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KDGen-BF: A Generative Site-Specific Multi-User Beamforming Approach

Ruihang Jiang, Zhaolin Wang, Yuanwei Liu

arXiv:2608.29838v1eess.SP

TL;DR

The paper addresses online multi-user beamforming when only low-dimensional RSRP observations are available and instantaneous CSI is unavailable. KDGen-BF uses conditional diffusion generation, KD-EMA training, and multi-candidate inference to produce joint beamforming weights beyond finite codebooks. Across multiple DeepMIMO scenarios, it reports strong max–min fairness, particularly under limited probing budgets and noisy RSRP measurements.

  • Problem

    Accurate CSI is costly to acquire, while low-dimensional RSRP observations create ambiguity and multi-user interference couples the beamforming decisions.

  • Method

    KDGen-BF conditionally generates joint multi-user beamforming weights from RSRP observations using a diffusion transformer, SOC-guided KD-EMA training, and DDIM-based multi-candidate inference.

  • Results

    Across multiple DeepMIMO scenarios, KDGen-BF outperforms non-exhaustive baselines, approaches DFT Exhaustive with larger probing budgets, and remains robust under noisy RSRP observations.

  • Takeaways & Limitations

    Generative modeling can support site-specific multi-user beamforming when online observations are low-dimensional or imperfect.

Abstract

from arXiv · show

This paper proposes knowledge-distilled generative beamforming (KDGen-BF) framework for site-specific multi-user beamforming. KDGen-BF generates a multi-user beamforming weights from low-dimensional reference signal received power (RSRP) observations without acquiring instantaneous channel state information (CSI). To address the ambiguity caused by limited RSRP observations and interference coupling, KDGen-BF formulates multi-user beamforming as a conditional generation problem and directly outputs beamforming weights beyond a finite codebook. A diffusion transformer is trained through knowledge-distillation and exponential-moving-average (KD-EMA) guidance, and multi-candidate strategy is used for online deployment. Numerical results on multiple DeepMIMO scenarios demonstrate that: 1) under limited probing budgets, KDGen-BF outperforms all baselines; 2) with larger probing budgets, KDGen-BF achieves performance comparable to exhaustive search over the discrete Fourier transform (DFT) codebook and outperforms all other baselines; and 3) under noisy RSRP observations, KDGen-BF remains robust and outperforms all compared baselines.

I. INTRODUCTION

Multi-user beamforming must jointly enhance desired signals and control interference, but conventional CSI-based optimization is costly and codebook methods suffer quantization and interference-selection limits. KDGen-BF addresses these issues by conditionally generating joint beamforming weights from RSRP observations without instantaneous CSI, using KD-EMA training and multi-candidate inference.

  • Multi-user beams must jointly enhance desired signals while controlling inter-user interference on shared time-frequency resources.
  • Accurate instantaneous CSI enables conventional multi-user optimization but incurs substantial training overhead, processing cost, and decision latency.
  • GoB reduces CSI acquisition through RSRP probing but restricts solutions to predefined beams, causing quantization loss and complicating multi-user selection.
  • Discriminative and learned-codebook site-specific methods infer beams from incomplete observations, but learned-codebook decisions remain finite and deterministic approaches do not directly resolve multi-solution ambiguity.
  • Existing generative site-specific beamforming focuses mainly on single-user settings, whereas multi-user beams are coupled by interference and may have multiple optimal joint solutions.
  • B. Motivation and Contributions: KDGen-BF generates joint multi-user beamforming weights from RSRP observations beyond a finite codebook using a conditional DiT, SOC-guided KD-EMA training, and DDIM multi-candidate inference with UE feedback selection.
  • Experiments across multiple DeepMIMO scenarios report max–min fairness gains, especially under limited probing budgets and noisy RSRP observations.

B. Problem Formulation

The paper formulates site-specific multi-user beamforming as a max–min design problem and reformulates it as predicting feasible joint beamforming weights from low-dimensional RSRP observations without instantaneous CSI.

