Radar-Only Long-Term Beam Prediction in mmWave Vehicular Networks: An Empirical Study of Doppler Input and Cross-Modal Distillation

I. INTRODUCTION

• The paper identifies limited link-level effect-size reporting, untested long-term Doppler-resolved radar input, and untested transfer from a vision–radar teacher to a radar-only student on real measurements.The earlier cross-modal evidence described here used simulated data, single-step prediction, and a simulated point-cloud radar input.Source: §I · pp. 1–2
• The study uses real DeepSense 6G data, mainly from a straight-road site with one-directional passes at 2.8–4.7 m/s; the motivating high-mobility regime is argued, not tested.The controlled comparison focuses on Doppler-resolved input and cross-modal distillation for a radar-only long-term predictor.Source: §I · p. 2

A. Contributions

• Top-1 accuracy orders tested predictors nearly as received power does, but typical accuracy gaps amount to only tenths of a decibel.The paper therefore measures principal contrasts in decibels.Source: A. Contributions · p. 2
• Adding Doppler-resolved content yields a measurable link-level gain, traced to the Doppler content rather than the extra input and replicated at a second BS site.The contribution summary describes the gain as mostly in the tail of the loss.Source: A. Contributions · p. 2
• With the full training set, tested cross-modal distillation adds no measurable received-power gain, while exploratory scarce-data gains are mostly reproduced by a radar-only teacher.The null also holds for variants scored only in accuracy.Source: A. Contributions · p. 2

A. Sensing-Aided and Long-Term Beam Prediction

• Sensing-aided methods predict beams from sensor observations, while prior long-term multimodal forecasters keep all sensors at inference rather than learning from several and running on one.The surveyed work includes camera, radar, LiDAR, and multimodal predictors.Source: A. Sensing-Aided and Long-Term Beam… · p. 2

B. How These Methods Are Evaluated

• Most methods use top-k accuracy or DBA, but DBA's index tolerance is conventional and does not measure received power.A few works report link-level quantities, but none asks what an accuracy point is worth in received power.Source: B. How These Methods Are Evaluated · p. 2

C. Radar Representations

• Prior radar-only Doppler comparisons focused on replacing range–angle input for current-slot prediction; long-horizon CSI-free use and the useful Doppler projection remained unmeasured.Demirhan and Alkhateeb found range–angle best among the three current-slot radar representations; range–velocity was close behind.Source: C. Radar Representations · pp. 2–3

D. Knowledge Distillation for Efficient Beam Prediction

• Prior cross-modal distillation gains came from simulated, single-step prediction with a simulated point-cloud radar input, leaving real-measurement, long-horizon transfer to a Doppler-map student untested.Same-modality long-term distillation and multimodal students that retain both sensors at inference address different settings.Source: D. Knowledge Distillation for… · p. 3

III. MEASURED-LINK MODEL AND PROBLEM FORMULATION

• The link model uses measured powers across 64 beams to define the best available beam and the predicted-beam loss; common path loss and fading cancel, but beam-dependent fading does not.The measurements are an uplink sweep, with beam reciprocity assumed for the best receive and transmit beams.Source: §III · p. 3

A. Multimodal Sensing Observations

• A co-located RGB camera and FMCW radar supply observations without CSI; the camera serves training-side teacher and vision-only models, while deployment uses radar alone.The camera motion mask is generated by grayscale conversion, frame differencing, and thresholding.Source: A. Multimodal Sensing Observations · p. 3, Figure 1 · p. 4
• The reference radar input pairs a range–angle map with a range–Doppler map, and the sensing window uses L−1 aligned frames because differencing consumes one frame.The maps are derived from a range–Doppler–angle radar cube by averaging over one axis.Source: A. Multimodal Sensing Observations · p. 4

B. Problem Formulation

• At each window, the predictor classifies beams for the current slot and J future slots from sensing alone.The formulation uses C = 64 measured beams.Source: B. Problem Formulation · p. 4
• The link-level objective is evaluated alongside classification training on the arg-max beam label; recorded powers are not used as soft training targets.The protocol is open-loop and therefore an optimistic benchmark rather than a closed-loop performance estimate.Source: B. Problem Formulation · p. 4

IV. DOPPLER-AUGMENTED PREDICTOR AND DISTILLATION TESTBED

• The radar-only predictor encodes each observed frame, reads the feature sequence recurrently, and decodes a beam distribution for each horizon slot; the teacher adds a camera branch during training.At inference the student reads radar alone.Source: §IV · p. 4

A. Doppler-Augmented Modality Encoders

• The vision branch encodes motion masks, while the radar branch uses range–angle plus a Doppler-projection map as a two-channel input.The radar encoder jointly extracts position and radial-velocity features.Source: A. Doppler-Augmented Modality Encoders · pp. 4–5

