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Reassessing 3GPP NR CSI Codebook Structures in Near-Field Channels: Finite-Feedback Multilayer Precoding and Design Insights

Hongbo Xing, Jianhua Zhang, Yuxiang Zhang, Huixin Xu, Haiyang Miao, Lei Tian

arXiv:2609.16611v1eess.SP

TL;DR

NR Type-I and eType-II codebooks use plane-wave DFT bases even as standardized channels incorporate element-level spherical-wave propagation, leaving their effect on finite-feedback multilayer precoding uncertain. The paper evaluates both over paired FF/NF channels and finds projection reordering without a systematic FF/NF shift in singular-mode gains or SVD-EP rates. Its results favor stronger multilayer multibeam representation, with range states as a complementary refinement.

  • Problem

    How spherical-wave propagation changes finite-feedback multilayer precoding with NR CSI codebooks remains unclear, including whether spatial combinations or explicit range states should be prioritized.

    Source: C. Problem Statement and Scope · pp. 2–3

  • Method

    The authors evaluate Type-I and eType-II precoding on paired FF/NF 3GPP channels that share user locations, multipath parameters, polarization, and link budgets, differing only in wavefront model.

    Source: D. Contributions · p. 3

  • Results

    Paired channels show no systematic FF/NF displacement in singular-mode gains or SVD-EP rates, while spherical-wave phases reorder beam projections and eType-II attains higher absolute rates than Type-I at high ranks.

    Source: D. Contributions · p. 3, §V · p. 13

  • Takeaways & Limitations

    Large-port NR CSI codebooks should prioritize multilayer multibeam combinations and complex weights, with range states providing complementary compensation for curvature mismatch.

    Source: D. Contributions · p. 3, §V · p. 13

Abstract

from arXiv · show

3GPP TR 38.901 Rel-19 introduces antenna-element-level spherical-wave modeling, while NR Type-I and enhanced Type-II (eType-II) CSI codebooks continue to use plane-wave DFT beams. Whether this mismatch materially degrades finite-feedback multilayer precoding in standardized multipath channels remains unclear. To isolate its impact, we evaluate both codebooks over strictly paired far-field (FF) and near-field (NF) 3GPP channels that share user locations, multipath parameters, polarization, and link budgets and differ only in their wavefront models. Simulations cover Rank 1-4 transmission in 7-GHz UMi and 24-GHz InH-linear scenarios. We find no systematic FF/NF shift in singular-mode gains or equal-power SVD (SVD-EP) rates. Instead, spherical-wave phases reorder multipath projections onto plane-wave candidates and thereby alter codeword selection. For Rank-4 InH-linear users at 0.1 normalized Rayleigh distance, given FF-selected Type-I and eType-II codewords incur median direct mismatch losses of 2.28% and 5.34% on the NF channel, respectively; codebook reselection identifies better-matched codewords and reduces these losses to 0.770% and 3.28%. Nested candidate-set comparisons further show that relaxing Type-I interlayer constraints improves the SVD-EP-normalized rate by 20.7 percentage points, whereas finite-range sampling adds only 0.579 points. These results support prioritizing multilayer multibeam representation in large-aperture NR CSI codebooks, with range states providing complementary refinement.

I. INTRODUCTION

The paper asks whether spherical-wave propagation changes finite-feedback multilayer precoding with NR CSI codebooks, whose spatial bases remain plane-wave DFT beams. Paired-channel evaluation finds projection reordering but no systematic FF/NF shift in singular-mode gains or SVD-EP rates, and points to multilayer beam-combination capability as the stronger design priority.