  • B. Problem Formulation: The design objective is max–min beamforming under a total transmit-power budget and architecture-dependent feasible beamforming set.Ptot denotes the base-station transmit-power budget, while S captures the adopted transceiver architecture's feasibility constraints.
  • B. Problem Formulation: Coupled inter-user interference makes the optimization non-convex and prevents decomposition into independent per-user subproblems.Each user's rate depends on the entire beamforming matrix through interference terms.
  • B. Problem Formulation: The proposed reformulation predicts beamforming matrices directly from low-dimensional channel-probing observations rather than requiring the full instantaneous channel at inference.The online task is to generate the beamforming matrix from P or its prompt representation O without observing H.
  • C. Site-Specific Learning Reformulation: Beam probing has the base station transmit predefined beams while each user equipment reports corresponding RSRP values, yielding responses rather than full complex channel vectors.These measurements indicate how users respond to the probed directions but provide only low-dimensional information.
  • C. Site-Specific Learning Reformulation: Site-specific learning exploits stable deployment structure—such as scatterers, blockages, and long-term user distributions—to relate RSRP patterns to effective joint beamforming decisions.The propagation environment E is treated as fixed for a deployment and its effect is implicitly embedded in the prompt through probing observations.
  • C. Site-Specific Learning Reformulation: The multi-user prompt O is mapped by a learnable function to a joint beamforming matrix, followed by decoding and normalization.The decoding module enforces the total transmit-power and architecture-specific feasibility constraints.
  • C. Site-Specific Learning Reformulation: Training uses paired prompt and channel samples collected from the considered site to learn the relation between observations and joint beamforming weights.The paired samples support learning the site-specific mapping from O to Ŵ.
  • C. Site-Specific Learning Reformulation: Limited RSRP observations can correspond to different channel conditions, creating ambiguity in generating beamforming weights.The desired model learns to maximize the expected worst-user rate while evaluating generated weights under channel set H.

III. PROPOSED KDGEN-BF FOR SITE-SPECIFIC MULTI-USER BEAMFORMING

KDGen-BF predicts joint multi-user beamforming from low-dimensional RSRP observations without instantaneous CSI during online inference. Its prompt encoder combines per-user probing features with cross-user dependencies, while conditional diffusion uses timestep and global context signals.

  • Framework overview: KDGen-BF predicts a joint beamforming matrix from all users’ RSRP observations without requiring instantaneous CSI during online inference.The framework targets max–min fair multi-user beamforming in a site-specific setting.
  • Prompt construction: The model prompt is built from low-dimensional DFT-beam probing RSRP observations for each user.Each user’s probing vector contains RSRP measurements over a selected DFT beam subset.
  • Prompt construction: Standardized and peak-referenced RSRP features preserve relative responses while reducing scale differences across users.The two feature views are concatenated into a multi-user prompt representation.
  • Prompt conditioning: A prompt encoder applies self-attention across users so each context token incorporates cross-user dependency information.This representation reflects that fairness-oriented beamforming depends on multi-user coupling rather than independent per-user preferences.
  • Prompt conditioning: The denoiser receives separate prompt and timestep tokens, plus a global conditioning vector that summarizes the group context for shared layer modulation.The global vector is obtained by mapping the average of the user context tokens through an MLP.

C. Conditional DiT Denoiser

The conditional DiT operates on a real-valued DFT-domain representation of the target multi-user beams. Forward diffusion adds Gaussian noise, and denoising reconstructs the beam representation from the noisy sample under conditioning.

  • Beam representation: Target complex beamforming weights are represented as a real-valued matrix whose rows separately store users’ real and imaginary DFT coefficients.The DFT-domain representation aligns the probing measurements and generated beam output in the same coordinate system.
  • Beam decoding: The decoded DFT-domain beams are transformed to the spatial domain by inverse DFT and globally normalized to satisfy the total transmit-power constraint.The resulting user beams are concatenated into the final beamforming matrix.
  • Forward diffusion process: Forward diffusion progressively corrupts the target representation by injecting Gaussian noise according to a variance schedule.At each timestep, the denoising task is to predict the injected noise from the corrupted sample and conditioning representation.