IV. DOPPLER-AUGMENTED PREDICTOR AND DISTILLATION TESTBED

• The reference student trains on the task loss without distillation, while the vision–radar teacher is trained offline and distillation links are used only in those experiments.Feature, temporal-attention, and logit alignment are the tested transfer signals.Source: Figure 2 · p. 5

A. Doppler-Augmented Modality Encoders

• The paired range–angle and Doppler-resolved input extracts position and radial-velocity features; different map pairings perform alike within 0.02 dB despite their different shared axes.Separate input branches do no better, and the shared-axis hypothesis is not supported by the reported results.Source: A. Doppler-Augmented Modality Encoders · p. 5
• The single Doppler–angle map is a leaner candidate, but its deficit against range–Doppler pairing is unresolved, so the latter remains the reference configuration.The pilot favored range–Doppler, while the ten-seed comparison found the pairings indistinguishable.Source: A. Doppler-Augmented Modality Encoders · p. 5
• The teacher and student have separately optimized radar encoders of the same architecture, limiting teacher advantage attributable to a larger radar encoder.The compact radar branch adds only first-layer input weights for its second channel.Source: A. Doppler-Augmented Modality Encoders · p. 5

B. Cross-Attention Fusion in the Teacher

• Radar queries attend to vision keys and values, with a residual that keeps the fused representation anchored to radar features.The authors contrast this with concatenation, which would place the teacher in a feature space that a radar-only student cannot reproduce; their concatenation-teacher test does not support that hypothesis.Source: B. Cross-Attention Fusion in the Teacher · p. 5

C. Temporal Model With Positional Attention

• The GRU encoder summarizes past frames, then a zero-input decoder runs for future steps without feeding predictions back between steps.Learned positional encodings precede decoder-to-encoder attention; its rows indicate which past frames inform each predicted future slot.Source: C. Temporal Model With Positional… · p. 5
• The radar-only student shares the teacher’s temporal structure, making the teacher’s attention map available as an optional distillation target.The backbone adds decoder-to-encoder attention with learned positional encodings to the recurrent outputs.Source: C. Temporal Model With Positional… · pp. 5–6

D. Radar-Only Student

• The radar-only student uses a two-channel radar encoder, a one-layer GRU, and positional attention, producing features and beam logits.It has 92.5 k parameters at inference versus the teacher’s 1.84 M, but the passage does not establish that its inference latency or computation shrinks proportionally.Source: D. Radar-Only Student · p. 6

E. Composite Distillation Loss

• The composite loss combines the beam task with candidate distillation at the output, feature, and temporal-attention levels.Feature alignment projects student features toward the teacher’s fused representation; temporal alignment matches frame-importance maps row by row, using a fixed head-to-head pairing.Source: E. Composite Distillation Loss · p. 6
• The task term is focal loss for beam-class imbalance, while logit distillation uses temperature-scaled KL divergence between softened outputs.The reference student sets all three distillation weights to zero and trains on the task loss alone; the ablation adds the terms cumulatively.Source: E. Composite Distillation Loss · p. 6

F. Training Procedure

• Training uses three phases: task-loss teacher training, teacher self-distillation, then student training with the teacher frozen and vision available only to the teacher.At inference, the radar-only student is deployed alone.Source: F. Training Procedure · p. 6

A. Experimental Setup

• Scenario 9 contains 5,964 samples from 136 passes; chronological pass-boundary splits allocate 91 passes to training, 17 to validation, and 28 to testing.The seven future slots span 0.67 s; Scenario 31, a second base-station site, is reserved for Doppler-contrast replication.Source: A. Experimental Setup · p. 6
• Inputs are log-compressed to fixed 128×64 radar maps, and all learned arms use the same stored maps and preprocessing.The common input shape does not imply matching axes across map types.Source: A. Experimental Setup · p. 6
• The study compares radar-only students with and without distillation, vision-only students, and a vision–radar teacher under a shared split, budget, and checkpoint rule.The range–angle-only row removes the Doppler-resolved map from the testbed encoder; it is not an implementation of or.Source: A. Experimental Setup · pp. 6–7
• Capacity checks add 144 parameters to the two-channel encoder, while separate input branches do no better than the shared encoder.The range–angle comparison uses the better-performing mean-subtracted input.Source: A. Experimental Setup · p. 7
• Each window predicts seven slots, with top-k accuracy, ADBA, and per-slot beam-selection loss used to assess prediction quality.Link quality comparisons rest on beam-selection loss; ADBA is reported for comparability, and exact-at-current-slot comparators are read over t+1 to t+6.Source: A. Experimental Setup · p. 7
• Confidence intervals resample test passes as clusters and seeds, while Scenario 9 contrasts are not strictly confirmatory because earlier arms informed design and used its test passes.Only the Scenario 31 contrast had not been read on its test passes; small intervals clearing zero among many uncorrected comparisons are indicative only.Source: A. Experimental Setup · p. 7

