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BeamRMX: Radiation-Pattern-Driven Learning for Generalizable Beam Radio Map Prediction and Beam Management

Yue Zhang, Xiucheng Wang, Wenshuo Chen, Nan Cheng

arXiv:2609.00615v1eess.SPcs.LG

TL;DR

BeamRM prediction must handle multiple configuration-dependent power fields generated by one propagation scene, while existing methods use limited beam descriptors or generic architectures. BeamRMX makes spatial radiation the primary query, learns its interaction with scene geometry, and optionally uses same-scene cross-configuration evidence. It reports consistent gains in matched-domain and zero-shot evaluations, including 26.11% lower MAE on unseen scenes and 47.75% lower MAE on an unseen configuration.

  • Problem

    Beamformed MIMO systems generate configuration-dependent BeamRMs, but existing approaches do not fully represent or dedicatedly process the spatial excitation-to-field relationship.

  • Method

    BeamRMX uses XBase to learn multiscale interactions between a spatial radiation query and scene geometry, with an optional Evidence Adapter for same-scene source BeamRMs.

  • Results

    26.11% lower MAE is achieved on unseen scenes, and 47.75% lower MAE on an unseen configuration, with additional improvements across reported metrics.

  • Takeaways & Limitations

    Spatial radiation provides a common query domain for heterogeneous beam states, while cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

Abstract

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The evolution toward sixth-generation (6G) wireless networks is driving larger antenna arrays and highly directional multi-beam transmission, making accurate knowledge of beam-dependent spatial coverage important for beam management and environment-aware network operation. Radio maps (RMs) provide such a representation, yet conventional RM prediction assumes omnidirectional or transmitter-level radiation. In beamformed multiple-input multiple-output (MIMO) systems, one propagation scene instead gives rise to many configuration-dependent beam radio maps (BeamRMs), creating challenges in beam representation and generalization. Existing methods either condition prediction on beam descriptors or use beam maps as auxiliary inputs to generic architectures. We propose BeamRMX, which, to the best of our knowledge, is the first dedicated framework to treat the spatial radiation pattern as the primary BeamRM query and learn how scene geometry transforms it into the received power field. XBase learns multiscale interactions between the radiation query and scene geometry, while an optional Evidence Adapter uses a few cross-configuration BeamRMs from the same scene. Matched-domain and zero-shot experiments show consistent gains over deterministic and diffusion baselines, including mean absolute error reductions of 26.1\% on unseen scenes and 47.8\% on an unseen configuration. Cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

I. INTRODUCTION

BeamRMX addresses the one-scene–many-BeamRM problem by making spatial radiation the primary query and learning its interaction with scene geometry. An optional Evidence Adapter uses same-scene source BeamRMs to refine predictions without target observations or test-time parameter updates.

  • Implications: The framework targets generalization across heterogeneous beam states and configurations while supporting beam management, coverage assessment, network planning, and related environment-aware functions.Its source-assisted setting also addresses incremental network evolution without requiring exhaustive per-beam measurement.
  • Motivation: Beamformed MIMO systems produce distinct received power fields for different frequencies, arrays, and beamforming states within the same environment.This configuration dependence creates BeamRMs rather than a single transmitter-level spatial response.
  • Motivation: Existing BeamRM methods use codebook identities, continuous beamforming vectors, or beam maps as conditioning information, leaving target representation and processing as central issues.BeamRMX instead expresses heterogeneous radiation states in a common spatial domain.
  • BeamRMX: BeamRMX supports query-only prediction when no radio observation is available and optional source-assisted prediction when a few same-scene BeamRMs exist.The Evidence Adapter uses source excitations and maps as transferable evidence while keeping XBase frozen and excluding the target configuration.
  • BeamRMX: XBase treats spatial excitation as the primary BeamRM query, separately represents excitation and scene geometry, and learns their structured multiscale interaction.The formulation models how a propagation scene transforms specified radiation into received power.

A. Learning-Based Radio Map Prediction

Learning-based radio-map research has advanced efficient environment-to-coverage prediction, but BeamRM prediction requires explicit treatment of configuration-dependent spatial excitation. The remaining gap concerns learning the scene-conditioned transformation of that excitation rather than merely concatenating generic inputs.