3) One-dimensional DiT architecture:

The one-dimensional DiT treats DFT beam indices as a sequence and jointly denoises multi-user beam representations. Self-attention captures sequence structure, cross-attention injects conditioning, and AdaLN supplies shared modulation.

  • One-dimensional DiT architecture: A one-dimensional DiT processes the noisy DFT-domain beam representation as a sequence whose length equals the number of DFT beam indices.This structure is chosen instead of a two-dimensional image-oriented tokenization.
  • One-dimensional DiT architecture: The input sequence is projected into hidden tokens with positional embeddings and shallow input-related features.The projection maps the noisy beam representation into the DiT hidden token space.
  • One-dimensional DiT architecture: Each DiT block combines self-attention, cross-attention, feed-forward processing, and AdaLN-based modulation.Cross-attention receives timestep and prompt context, while AdaLN uses the global conditioning vector.
  • Denoising objective: The output head predicts Gaussian noise, and the denoising objective trains this prediction to match the injected noise.The predicted noise is used to reconstruct the target beam representation.
  • Denoising objective: Reconstruction errors are amplified at high-noise steps according to a timestep-related factor, after which the estimate is decoded into normalized beamforming weights.The pipeline performs DFT decoding, inverse Fourier transformation, and total-power normalization.

D. SOC Teacher Construction and KD-EMA Training

KDGen-BF uses offline CSI-based SOC solutions as pseudo-labels and transfers their supervision through teacher-student diffusion training. KD-EMA addresses the multi-solution structure of beamforming, while masked student prompts and an EMA teacher provide stabilized distillation.

  • SOC teacher construction: Offline max–min SINR optimization under a total transmit-power constraint produces SOC beamforming solutions used as pseudo-labels.The problem is solved by bisection over the target SINR and SOCP feasibility checks.
  • SOC teacher construction: Bisection with SOC feasibility checks yields a high-quality beamforming solution that is converted into a real-valued DFT-domain target.The target stacks the real and imaginary parts of the SOC solution’s DFT coefficients.
  • Motivation for KD-EMA: Per-user phase rotations leave all users’ SINRs unchanged, illustrating why joint beamforming has multiple equivalent solutions.Limited RSRP observations further enlarge the set of effective beamforming solutions, making single-target matching potentially collapse outputs toward one representation.
  • Teacher-student training: A teacher-online denoiser learns toward SOC-guided beam representations under full prompt conditioning.The SOC-derived target is corrupted through the forward diffusion process during teacher training.
  • Teacher-student training: An EMA copy of the teacher supplies a temporally smoothed and more stable distillation target for the student.The student uses a masked prompt and is trained with complementary objectives.

4) Student objectives:

The student combines diffusion denoising, EMA-teacher distillation, and SINR-oriented guidance, with scheduled optimization that transitions from stable reconstruction toward task-level beamforming performance.

  • Student objectives:: KDGen-BF trains the student with diffusion denoising, teacher-guided distillation, and SINR-oriented guidance losses.These objectives preserve denoising ability, transfer EMA-teacher predictions, and guide worst-user performance.
  • Student objectives:: The EMA teacher uses the full prompt while the student uses a masked prompt, improving robustness to incomplete conditioning information.The teacher supplies a stable denoising target under the same corrupted sample.
  • Student objectives:: The SINR guidance term encourages generated beamforming weights to improve the worst-user performance through a soft-min objective.The student prediction is reconstructed and decoded into a beamforming matrix before evaluating user SINRs.
  • Student objectives:: The optimization schedule jointly samples diffusion steps and adjusts the student-loss weights across training epochs.Large diffusion steps emphasize coarse structure, while smaller steps support local refinement.
  • Student objectives:: Training begins with denoising and distillation losses, then gradually increases SINR guidance after meaningful beamforming structures emerge.This schedule avoids unstable early SINR gradients and shifts learning toward task performance.