A. Background and Motivation

  • NR TR 38.901 Release 19 adds element-level near-field propagation, while Type-I and eType-II retain plane-wave DFT bases, motivating reassessment in standardized multipath channels.The paper places this question in the context of growing apertures and shorter wavelengths bringing more users and scatterers into the radiative near field.Source: A. Background and Motivation · p. 1

B. Related Work

  • Spherical-wave phases alter coherent path superposition and redistribute existing mode gains; with a small UE aperture, additional LoS modal growth is substantially limited.Related work also describes spherical-wave responses as spreading across multiple DFT frequency bins and notes angle–range beam-training and focusing approaches.Source: B. Related Work · pp. 1–2

C. Problem Statement and Scope

  • The study asks how spherical-wave propagation changes MIMO-mode gains, plane-wave candidate projections, and multilayer rates, and whether range states or stronger spatial combinations merit priority.Earlier comparisons of single-stream beam gain and rate do not determine the effect on finite-feedback multilayer precoding over dual-polarized multipath channels.Source: C. Problem Statement and Scope · pp. 2–3

D. Contributions

  • The authors evaluate strictly paired FF/NF channels that preserve user locations and path parameters while changing the element-level wavefront, then compare codebook rates and reselection.Their framework separates fixed-codeword response from recovery after NF-based codebook reselection and distinguishes spatial-combination gains from range-sampling gains.Source: D. Contributions · p. 3, C. Problem Statement and Scope · p. 3
  • The paired-channel singular-mode gains and SVD-EP rates show no systematic FF/NF displacement, while eType-II attains higher absolute rates than Type-I at high ranks in both scenarios.Spherical-wave phases reorder plane-wave candidate projections, and Type-I rank-dependent indices can exclude a higher-gain candidate from the rate-maximizing codeword.Source: D. Contributions · p. 3

E. Paper Organization

The methodology pairs far-field and near-field channels for the same link and compares precoding under shared stochastic and link conditions. The section also outlines the paper’s progression from system modeling through codebook evaluation and design comparisons.

E. Paper Organization

  • The paper proceeds from paired channels, rate metrics, codebooks, and settings to channel and codebook results, design comparisons, and conclusions.The results sequence covers LoS geometry, mode gains and rates, frozen FF-selected codewords on NF channels, and reselection.Source: E. Paper Organization · p. 3

II. SYSTEM MODEL AND EVALUATION METHODOLOGY

A. Paired FF/NF 3GPP Channel Model

  • The paired TR 38.901 Release 19 channels share user location, path parameters, polarization, path loss, and noise, differing only in the element-level wavefront model.The model combines LoS and NLoS components into the narrowband spatial channel used for evaluation.Source: A. Paired FF/NF 3GPP Channel Model · p. 3, §1 · pp. 4–5

1 KR + 1HNLoS,(X)

  • The FF branch retains the path’s angles, element patterns, polarization, and Doppler terms but replaces exact spherical-wave phase with first-order plane-wave phase.For NLoS, the channel superposes multiple clusters and rays whose element-level phases use spherical distances in NF and linear reference-point phases in FF.Source: §1 · p. 4

B. Rate Model and Evaluation Benchmark

The rate model evaluates rank-ν precoding under equal layer power, with codeword selection based on instantaneous CSI. SVD-EP provides a same-rank, same-power benchmark.

B. Rate Model and Evaluation Benchmark

  • The received signal is modeled as y_X = √P_t H_X W s + n, with noise power determined by N_0, bandwidth, and receiver noise figure.The rank-ν precoder has equal power across layers and unit Frobenius norm.Source: B. Rate Model and Evaluation Benchmark · p. 5
  • The receiver selects a rank-ν candidate codeword from instantaneous CSI and feeds back its index; path loss and shadow fading are already included in H_X, not ρ.The candidate set is denoted C(c,ν).Source: B. Rate Model and Evaluation Benchmark · p. 5
  • SVD-EP allocates total transmit power equally across the first ν channel eigenmodes and is compared with the codebooks at the same rank and power constraint.The benchmark uses the channel’s right singular vectors and singular values.Source: B. Rate Model and Evaluation Benchmark · p. 5

C. Type-I/eType-II Codebooks and Port Extrapolation

Type-I forms multilayer codewords from oversampled two-dimensional DFT beams with rank-dependent coupling. eType-II instead selects a shared multibeam basis and quantized complex layer coefficients; both structures are evaluated in extrapolated port dimensions.