  • Existing RM prediction: Geometry-conditioned, adversarial, graph-based, and diffusion predictors mainly target transmitter-level radio maps under omnidirectional or weakly directional assumptions.Their primary mapping is from environment information to coverage, with beam excitation omitted or represented through auxiliary parameters.
  • Beam representation: Directional BeamRM methods condition on beam identities, continuous beamforming vectors, antenna-pattern projections, or configuration-dependent beam maps.These representations progressively expose directional information but differ in whether radiation is represented spatially or globally.
  • Beam representation: Beam maps analytically convert configuration-dependent radiation into grid-aligned spatial features before environment-dependent blockage and multipath are introduced.They provide a more explicit radiation prior than scalar configuration encoding.
  • Methodological gap: Generic architectures commonly concatenate spatial excitation and environmental information, leaving their interaction to be learned implicitly.This creates a methodological gap between representing the beam and modeling how the scene transforms it into received power.
  • Radio evidence: Source BeamRMs differ from sparse target observations because they describe other excitations transformed by the same environment rather than directly sampling the target field.The source-assisted setting therefore requires transferable evidence extraction, a reliable query-only path, and no parameter updates at inference.
  • Synthesis: Generalizable BeamRM prediction combines a common spatial radiation representation, learned excitation-to-field transformation, and source-assisted use of cross-configuration responses.These requirements motivate separating target excitation, propagation scene, and optional same-scene radio evidence.

A. BeamRM Prediction Conditioned on Spatial Excitation

The paper formulates BeamRM prediction as learning a scene-conditioned transformation from a specified spatial excitation to a received power field. The query combines radio configuration and directional radiation state, while the model-ready excitation incorporates the beam map and transmitter-relative spatial cues.

  • Inputs: A propagation scene is represented over an H × W spatial region together with environmental information and a registered evaluation grid.The grid registration is relative to the transmitter.
  • Inputs: A target query q = (c, ρ) specifies radio configuration c and directional radiation state ρ, such as beamforming or steering.The raw beam map is deterministically computed over the scene’s evaluation grid.
  • Inputs: Once the query and evaluation grid are fixed, the beam map contains the radiation representation but no scene-dependent blockage or multipath information.Those propagation effects must be learned from the scene information rather than copied from the beam map.
  • Model-ready representation: The model-ready excitation combines the beam map with transmitter-relative spatial cues, and the query-only path supplies no separate query embedding to XBase.The beam map is therefore the route through which q affects query-only prediction.
  • Output: The target BeamRM is the received power field, while its valid-region mask identifies pixels used for supervision and evaluation.The mask is not treated as target-side radio evidence.
  • Formulation: BeamRM prediction learns the unknown scene-conditioned transformation that maps specified spatial excitation to the corresponding received power field.Different radiation queries consequently produce different BeamRMs for a fixed scene.

B. Query-Only Generalization Regimes

The paper distinguishes matched, scene-zero-shot, and configuration-zero-shot evaluation for query-only BeamRM prediction, then defines strict-small source-assisted prediction using same-scene BeamRMs from other configurations. These settings exclude target BeamRM observations and inference-time parameter updates.

  • Evaluation regimes: Query-only prediction is evaluated in matched, scene-zero-shot, and configuration-zero-shot regimes.Scene-ZS tests unseen propagation environments, while Config-ZS tests configurations and directional states absent from training.
  • Evaluation regimes: In every query-only regime, no same-scene BeamRM is available at inference time.
  • Source-assisted prediction: Strict-small source-assisted prediction uses a few BeamRMs from the same scene under other radio configurations.Each source query is paired with the source configuration and beam map that generated its BeamRM.
  • Source-assisted prediction: Strict-small support excludes the target configuration, target BeamRM pixels, and inference-time parameter updates.Support configurations are drawn from a predefined lower-complexity configuration set.
  • Source-assisted prediction: Cross-configuration source BeamRMs provide realized evidence about the common environment rather than direct observations of the target field.

IV. PROPOSED BEAMRMX FRAMEWORK

BeamRMX has an asymmetric design: XBase is a complete query-only predictor, while an optional Evidence Adapter refines its frozen output when same-scene cross-configuration evidence is available.

  • Framework overview: XBase approximates the scene-conditioned transformation from target spatial excitation and scene geometry to the BeamRM.
  • Framework overview: The Evidence Adapter refines rather than replaces the frozen XBase prediction.
  • Framework overview: The target spatial excitation and scene geometry define the query-only prediction path.
  • Framework overview: For K > 0, the Evidence Adapter estimates a residual correction from the frozen XBase anchor and support set.
  • Framework overview: For K = 0, the support branch is bypassed and BeamRMX returns the complete XBase prediction unchanged.

B. XBase: Scene-Conditioned Excitation-to-Field Learning

XBase separately encodes target spatial excitation and scene geometry, then learns their multiscale interaction to predict the received power field with propagation-informed residual refinements.