B. Long-Term Prediction Accuracy

• The gain comes from Doppler content, not an extra input: an all-zero second map changes the range–angle student’s loss by less than 0.01 dB.Every radar-only configuration with a Doppler-resolved map lands within 0.13 dB of the others, while the range–angle-only student is the 0.91 dB outlier.Source: B. Long-Term Prediction Accuracy · p. 7
• +0.14 dB for the range–Doppler pairing replicates at Scenario 31 under the pre-written decision rule; after label correction and retraining, the gain is +0.20 dB.At that site persistence beats both radar arms over t+1 to t+6, where the optimal beam stands still on 40% of frames versus 15% at the discovery site.Source: B. Long-Term Prediction Accuracy · p. 7, Figure 3 · p. 8
• −0.01 dB received-power difference ([−0.07, +0.06]) separates the distilled and undistilled RA+RD students on the full training set.The teacher leads the student by 0.24 dB, but distillation recovers at most a limited share; the vision-only student accounts for 0.19 dB of the lead.Source: B. Long-Term Prediction Accuracy · pp. 7–8
• 0.28 dB lower mean beam-selection loss for the range–Doppler pairing than range–angle alone ([0.14, 0.41]).The undistilled student also gains 4.0 to 4.6 pp of ATop-1 when paired with a Doppler-resolved map.Source: B. Long-Term Prediction Accuracy · p. 7, Figure 3 · p. 8
• On the clear-weather daytime scenario, the full-size motion-mask vision-only student leads every radar arm and approaches the teacher.A vision-only student reduced to the radar-only student’s size trails it by 0.34 dB in an exploratory matched design.Source: B. Long-Term Prediction Accuracy · p. 8

C. Comparison With Nonlearned References

• 41.8% accuracy and 0.65 dB loss for the reference student beat the anchored reader’s 18.6% and 1.68 dB over t+1 to t+6.The anchored reader is the most accurate of the five nonlearned predictors over that horizon.Source: C. Comparison With Nonlearned References · p. 8
• The tracker estimates along-road position and speed from the strongest moving radar return using range, angle centroid, and signed Doppler centroid.It is an extended Kalman filter in road coordinates, fitted on the training passes.Source: C. Comparison With Nonlearned References · p. 8
• The student leads the tracker’s better feedback-free variant by 20.8 percentage points and 0.56 dB, while its 0.21 dB lead over the anchored variant has an interval including zero.The radial velocity does not help the filter here because along-road speed barely varies; anchoring uses the last measured beam.Source: C. Comparison With Nonlearned References · p. 8
• The learned student stays between 41.1% and 43.0% accuracy at every slot, while persistence falls from exact at the current slot to 0.0% at t+6.Using only the last frame costs the student 2.2 percentage points in accuracy in an exploratory test.Source: C. Comparison With Nonlearned References · p. 8

VI. RECEIVED POWER AS THE COMMON SCALE FOR COMPARING PREDICTORS

• Top-1 accuracy is coarse on this codebook: the second-best beam is within 0.21 dB of the best at the median, and an immediate neighbor 87.4% of the time.A flat beam peak makes accuracy treat near and far misses alike, obscuring their different power costs.Source: §VI · p. 8
• The Doppler-resolved student stays ahead of the range–angle student at every horizon slot, while distillation tracks the undistilled student.The figure reports top-1 accuracy and mean beam-selection loss at each slot.Source: Figure 4 · p. 9
• The nine predictors’ 8.5-point accuracy spread corresponds to 0.51 dB of mean loss, with a descriptive fitted slope of −0.062 dB per percentage point.Across 36 predictor pairs, 34 have the same ordering by accuracy and received power; the two inversions are within half a point.Source: §VI · p. 9, Figure 5 · p. 9
• With the Doppler-resolved map, slots losing more than 3 dB fall from 8.2% to 4.2%; distillation moves no tail statistic measurably.Removing the camera costs 0.19 dB in mean loss but 3.2 dB at the 99th percentile, so the mean understates the worst-slot cost.Source: §VI · p. 9

A. Ablation: Distillation Signals

• Adding logit, feature, and temporal-attention distillation terms changes received power by −0.01 to −0.03 dB, with every interval covering zero.Other RA+RD teachers and a concatenation teacher produce the same null; varying the logit weight over two decades keeps the student within 0.03 dB of no distillation.Source: A. Ablation: Distillation Signals · p. 10