C. Type-I/eType-II Codebooks and Port Extrapolation

  • Type-I uses oversampled two-dimensional DFT beams, with rank-dependent offsets coupling the beams used by different layers and limiting simultaneous coverage of angularly separated clusters.The rank-2 basis-beam offset is mapped from a finite set of legal combinations.Source: C. Type-I/eType-II Codebooks and Port… · p. 5
  • eType-II selects L beams from a common oversampled subgrid and uses quantized complex coefficients for each polarization and layer.The baseline uses L = 4; the same structure is extended to L = 6 and L = 8, with N3 = Mν = 1 to exclude cross-subband compression.Source: C. Type-I/eType-II Codebooks and Port… · p. 5
  • The 160- and 4418-port configurations exceed TS 38.214’s specified range, so the codebook structures are evaluated in extrapolated dimensions.Each dual-polarized element is mapped to an independent port.Source: C. Type-I/eType-II Codebooks and Port… · p. 5

D. Simulation Configuration

The simulations use two array configurations with different apertures and Rayleigh distances, while idealizing receiver knowledge and excluding interference and coding.

D. Simulation Configuration

  • UMi uses a 47 × 47-element-per-polarization planar array with a 1.393 m diagonal aperture and 90.6 m Rayleigh distance; InH-linear uses an 80-element-per-polarization ULA with a 0.494 m span and 39.0 m Rayleigh distance.The aperture is the largest separation between two elements of one polarization.Source: D. Simulation Configuration · p. 6
  • Each user has one narrowband spatial channel matrix, while receiver noise is calculated over the 100- and 400-MHz system bandwidths listed in Table I.The supplied passages do not specify which bandwidth belongs to each scenario.Source: D. Simulation Configuration · p. 6
  • The evaluation uses ideal instantaneous CSI and excludes inter-cell interference and channel coding to isolate the codebook’s multilayer representation capability.Fixed-rank evaluation is used.Source: D. Simulation Configuration · p. 6

III. NEAR-FIELD CHANNEL CHARACTERISTICS AND CODEBOOK RESPONSE

The LoS analysis distinguishes aperture coupling that could increase spatial degrees of freedom from coherent mismatch between a fixed plane-wave codeword and a spherical-wave path.

III. NEAR-FIELD CHANNEL CHARACTERISTICS AND CODEBOOK RESPONSE

A. Theoretical Analysis of Spherical-Wave Effects on the LoS Path

  • The LoS spatial-DoF approximation reaches maxima of 0.0433 for UMi and 0.1148 for InH-linear, both far below unity and suggesting no additional appreciable LoS modes in these configurations.The approximation describes DoF growth with aperture coupling and is not a literal mode count below unity.Source: A. Theoretical Analysis of… · p. 6
  • As range decreases, wavefront curvature most reduces coherent gain for an angularly aligned DFT codeword; with angular offset, the additional finite-range reduction is generally smaller.Angular and curvature phases remain coupled in the coherent sum, so their losses are not separable when the direction is misaligned.Source: A. Theoretical Analysis of… · pp. 6–7

B. Paired-Channel Singular Modes and SVD-EP Rates

Paired FF/NF comparisons show no discernible systematic SVD-EP rate gain, even though individual singular-mode changes vary across users and modes.

B. Paired-Channel Singular Modes and SVD-EP Rates

  • The analysis defines paired changes for singular mode i and rank-ν SVD-EP rate across the FF and NF channel branches.The comparison is made for paired users and channels.Source: B. Paired-Channel Singular Modes and… · p. 7
  • Median singular-mode changes range from −0.0003 to 0.0075 dB in UMi and −0.0034 to 0.0120 dB in InH-linear, while weaker-mode user spreads are wider.For SV4, P10–P90 intervals are [−0.0479, 0.138] dB in UMi and [−0.215, 0.261] dB in InH-linear.Source: B. Paired-Channel Singular Modes and… · p. 7
  • At rank 4, SVD-EP rate-change P10–P90 intervals are [−0.0309, 0.0814] bit/s/Hz in UMi and [−0.104, 0.144] bit/s/Hz in InH-linear, with no discernible systematic rate gain.Lower ranks have narrower intervals, and the distributions cross zero.Source: B. Paired-Channel Singular Modes and… · p. 7

C. Absolute Rate and SVD-EP-Normalized Rate

Across both scenarios, FF and NF rates for a given codebook are often close, while the gap between codebook structures grows at higher rank. In the deep near field, frozen-codeword changes generally weaken with range, and reselection can reduce mismatch losses.