  • Dual-stream encoding: XBase processes target spatial excitation and scene geometry through separate four-stage ConvNeXt V2 encoders.The excitation stream represents the target radiation state, while the geometry stream represents building and boundary-related scene structure.
  • Dual-stream encoding: The target BeamRM is never included in either XBase input stream.The implementation uses five excitation channels and eleven geometry channels.
  • Multiscale interaction: Cross-conditioned fusion models excitation–geometry interactions across multiple spatial scales while preserving the streams’ distinct information roles.Learned masks condition each stream on the other before fusion, unlike input-level concatenation.
  • Prediction heads: A feature-pyramid decoder produces a decoded representation that is mapped to a dominant response and scene-dependent modulation map.
  • Prediction heads: Directional and boundary residual heads capture local excitation–geometry deviations and boundary-sensitive details.These are propagation-related inductive biases, not explicit decompositions of individual physical mechanisms.
  • Prediction heads: BeamRMX combines the decoded dominant response, modulation, and residual components into the final query-only prediction.

C. Evidence Adapter: Cross-Configuration Propagation Evidence

The Evidence Adapter aggregates same-scene source BeamRMs and their excitations, weighting them by query relations and gating corrections according to evidence quality and relevance.

  • Evidence construction: Each support BeamRM is paired with its source excitation to expose realized source-response information for adapter processing.The support input is encoded with detail-, gradient-, and boundary-sensitive cues.
  • Relation-aware aggregation: Attention-based relation weighting accounts for frequency, antenna-configuration, and directional-state differences between target and source queries.
  • Relation-aware aggregation: Candidate supports are selected before learned aggregation over the selected set.
  • Evidence construction: The adapter aggregates multiscale support features and fuses them with the frozen XBase representation.
  • Residual refinement: The adapter’s support-derived target estimate and two residual proposals provide broad calibration and localized detail corrections.
  • Controlled refinement: Gating restricts correction when evidence is weak, spatially irrelevant, or inconsistent with the target query.The gate uses shot, support-quality, region, and confidence factors.

D. Two-Stage Learning and Inference

BeamRMX uses a two-stage design: XBase learns query-only prediction first, then a frozen XBase is optionally refined by an Evidence Adapter using same-scene source BeamRMs. Training objectives supervise reconstruction, structured outputs, detail consistency, evidence-conditioned corrections, and protection against harmful adaptation.

  • XBase is first optimized independently as the query-only predictor, after which its parameters are frozen for Evidence Adapter training.
  • The training objective supervises valid-region reconstruction, auxiliary structured outputs, and region/detail-sensitive consistency without path-level physical labels.
  • The combined adapter objective trains reconstruction, evidence-conditioned estimates and corrections, spatially constrained adaptation, and knowledge transfer to low-shot settings.
  • A margin-based no-harm term discourages substantial degradation relative to the frozen XBase anchor while allowing corrections whose pixels do not all improve.
  • During inference, K = 0 returns the query-only prediction, while K > 0 applies one gated correction without target observations, parameter updates, or test-time fine-tuning.

V. EXPERIMENTAL RESULTS AND DISCUSSION

The experiments evaluate BeamRMX under matched-domain, unseen-scene, and unseen-configuration protocols on a diverse XL-MIMO BeamRM dataset. BeamRMX consistently leads the evaluated methods, with strong quantitative and qualitative gains but residual uncertainty on unseen scenes.

  • Experimental scope: The evaluation covers query-only prediction, same-scene evidence assistance, and evidence-mechanism analysis across complementary protocols.
  • Experimental setup: The dataset contains 78,400 ray-tracing-based BeamRMs from 800 urban scenes, spanning five carrier frequencies, multiple array configurations, and up to 1024 antenna elements.
  • Evaluation protocols: Query-only experiments use matched-domain, Scene-ZS, and Config-ZS splits, with Scene-ZS testing scenes entirely absent from model training.
  • Matched-domain results: MAE of 2.0991 dB reduces the best competing MAE by 56.91% in the matched-domain setting, while RMSE decreases by 39.85%.
  • Scene-ZS results: 26.11% lower MAE is achieved in Scene-ZS, although the 7.66% relative RMSE reduction indicates that difficult high-error regions remain challenging on unseen environments.
  • Config-ZS results: 47.75% and 31.47% reductions in MAE and RMSE, respectively, are obtained on the unseen 6.7-GHz, 256-element, 16-beam Config-ZS configuration.
  • Robustness: Scene-ZS MAE is 4.9359 ± 0.0344 dB and Config-ZS MAE is 2.8567 ± 0.0787 dB across three training seeds.
  • Qualitative analysis: Qualitative examples show BeamRMX more closely follows localized high- and low-response regions, with common row-wise power scales preventing independent normalization from exaggerating differences.

C. Strict-Small Source-Assisted Prediction in Unseen Scenes

The strict-small experiment tests whether a few lower-complexity, same-scene BeamRMs improve prediction of an unobserved target configuration in unseen scenes. BeamRMX benefits most from the first supports, outperforming support-enhanced baselines while using gated evidence refinement.

