCHEME FOR XL-RIS
The paper designs an XL-RIS near-field codebook from near-field cascaded steering vectors and introduces exhaustive and hierarchical training schemes. The hierarchical design searches smaller sub-codebooks successively to reduce overhead.
- The proposed near-field codebook is designed to match the XL-RIS near-field channel model and its cascaded array steering vector.
- The paper proposes a near-field beam-training scheme and a hierarchical near-field codebook with corresponding training to reduce beam-training overhead.
- The codebook construction extends near-field array-steering-vector dictionary design from a 2D plane to 3D space for the planar XL-RIS.
- Each XL-RIS codeword must represent a pair of sampled 3D points because the cascaded steering vector depends on summed propagation distances from both paths.
1) Near-Field Codebook Design:
The near-field XL-RIS codebook is generated from the near-field cascaded array steering vector using paired sampled points and duplicate-codeword removal. The procedure outputs the codebook and its size for subsequent beamforming.
- Sampling steps cover three coordinate axes for each of the two sampled-point collections and are grouped into Δ.
- Algorithm 1 iterates over sampled-point pairs to construct the near-field XL-RIS codebook.
- The near-field codeword is generated from the cascaded array steering vector associated with a pair of sampled points.
- Different sampled-point pairs can yield the same effective sampled distance and therefore the same codeword.
- The procedure retains only new codewords, then outputs the codebook W and its size L.
2) Near-Field Beam Training:
Near-field beam training exhaustively searches the designed XL-RIS codebook through transmissions over successive time slots. The user identifies and feeds back the optimal codeword index to the XL-RIS.
- All L codewords are traversed, producing a training procedure divided into L time slots.
- Each codeword is assigned to the RIS reflecting beamforming vector in a separate time slot.
- The near-field beam-training procedure uses the designed XL-RIS codebook W as its input.
- The user compares received-signal magnitudes to select the optimal codeword and feeds its index back to the XL-RIS.
- Because the cascaded steering vector depends jointly on a pair of sampled points, the codebook size L is usually large and exhaustive training has high overhead.
B. Proposed Hierachical Near-Field Codebook Design and Beam training
The hierarchical near-field codebook reduces training overhead by dividing the sampling space into progressively finer sub-codebooks. Beam training searches these levels sequentially, using each selected codeword to determine the next search range.
- Trade-off: Increasing the number of levels reduces codebook size but degrades beam-training performance because the relevant scatterers become harder to locate accurately.
- Hierarchical codebook design: The hierarchical codebook contains K sub-codebook levels defined by different sampling ranges and sampling steps.
- Hierarchical codebook design: Sampling ranges and steps become smaller across levels, keeping each level’s codebook size relatively small.
- Hierarchical beam training: Hierarchical beam training searches sub-codebooks from the first to the K-th level, with each later range determined by the previously selected codeword.
- Hierarchical beam training: The procedure has K stages, generates and searches one sub-codebook per stage, and feeds back the selected index to generate the next range and sampling steps.
- Hierarchical beam training: Each level has size L_k much smaller than the full codebook size L, reducing the overall training overhead to P^K.
IV. SIMULATION RESULTS
Simulations compare the proposed near-field and hierarchical near-field beam training schemes with an existing far-field scheme. The near-field schemes achieve better rate performance, while the hierarchical scheme substantially reduces overhead with limited rate loss.
- Simulation setup: Simulations compare the proposed near-field schemes with the existing far-field beam training scheme using achievable rate and training overhead.The setup includes XL-RIS and BS system parameters, sampling-step variations, and a perfect-CSI beamforming reference.
- Achievable-rate comparison: The two proposed near-field beam training schemes achieve better achievable rate performance than the existing far-field scheme.The comparison is reported for achievable rate versus SNR with ∆s = 100d.
- Achievable-rate comparison: The hierarchical scheme performs slightly worse than the non-hierarchical near-field scheme because errors propagate across sub-codebook search levels.This performance difference is attributed to hierarchical search across multiple levels.
- Training-overhead comparison: The hierarchical near-field scheme greatly reduces beam training overhead as the sampling step varies.Figure 5 compares the two proposed near-field schemes against the sampling step ∆s.
- Training-overhead comparison: At ∆s = 100d, training overhead is 147628 for the near-field scheme and 15927 for the hierarchical scheme.The hierarchical scheme’s overhead is reported as only about 10% of the non-hierarchical scheme’s overhead.
V. CONCLUSIONS
The paper proposes two near-field beam training schemes using a near-field codebook for XL-RIS-assisted systems. Both outperform the existing far-field scheme, while the hierarchical scheme reduces overhead by about 90% with about 92% achievable rate performance.
- Conclusions: The paper proposes two near-field beam training schemes based on a near-field codebook for the XL-RIS-assisted system.The paper’s conclusion identifies near-field codebook design as the basis of both schemes.
- Conclusions: Both proposed near-field beam training schemes achieve better performance than the existing far-field beam training scheme.This is the paper’s overall reported comparison with the existing approach.
- Conclusions: The hierarchical scheme reduces beam training overhead by about 90% while achieving about 92% achievable rate performance relative to the near-field scheme.The conclusion presents the overhead reduction and rate performance together as the main trade-off.
- Conclusions: Future work may apply multi-beam training to near-field XL-RIS beam training to further reduce overhead.The paper identifies multi-beam training as a possible future direction.