C. Absolute Rate and SVD-EP-Normalized Rate

  • At rank 4, mean NF rates are 44.7 and 61.6 bit/s/Hz for Type-I and eType-II in UMi, and 27.0 and 36.0 bit/s/Hz in InH-linear; same-scheme FF/NF boxes largely overlap.The wavefront-model displacement is smaller than the separation between codebook structures.Source: C. Absolute Rate and SVD-EP-Normalized… · p. 7, Figure 5 · p. 8
  • In UMi, mean normalized-rate differences between FF and NF are at most 0.28 percentage points; in InH-linear, the mean drops 1.89 points for Type-I at rank 1 and 1.19 points for eType-II at rank 4.The remaining InH-linear combinations show smaller changes.Source: C. Absolute Rate and SVD-EP-Normalized… · p. 8, Figure 6 · p. 8
  • At rank 4, mean NF normalized rates are 67.7% and 93.6% for Type-I and eType-II in UMi, and 65.7% and 88.1% in InH-linear.The passages attribute the high-rank gap to Type-I’s constrained layer combinations; eType-II combines multiple basis beams with complex coefficients.Source: C. Absolute Rate and SVD-EP-Normalized… · p. 8, Figure 6 · p. 8

D. Frozen-Codeword Response and Range Dependence

  • As normalized distance α increases, frozen-codeword and final total-rate changes generally contract toward the FF baseline, while gains and losses can coexist within a range group.The perturbation weakens with range, but its sign depends on the user channel and codebook structure.Source: D. Frozen-Codeword Response and Range… · p. 9, Figure 7 · p. 9
  • Across sampled ranges, eType-II is predominantly lossy in both scenarios, whereas Type-I changes straddle zero; eType-II frozen-codeword losses decrease with range.At the same α, eType-II shows similar frozen-codeword losses in the two scenarios.Source: D. Frozen-Codeword Response and Range… · p. 9, Figure 7 · p. 9
  • At α = 0.10 in InH-linear, median frozen-codeword changes are −2.28% for Type-I and −5.34% for eType-II, shrinking after reselection to −0.770% and −3.28%, respectively.At α = 0.15 in UMi, the median Type-I change is 0.157% frozen and 4.03% final; the final P25–P75 interval is [0.0910%, 15.8%].Source: D. Frozen-Codeword Response and Range… · p. 9

E. Representative-User Beam Reselection

For a representative InH-linear user, spherical-wave phases reorder beam responses, and the codebooks respond differently when they reselect beams. Type-I remains constrained by its legal offsets, while eType-II’s multibeam weights recover much of the frozen-codeword loss.

E. Representative-User Beam Reselection

IV. CODEBOOK DESIGN INSIGHTS AND FEEDBACK COST

The design comparisons separate the effects of relaxing Type-I’s interlayer offsets from adding finite-range states, then consider increasing eType-II’s plane-wave basis-beam count. The supplied passages define these comparisons and their feedback accounting, but do not report their rate outcomes.

IV. CODEBOOK DESIGN INSIGHTS AND FEEDBACK COST

A. Type-I Interlayer Combination and Finite Range States

  • PW removes Type-I’s fixed interlayer offsets, allowing layers to select distinct plane-wave atoms; PD adds finite-range spherical-wave atoms to that free multilayer combination.These successive expansions isolate multilayer beam combination and range-state effects.Source: A. Type-I Interlayer Combination and… · p. 11
  • The structural, range, and total increments are measured in SVD-EP-normalized rate, with the total equal to the structural plus range increments.The structural increment compares PW with Type-I; the range increment compares PD with PW.Source: A. Type-I Interlayer Combination and… · p. 11
  • For the 80-element ULA with oversampling factor 4, adjacent angular-codeword correlation is 0.90033; Δ = 0.90 is the resolution-matched baseline and Δ = 0.95 the denser check.The 320-state plane-wave grid uses at most five or seven states per direction, respectively, including ρ = ∞.Source: A. Type-I Interlayer Combination and… · p. 11, Table III · p. 11
  • The range-state configurations fit a 3-bit range field, and reported rank-1–4 payloads are 20, 35, 50, and 64 bits.Those payloads include angular, range, and polarization co-phase bits per layer, plus RI, LI, and CQI.Source: A. Type-I Interlayer Combination and… · p. 11