  • Experimental setting: The experiment predicts a 6.7-GHz, 1024-element, 64-beam target on 160 unseen scenes using supports from the same scene and configurations with at most 64 antenna elements.
  • Support selection: Admissible supports are filtered by the strict-small constraint and ranked using query-aware relations, validity and detail cues, anchor consistency, and redundancy penalties.
  • Evaluation protocol: The K = 0 condition is the frozen query-only anchor for the same target configuration, while the Evidence Adapter is bypassed exactly at K = 0.
  • Evidence benefits: A single support reduces BeamRMX MAE from 5.9665 to 3.9178 dB, a 34.3% reduction, while RMSE, PSNR, and SSIM improve simultaneously.
  • Small-shot scaling: Increasing support size from K = 1 to K = 2 lowers MAE from 3.9178 to 3.7237 dB, whereas K = 4 yields only marginal improvement to 3.7095 dB.
  • Baseline comparison: At K = 4, BeamRMX MAE is 22.1% lower than BeamCKM-Support and 28.5% lower than RadioDiff-Support, while retaining diminishing improvement as support increases.
  • Interpretation: The Evidence Adapter treats source BeamRMs as configuration-conditioned observations of shared propagation rather than direct target-field approximations, using relation-aware aggregation and gated residual refinement.

D. Evidence Mechanisms and Intra-Sector Beam Refinement Utility

Controlled diagnostics show that realized same-scene BeamRMs and spatially gated correction drive the source-assisted gains. These reconstruction improvements extend to intra-sector beam refinement across 160 unseen scenes.

  • Evidence mechanism diagnostics: The fixed-checkpoint diagnostics isolate source BeamRM content, spatial region gating, and support-selection relevance as complementary evidence mechanisms.The diagnostics use a fixed 40-scene subset and the same trained checkpoint and strict-small support pool across K = 2 variants.
  • Evidence mechanism diagnostics: Removing source BeamRM content raises MAE from 3.4252 to 5.5363 dB, nearly returning to the K = 0 XBase level.The result indicates that realized same-scene radio evidence, rather than adapter structure or source metadata alone, provides the primary source-assisted gain.
  • Evidence mechanism diagnostics: Removing the spatial region gate increases MAE to 6.9513 dB and raises the no-harm violation rate to 52.56%.Uncontrolled residual injection can therefore introduce negative transfer, supporting the gated-residual design.
  • Evidence mechanism diagnostics: The full method improves MAE from 3.6979 to 3.4252 dB over random admissible support selection, with better HF accuracy and a lower no-harm violation rate.Support relevance affects how effectively same-scene information is transferred, while realized source BeamRMs provide the larger gains.
  • Intra-sector beam refinement utility: Beam-selection regret measures received-power loss from choosing the beam favored by predicted BeamRMs instead of the true best beam; zero regret indicates a ground-truth optimal selection.The Top-3 hit rate counts selections belonging to the three beams with highest ground-truth received powers.
  • Intra-sector beam refinement utility: K = 2 reduces serving-power MAE by 40.5% and mean beam-selection regret by 16.5% relative to the query-only anchor.It also improves Top-3 hit rate, P95 beam-selection regret, and high-response footprint overlap, achieving the best result across communication-oriented metrics.
  • Intra-sector beam refinement utility: A paired scene-level bootstrap estimates a 2.460 dB mean serving-power MAE improvement, with a 95% confidence interval of [2.224, 2.715] dB, across all 160 test scenes.The CDF shift toward lower serving-power MAE and mean regret is therefore not driven by only a small number of favorable environments.

VI. CONCLUSION

BeamRMX targets generalizable prediction in beamformed systems, where one scene yields distinct received-power fields across beam and radio configurations. It explicitly models the spatial radiation query and scene interaction, with optional same-scene evidence refining predictions and improving serving-power estimation and intra-sector beam refinement.

  • VI. CONCLUSION: BeamRMX addresses the one-scene–many-BeamRM setting by representing the target radiation state explicitly in the spatial domain.The formulation learns how scene geometry transforms the spatial radiation query into the corresponding received power field.
  • VI. CONCLUSION: The common spatial representation supports prediction across heterogeneous beam states and configurations, while XBase explicitly learns interactions between radiation and scene geometry.
  • VI. CONCLUSION: Matched-domain, unseen-scene, and unseen-configuration experiments validate the effectiveness and generalization of the formulation.
  • VI. CONCLUSION: When same-scene radio evidence is available, the optional Evidence Adapter further refines predictions without target observations or test-time updates.
  • VI. CONCLUSION: The resulting BeamRMs improve serving-power estimation and intra-sector beam refinement.
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