Codebook Design and Beam Training for Extremely Large-Scale RIS: Far-Field or Near-Field?

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.Source: §I · p. 2
• 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.Source: §I · p. 3

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.Source: §I · p. 3
• 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.Source: §I · pp. 3–4

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.Source: §I · p. 4

Signal model

• The section first introduces the signal model for the XL-RIS-assisted communication system.Source: §II · p. 5

Far-field model

• It reviews the existing far-field channel model and far-field beam-training codebook.Source: §II · p. 5

Near-field model

• It then presents the near-field channel model for the XL-RIS-assisted system.Source: §II · p. 5

• The XL-RIS is deployed between an M-element BS antenna array and a single-antenna user to provide a reflecting communication link.Source: A. Signal Model · p. 5
• The received signal depends on the BS beamforming vector, RIS reflecting coefficients, transmitted symbol, and receiver noise.Source: A. Signal Model · p. 6
• 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.Source: A. Signal Model · p. 6
• Beam training instead searches the main-path physical direction rather than explicitly estimating the entire channel, reducing the CSI acquisition task.Source: A. Signal Model · p. 6
• 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.Source: A. Signal Model · p. 6

• The far-field model represents the BS–XL-RIS and XL-RIS–user channels using far-field array steering vectors associated with spatial angles.Source: B. Far-Field Channel Model and… · pp. 6–7
• The steering-vector spatial variables are determined by physical azimuth and elevation angles, carrier wavelength, and half-wavelength element spacing.Source: B. Far-Field Channel Model and… · p. 7
• With the BS beam designed, the cascaded far-field channel combines the two path gains and the RIS spatial-angle response.Source: B. Far-Field Channel Model and… · p. 7
• Far-field beam training tests different RIS codewords across time slots, and the user feeds back the codeword producing the strongest received signal.Source: B. Far-Field Channel Model and… · p. 7
• The existing codebook forms codewords from sampled spatial angles, but its applicability to XL-RIS can fail as the RIS aperture grows.Source: B. Far-Field Channel Model and… · p. 7

• 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.Source: C. Near-Field Channel Model · p. 8
• Near-field XL-RIS channels should use a spherical-wave assumption rather than the planar-wave model used for conventional RIS.Source: C. Near-Field Channel Model · p. 8
• 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.Source: C. Near-Field Channel Model · pp. 8–9
• For the cascaded BS–XL-RIS–user channel, the effective distance combines the distances associated with both propagation paths.Source: C. Near-Field Channel Model · p. 9
• Unlike the far-field steering vector, the near-field cascaded steering vector is determined by a pair of 3D points rather than angles alone.Source: C. Near-Field Channel Model · p. 9
• 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.Source: C. Near-Field Channel Model · p. 9

• The proposed near-field codebook is designed to match the XL-RIS near-field channel model and its cascaded array steering vector.Source: §III · p. 10, A. Proposed Near-Field Codebook Design… · p. 10
• The paper proposes a near-field beam-training scheme and a hierarchical near-field codebook with corresponding training to reduce beam-training overhead.Source: §III · p. 10
• The codebook construction extends near-field array-steering-vector dictionary design from a 2D plane to 3D space for the planar XL-RIS.Source: A. Proposed Near-Field Codebook Design… · p. 10
• 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.Source: A. Proposed Near-Field Codebook Design… · p. 10

• Sampling steps cover three coordinate axes for each of the two sampled-point collections and are grouped into Δ.Source: 1) Near-Field Codebook Design · p. 11
• Algorithm 1 iterates over sampled-point pairs to construct the near-field XL-RIS codebook.Source: 1) Near-Field Codebook Design · p. 11
• The near-field codeword is generated from the cascaded array steering vector associated with a pair of sampled points.Source: 1) Near-Field Codebook Design · p. 11
• Different sampled-point pairs can yield the same effective sampled distance and therefore the same codeword.Source: 1) Near-Field Codebook Design · p. 11
• The procedure retains only new codewords, then outputs the codebook W and its size L.Source: 1) Near-Field Codebook Design · pp. 11–12

• All L codewords are traversed, producing a training procedure divided into L time slots.Source: 2) Near-Field Beam Training · p. 12
• Each codeword is assigned to the RIS reflecting beamforming vector in a separate time slot.Source: 2) Near-Field Beam Training · p. 12
• The near-field beam-training procedure uses the designed XL-RIS codebook W as its input.Source: 2) Near-Field Beam Training · p. 12
• The user compares received-signal magnitudes to select the optimal codeword and feeds its index back to the XL-RIS.Source: 2) Near-Field Beam Training · p. 12
• 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.Source: 2) Near-Field Beam Training · pp. 12–13

Trade-off

• Increasing the number of levels reduces codebook size but degrades beam-training performance because the relevant scatterers become harder to locate accurately.Source: B. Proposed Hierachical Near-Field… · p. 13

Hierarchical codebook design

• The hierarchical codebook contains K sub-codebook levels defined by different sampling ranges and sampling steps.Source: B. Proposed Hierachical Near-Field… · p. 13
• Sampling ranges and steps become smaller across levels, keeping each level’s codebook size relatively small.Source: B. Proposed Hierachical Near-Field… · p. 13

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.Source: B. Proposed Hierachical Near-Field… · p. 14
• 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.Source: B. Proposed Hierachical Near-Field… · p. 14
• Each level has size L_k much smaller than the full codebook size L, reducing the overall training overhead to P^K.Source: B. Proposed Hierachical Near-Field… · p. 15

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.Source: §IV · pp. 15–16

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.Source: §IV · p. 16
• 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.Source: §IV · p. 16

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.Source: §IV · p. 16, Figure 5 · p. 17
• 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.Source: §IV · p. 16

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.Source: §V · p. 18
• 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.Source: §V · p. 18
• 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.Source: §V · p. 18
• 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.Source: §V · p. 18