B. Rate Gains from Multilayer Combination and Range Sampling

Relaxing Type-I’s fixed interlayer offsets yields the main high-rank rate gain, while finite range sampling adds comparatively little. Increasing eType-II’s basis-beam count improves rates in both FF and NF channels, with an additional NF gain concentrated at shorter range.

B. Rate Gains from Multilayer Combination and Range Sampling

  • At rank 4, multilayer combination adds 20.7%, range sampling adds 0.579%, and the total SVD-EP-normalized gain is 21.3%.The multilayer-combination gain grows from zero at rank 1; each box is normalized by the matched NF SVD-EP rate for the same user and rank.Source: B. Rate Gains from Multilayer… · p. 11
  • At rank 4, relaxing the Type-I constraint adds 8.28 bit/s/Hz to its 27.04 bit/s/Hz mean NF rate, while range states add 0.239 bit/s/Hz.The resulting polar codebook rate is 35.56 bit/s/Hz, close to eType-II L = 4 at 36.02 bit/s/Hz.Source: B. Rate Gains from Multilayer… · p. 11

C. eType-II Multi-Beam Extension

B. Rate Gains from Multilayer Combination and Range Sampling

  • Increasing ∆ to 0.95 adds only 0.0350 bit/s/Hz on average, while multilayer-combination gain remains dominant across distance groups.The passage characterizes denser range sampling as providing little further improvement.Source: B. Rate Gains from Multilayer… · p. 12

D. Feedback–Rate Tradeoff

The feedback–rate comparison shows that Type-I’s fixed interlayer offsets account for the main rate gap, while additional range states or basis beams bring smaller gains as payload grows. The conclusion recommends prioritizing multilayer multibeam combination and complex weights, with range states as complementary refinement.

D. Feedback–Rate Tradeoff

  • At rank 4, Type-I and polar achieve 27.0 and 35.6 bit/s/Hz with 19 and 64 bits; eType-II L = 2, 4, 6, and 8 achieves 34.2, 36.0, 37.0, and 37.6 bit/s/Hz with 62, 120, 177, and 227 bits.At similar payload, polar exceeds eType-II L = 2 by 1.3 bit/s/Hz.Source: D. Feedback–Rate Tradeoff · p. 12
  • The eType-II L = 2→4, 4→6, and 6→8 steps add 58, 57, and 50 bits for 1.8, 0.97, and 0.63 bit/s/Hz, respectively.The reported rate increments show diminishing returns as feedback payload grows.Source: D. Feedback–Rate Tradeoff · p. 12
  • Across Figs. 9–11, relaxing Type-I’s fixed interlayer offsets provides the main rate increase; added range states or basis beams improve rate with decreasing marginal return per feedback bit.This comparison spans multilayer combination, range sampling, and eType-II basis-beam extensions.Source: D. Feedback–Rate Tradeoff · p. 13

V. CONCLUSION

  • Paired multipath results show no systematic FF/NF displacement in singular-mode gains or SVD-EP rates, while spherical-wave phases reorder plane-wave projections and alter codeword selection.The conclusion reports that the final change depends jointly on the multipath response and the codebook’s adaptation capability.Source: §V · p. 13
  • Large-port NR CSI codebooks should prioritize multilayer multibeam combination and complex-weight capability, using range states to compensate residual wavefront-curvature mismatch.The conclusion reports that eType-II’s multiple basis beams and complex weights give higher absolute rates than Type-I at high rank.Source: §V · p. 13
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