E. Inference with DDIM and Candidate Selection

Online inference deploys only the student denoiser, which generates beamforming candidates from low-dimensional RSRP prompts using accelerated DDIM reverse denoising.

  • E. Inference with DDIM and Candidate Selection: Online beam generation uses low-dimensional RSRP observations and the student model without CSI or online SOC optimization.The teacher networks and SOC solver are excluded from deployment.
  • E. Inference with DDIM and Candidate Selection: DDIM replaces the DDPM reverse process to generate high-quality solutions with fewer reverse steps under latency constraints.This makes the sampling procedure more suitable for online beamforming deployment.
  • E. Inference with DDIM and Candidate Selection: Each candidate starts from an independent Gaussian initialization and is iteratively denoised along the DDIM reverse schedule.The final estimate is decoded into a beamforming matrix after completing the reverse process.
  • E. Inference with DDIM and Candidate Selection: The system repeats DDIM sampling for N_cand initializations to form multiple beamforming candidates.Multi-candidate generation addresses sampling variability and mode bias.

3) Candidate selection:

Candidate selection evaluates generated beamformers with short pilots and scalar UE feedback, then chooses the candidate with the largest measured desired-signal/interference utility.

  • 3) Candidate selection:: The BS ranks generated candidates using a feedback-based utility rather than instantaneous CSI acquisition.The procedure is summarized as deployable DDIM inference with candidate selection.
  • 3) Candidate selection:: Short pilots allow each UE to estimate desired-signal and interference quantities for every candidate beamforming matrix.The resulting scalar estimates are fed back to the BS.
  • 3) Candidate selection:: The BS selects the beamforming candidate with the largest utility after aggregating scalar UE feedback.The candidate utility is based on the minimum user-level feedback value.
  • 3) Candidate selection:: With multiple candidates, the inference procedure samples, denoises, decodes, probes, and ranks each generated beamformer.A single candidate is returned directly when N_cand = 1.
  • 3) Candidate selection:: The utility omits the noise term because the multi-user setting is dominated by interference, enabling lightweight selection without noise-power estimation.All deployable methods use low-dimensional RSRP observations and share the same feedback-based selection protocol.

1) DFT Greedy:

The baselines range from independently selected DFT beams to reduced or learned codebooks and deterministic grid-free prediction, differing in whether they model inter-user coupling and finite-codebook constraints.

  • 1) DFT Greedy:: DFT Greedy selects each user’s beam independently using the largest probing RSRP.Its resulting combination does not explicitly account for inter-user interference.
  • 1) DFT Greedy:: DFT Exhaustive enumerates all combinations of probed DFT beams and selects the best using the feedback-based utility.This accounts for inter-user coupling but requires combinatorial enumeration.
  • 1) DFT Greedy:: Hier-DFT reduces exhaustive search through coarse-to-fine sector probing and evaluation of a reduced candidate-combination set.Users retain top sectors during coarse probing and top beams during fine probing.
  • 1) DFT Greedy:: NN-LSS-Codebook trains a site-specific codebook offline and selects combinations from learned codewords during online evaluation.The BS evaluates a reduced combination set formed from each user’s top-B codewords.
  • 1) DFT Greedy:: Grid-free baselines are not restricted to finite codebooks, while the deterministic counterpart directly predicts and decodes the target beam representation.The deterministic model uses the same group prompt and DFT-domain decoding pipeline as described.

2) Single-user Direction-SOC:

Single-user Direction-SOC generates per-user beam candidates, selects directions from RSRP, and then solves an SOC-based max–min beamforming problem. The evaluation compares its multi-user performance and BS-side decision complexity with other methods across probing budgets and DeepMIMO scenarios.