B. Alternative Explanations for the Null

• A concatenation teacher yields the same distillation null, and widening the undistilled student changes received power by no more than 0.04 dB.Distilling a larger teacher–student accuracy gap changes received power by +0.06 dB, consistent with the original null.Source: B. Alternative Explanations for the Null · p. 10
• At ten training passes, exploratory distillation gains 0.64 dB, shrinking monotonically to −0.01 dB with all 91 passes; a radar-only teacher recovers 0.55 dB of the ten-pass gain.The additional 0.09 dB for the vision–radar teacher has an interval spanning zero.Source: B. Alternative Explanations for the Null · p. 10

• 0.235 dB at the current slot and 0.385 dB at t+6 are the Doppler-augmented student’s gains over range–angle; growth across the horizon is not established.The gain appears at every slot, while the endpoint difference is only marginal in decibels and absent in top-1 accuracy.Source: C. What the Doppler-Resolved Map… · p. 10
• Per-angle Doppler centroids, with or without spread, fall short of the full distribution, while whether velocity-bin ordering or magnitudes matter remains unresolved.Collapsing the Doppler axis of Doppler–angle leaves the student indistinguishable from range–angle alone; permuting rows does not resolve the ordering question.Source: C. What the Doppler-Resolved Map… · p. 11, Table III · p. 11
• Removing range localization from the range–Doppler map causes no resolved top-1 loss, with the interval bounding the cost at no more than 3.0 pp.The control permutes the range axis while retaining each velocity bin’s total.Source: C. What the Doppler-Resolved Map… · p. 11, Table III · p. 11
• 5.5 pp is lost when the Doppler–angle map is pooled to one group, but only 0.05 pp at 32 groups, for this encoder.The sweep is interpretable only within itself because its baseline is 1.2 pp above Table I; this is encoder resolution, not radar acquisition resolution.Source: C. What the Doppler-Resolved Map… · p. 11
• 0.74 dB loss for range–Doppler versus 0.91 dB for range–angle and 0.67 dB for Doppler–angle makes Doppler presence the first-order distinction among single maps.Each Doppler-resolved input beats range–angle alone on an interval excluding zero; residual angle effects among Doppler-resolved inputs remain unresolved.Source: C. What the Doppler-Resolved Map… · p. 11
• The column-total-at-centroid representation is 0.35 dB worse than the full map, while the permuted map is not separated from the Gaussian or full-map arms.The controls compare alternative summaries of each column’s Doppler distribution; two of the four exploratory predictions were wrong.Source: C. What the Doppler-Resolved Map… · p. 11, Table III · p. 11
• A Doppler-centroid-to-beam reader errs by 11.7 indices RMS, versus 6.8 for the same maps’ angle-axis peak, so the tested simple bearing interpretation is unsupported.The authors expect moving-target cues to weaken through turns and intersections because they depend on direction persistence.Source: C. What the Doppler-Resolved Map… · p. 11
• Adding range–Doppler lowers angular misalignment from 2.28° to 1.82°; the difference from prior single-slot results cannot be assigned to horizon alone.The studies also differ in input, network, and split, and no measurement isolates the remaining factors.Source: C. What the Doppler-Resolved Map… · pp. 11–12

• 0.28 dB ([0.14, 0.41]) lower mean beam-selection loss comes from adding range–Doppler to range–angle, and the gain replicates at a second base station.The replication is +0.14 dB as pre-specified and +0.20 dB after label correction; holding the last measured beam beats both radar arms there.Source: §VIII · p. 12
• −0.01 dB ([−0.07, +0.06]) is the received-power change from distillation by a motion-mask vision–radar teacher; tested teacher, student, fusion, and distillation variants show the same metric-specific null.The interval excludes recovering over a quarter of the source teacher’s 0.24 dB advantage.Source: §VIII · p. 12
• A top-1 accuracy point is worth 0.062 dB of mean beam-selection loss here, so accuracy differences should not substitute for link-level measurement.The tested predictors are ordered nearly the same by top-1 accuracy and received power.Source: §VIII · p. 12
• For a ten-pass student, a radar-only teacher trained on all passes reproduces 0.55 of the 0.64 dB gain; this exploratory comparison does not isolate the camera’s effect.The teachers differ in architecture and size, and teacher data and soft targets remain confounded.Source: §VIII · p. 12
• The learned contrasts use one CNN–GRU family and principally one site, vehicle, and travel direction; open-loop, frame-clock-aligned windows are optimistic benchmarks, not deployed performance.The principal data are daylight, clear-weather passes at median speeds of 2.8–4.7 m/s, without turns or intersections.Source: §VIII · p. 12
• All models train with an arg max beam classification loss; whether training on measured power vectors changes either finding remains untested.The per-slot power-capture ratio also excludes scheduling and retransmission.Source: §VIII · p. 12