Feedback-Efficient Beam-User Association for Near-Field mmWave Hybrid Beamforming Systems

I. INTRODUCTION

• As carrier frequency and array aperture grow, near-field responses depend jointly on angle and distance, allowing co-angular UEs to be distinguished by focal distance.This requires beam acquisition and association over a joint angle–distance codebook rather than an angular-only codebook.Source: §I · p. 1
• Hybrid beamforming splits precoding between a phase-shifter analog stage and a reduced-dimensional digital stage.This is the architecture considered for the proposed near-field association framework.Source: §I · p. 1
• Standardized Type-I and Type-II CSI codebooks remain angular-domain representations and carry no focal-distance information, leaving near-field multiuser association insufficiently addressed.The proposed compact report supports scheduling and analog-beam selection; scheduled UEs subsequently report reduced-dimensional effective channels for digital precoding.Source: §I · p. 1
• The proposed framework combines an EBRD-based focusing codebook, compact top-M reports, and interference-aware proportional-fair association; simulations show 99.11% less feedback than full-CSI feedback with under 0.6% SE loss versus full-metric reporting.The association uses report-carried leakage terms and known codeword correlations; M is dimensioned from assignment infeasibility rather than set equal to the stream count.Source: §I · p. 1

II. SYSTEM MODEL AND SIGNAL PROCESSING

• The BS uses an analog precoder and a reduced-dimensional digital baseband precoder to serve single-antenna UEs over an FDD downlink, where instantaneous downlink CSI generally cannot be inferred from uplink reciprocity.The setup assumes K ≥ NRF and NS = NRF serving streams.Source: §II · p. 2
• Near-field spherical wavefronts make element-to-UE propagation distances nonuniform within the Rayleigh distance RF = 2D^2/λ, so association uses a focusing rather than angular codebook.The channel is modeled as a superposition of L spherical-wave components with path gains and angle, elevation, and distance parameters.Source: §II · p. 2
• Angular codebook directions use centered DFT samples in the supported direction-cosine domain, matched to the array resolution.The valid angular directions satisfy the stated support condition.Source: §II · p. 2
• The EBRD is the largest focal distance distinguishable from the far-field codeword at coherence threshold ρ0; beyond it, one far-field codeword per direction suffices.Within the EBRD, consecutive focal distances are spaced by the beam-depth condition ρ(ri, ri+1) = ρ0; ρ0 = 0.5 recovers the classical 3-dB effective Rayleigh distance, and larger thresholds produce denser radial grids.Source: §II · p. 2
• The hybrid codebook cardinality follows from array geometry, while uniform-r, uniform-1/r, and angular-only DFT codebooks serve as baselines.After scheduling, the BS forms the analog precoder and designs the digital precoder using regularized zero-forcing.Source: §II · p. 2

• Direct CSI feedback is costly because each UE would report NT complex coefficients.Source: . FRFHH · p. 3
• The compact report is used only for scheduling and analog beam selection.Source: . FRFHH · p. 3
• After FRF is fixed, scheduled UEs estimate gH k FRF from dedicated pilots and report quantized coefficients that the BS stacks into Heff; the narrowband model needs no subband-specific report.Source: . FRFHH · p. 3

III. PROPOSED STRATEGY

• After scheduling and analog beam selection, scheduled UEs provide reduced-dimensional effective-channel feedback for digital precoding.The procedure constructs the analog precoder from selected UE–beam pairs, then acquires effective channels and computes the digital precoder.Source: §III · p. 3
• Each UE probes all codewords but reports only its M strongest candidates, with M set from measured assignment infeasibility rather than the number of streams.The report supports scheduling and analog beam selection; effective-channel feedback follows for scheduled UEs.Source: §III · pp. 3–4
• The BS uses a proportional-fair metric to select UE–beam pairs, incorporating the UE’s prior rate history.The PF rate is recursively updated across transmission time intervals, and unscheduled UEs have a previous rate of zero.Source: §III · p. 3
• The association assigns each UE and beam at most once and enforces exactly N_S = N_R_F active pairs.The binary variable x_k,s indicates whether beam s is assigned to UE k.Source: §III · p. 3
• Scoring each candidate against already selected pairs uses reported leakage and known codeword correlations to discourage interference and near-duplicate beams.Both factors equal one for an empty assignment, recovering the interference-blind metric; pairs are then selected sequentially.Source: §III · p. 3
• The ranking metric and sequential association are not jointly optimal, but are presented as a practical low-complexity design for large near-field codebooks.The proposed overhead includes top-M candidate reports and quantized effective-channel coefficients from scheduled UEs.Source: §III · p. 4

IV. SIMULATION RESULTS

• The simulations use a 128×8 array with RF=80.9 m and place 75% of UEs in three co-angular clusters.The channel uses an exact spherical response while the codebook uses a Fresnel expansion, so the evaluation includes model mismatch.Source: §IV · p. 4
• The proposed scheme stays within 0.6% reduction of FULL-FB across transmit SNR, while its gap to PF-BDP reaches 18.7% at 12 dB.FULL-FB retains the better of full-report and compact solutions in every slot, making it an optimistic complete-feedback reference.Source: Figure 1 · p. 4, §IV · p. 4
• Across K, the proposed scheme tracks FULL-FB within 0.7%; its PF-BDP gap grows from 1.4% at K=8 to 18.0% at K=64, and at K=64 it exceeds FC-OMP by 6.6%.It also exceeds SUS by 15.3% at K=64 and overtakes FC-OMP for K≥32.Source: Figure 2 · p. 4, §IV · pp. 4–5
• At 1456 bits/TTI, proposed reporting reduces feedback by 99.11% versus full-CSI feedback and 99.21% versus FULL-FB.Each UE reports only M index–metric pairs; the proposed and FULL-FB schemes have the same probing burden and differ only in reporting.Source: Figure 3 · p. 5, §IV · p. 5
• M=3 is adopted: sum-SE reaches 3.449 bps/Hz from 3.403 at M=1 and is flat thereafter within 0.02%.Infeasibility is 1.75% at M=1 and vanishes for M≥2; association time is 2.4–2.6 ms/TTI. The chosen M is one step above the feasibility threshold.Source: Figure 4 · p. 5, §IV · p. 5
• The proposed codebook stays within 1.2% of inverse-r and beats best uniform-r (Nr=8, Nb=3520) by 1.5% with 45.9% fewer codewords; DFT is 18.7% below.Within the proposed family, sum-SE is flat to within 0.8% for ρ0∈[0.7, 0.9], and ρ0=0.7 is selected as the smallest codebook in that flat region.Source: §IV · p. 5

V. CONCLUSION

• M = 3 keeps sum-SE within 0.6% of an optimistic full-metric reporting reference, while total feedback falls by 99.21% versus that reference and 99.11% versus full-CSI feedback.The BS acquires the scheduled UEs’ low-dimensional effective channel for RZF precoding.Source: §V · p. 5
• Up to 18.7% of sum-SE is lost when the proposed association metric is replaced by its interference-blind counterpart.An angular-only codebook costs up to 21.2% of sum-SE.Source: §V · p. 5
• EBRD-based radial-grid sizing exceeds the best uniformly sampled polar codebook by 1.5% while requiring 45.9% fewer codewords to probe.Source: §V · p. 5