  • Single-user Direction-SOC: Each user’s single-user generator produces multiple candidate transmit beam directions, and the candidate with the largest UE-side received power is selected.The selected beam is normalized and used as an estimated channel direction.
  • Single-user Direction-SOC: The selected per-user directions form an estimated channel matrix for an SOC-based max–min beamforming solve.The resulting beamforming weights are denoted ˆWsu+soc = SOC(ˆHsu).
  • Complexity Analysis: BS-side serial decision complexity counts RSRP processing and joint candidate selection while excluding over-the-air probing, UE measurement, and feedback signaling.Feedback-based baselines evaluate all B^K joint combinations, while neural methods process one whole K-user group per forward pass.
  • Complexity Analysis: N_p^K gives DFT Exhaustive inherent exponential scaling over the full probed codebook, whereas KDGen-BF uses N_candN_step multi-user student-denoiser evaluations with teacher and SOC operations offline.Hier-DFT and NN-LSS-Codebook can additionally incur B^K feedback-based joint-search costs.
  • Experimental Setup: Across three DeepMIMO scenarios and K ∈ {2, 3, 4}, the evaluation uses a common preprocessing, grouping, probing, and data-splitting protocol.The default settings are N_p = 64, N_step = 50, and N_cand = 64, with performance measured by downlink SINR including inter-user interference.
  • Evaluation under Different Probing Budgets: At N_p = 64, KDGen-BF reaches 7.66 dB in I2_28B versus 8.66 dB for DFT Exhaustive, while it improves from 5.15 dB to 11.26 dB in Boston5G_28.At N_p = 16 in Boston5G_28, KDGen-BF achieves 7.31 dB versus 3.37 dB for DFT Exhaustive, 3.45 dB for NN-LSS-Codebook, and 0.99 dB for Gen-BF.

C. From Single-User Fitting to Multi-User Generalization

As user groups grow, multi-user beamforming targets become less similar to training examples, exposing the limits of memorization and single-user fitting. KDGen-BF addresses this complexity through KD-EMA training and multi-candidate generation, improving fairness and robustness under limited or corrupted observations.

  • Generalization from single-user to multi-user: As K increases, target similarities decrease and become more dispersed, requiring joint modeling of interference coupling and fairness-oriented coordination.For K = 1, most test targets have close training counterparts; larger groups are less covered by the training target space.
  • Generalization from single-user to multi-user: From K = 2 to K = 4, NN-LSS-Codebook falls from 31.16 dB to 4.54 dB, while the deterministic Transformer falls from 6.75 dB to −8.35 dB.The corresponding SU Dir.-SOC values decline from −4.67 dB to −15.98 dB, and baseline gaps to the Upper Bound enlarge.
  • Effect of KD-EMA training: For K = 4, KDGen-BF reduces the gap to the Upper Bound to 4.28 dB, versus 11.00 dB for NN-LSS-Codebook and 23.89 dB for the deterministic Transformer.The comparison is reported for mean group min-SINR on Boston5G_28.
  • Effect of KD-EMA training: At Ncand = 64, KDGen-BF raises mean group minimum SINR over Gen-BF from 6.47 dB to 11.26 dB for K = 4.The K = 2 and K = 3 improvements are 22.51 dB to 27.36 dB and 11.29 dB to 14.64 dB, respectively.
  • Effect of candidate number: Increasing Ncand from 1 to 64 improves KDGen-BF from −8.48 dB to 11.26 dB for K = 4, with the largest gain in the most strongly coupled setting.Multi-candidate generation improves coverage of the conditional beamforming solution space, while selection uses scalar desired and interference measurements.
  • Robustness to noisy RSRP: At RSRP measurement SNR = 5 dB, KDGen-BF achieves 6.28 dB mean group minimum SINR, compared with 0.47 dB for Gen-BF and −5.52 dB for DFT Exhaustive.At 40 dB measurement SNR, KDGen-BF reaches 11.26 dB; the experiment evaluates corrupted RSRP prompts rather than downlink data-transmission noise.
  • Robustness to noisy RSRP: Masked prompt student training and standardized, peak-referenced RSRP features support robustness without a dedicated noise-robust training module.The student learns to recover beamforming structure from partially masked prompts under full-prompt EMA-teacher guidance.
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