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Spatial MIMO Channel Rendering: A 3D Gaussian Splatting Approach

Juntaek Han, Geonha Kim, Chaozheng Wen, Ahmed Alkhateeb, Jun Zhang, Jeonghun Park

arXiv:2610.36880v1eess.SP

TL;DR

Spatial prediction must account for the propagation geometry that shapes channels at unmeasured locations, while conventional CSI acquisition consumes resources repeatedly. MIMO-GS learns a latent beamspace scene and renders joint beam-pair power maps; in beam management, it attains 97 to 99% of the genie-aided benchmark across the scheduled-user range.

Abstract

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The achievable gains of multiple-input multiple-output (MIMO) systems depend on channel state information (CSI), whose acquisition consumes pilot and feedback resources for every user in every coherence interval. Meanwhile, the propagation environment that shapes the channel persists. Exploiting such information will help to greatly reduce the overhead of CSI acquisition. This paper investigates the spatial MIMO channel rendering problem, which learns a latent beamspace channel scene from sparse observations and renders the long-term transmit and receive beam pair power map at unobserved user locations. Motivated by 3D Gaussian splatting in visual scene rendering, the proposed MIMO Gaussian splatting (MIMO-GS) represents the scene with pairs of receive and transmit 3D Gaussians, projects them from the user and base station onto the corresponding beam domains, and accumulates the beam associations through beam pair splatting. On a simulated urban scenario and measured indoor channels, MIMO-GS renders 5.5 times faster than ray tracing without a calibrated replica. Applied to multiuser beam management, the rendered maps allow users and transmit beams to be scheduled without sounding while accounting for the inter-user interference, and the net sum rate reaches 98% of the genie-aided benchmark, 19% above a position-based predictor.

I. INTRODUCTION

CSI acquisition is costly and must be repeated, while the propagation environment persists; spatial rendering therefore seeks reusable channel information at unmeasured locations. Prior environment-based methods do not directly provide the joint transmit–receive beam-pair map targeted here.

I. INTRODUCTION

  • CSI consumes pilot and feedback resources and must be reacquired for every user in every coherence interval, while the propagation environment persists across realizations.Spatial prediction can reuse environment structure across users and channel realizations when the scene and operating configuration remain unchanged.Source: §I · pp. 1–2
  • Unlike temporal and spectral prediction, spatial prediction must account for scatterers, reflectors, and blockages because no simple model captures their effects on channels at unobserved locations.Blockage or visibility boundaries can change the effective paths and shift dominant beam pairs abruptly, even between nearby locations.Source: §I · p. 2
  • Channel rendering learns a reusable beamspace scene from finite channel observations and renders the long-term joint transmit–receive beam-pair power map at an arbitrary UE location.The UE location is the viewpoint, and the map at an unmeasured location is the rendered output.Source: §I · p. 2

A. Related Works

  • Ray tracing depends on a high-fidelity digital replica and can be computationally expensive, while implicit radio neural fields can require repeated network evaluations over many samples or rays.Existing Gaussian-based RF methods span several rendered quantities, but prior approaches commonly render from one side rather than the joint MIMO beam-pair domain.Source: A. Related Works · p. 2

B. Contributions

The paper proposes MIMO-GS to learn a continuous, long-term beamspace scene and render joint beam-pair power maps from sparse channel observations. It also formulates the rendering target and identifies the spatial and joint-beam structure the renderer must preserve.

B. Contributions

  • MIMO-GS learns an explicit latent scene from channel observations and renders long-term beam-pair maps for use as statistical CSI in multiuser beam-domain transmission.The proposed scheme configures CSI-RS resources only on beams scheduled from the rendered map.Source: B. Contributions · p. 3

II. CHANNEL MODEL AND PROBLEM FORMULATION

  • The rendering target is the expected long-term power over receive and transmit DFT beam pairs, preserving the coupled angular structure of each propagation component.The map is defined over the joint beam-pair grid, rather than as separate transmit- and receive-domain outputs.Source: B. Contributions · p. 3, §II · p. 4

B. Contributions

  • The scene representation pairs receive and transmit Gaussians, projects them from the UE and BS into their beam domains, and uses location-conditioned gains and differentiable beam-pair splatting to aggregate contributions.The framework is validated on a ray-traced urban scenario and over-the-air measured indoor channels.Source: B. Contributions · p. 3

II. CHANNEL MODEL AND PROBLEM FORMULATION

  • Given observations at UE locations, the learned renderer produces a beam-pair power map at an arbitrary location within the learned scene, not an extrapolation to another propagation environment.Training minimizes reconstruction loss between rendered and observed maps.Source: §II · p. 4
  • A renderer must represent the environment-induced scene because angular drift can vary maps smoothly, while path visibility changes can shift dominant beam pairs abruptly.The formulation seeks a differentiable representation that captures both smooth trends and sharp spatial transitions.Source: §II · p. 4

III. PRELIMINARIES: 3D GAUSSIAN SPLATTING

3D Gaussian splatting represents a scene explicitly with anisotropic Gaussian primitives, projects them into an observation domain, and differentiably accumulates their contributions. In MIMO-GS, the rendered quantity is beamspace power, not visual appearance.

III. PRELIMINARIES: 3D GAUSSIAN SPLATTING

  • 3D-GS represents a scene with explicit anisotropic Gaussian primitives instead of an implicit neural field requiring dense sampling and many network evaluations.Each primitive has a center, covariance, opacity, and learnable attribute vector.Source: §III · pp. 4–5
  • MIMO-GS adapts Gaussian primitives to represent a channel scene: paired receive and transmit Gaussians project into their beam domains and splat contributions into a beamspace power map.The Gaussians are latent channel-scene primitives, not identifiable physical surfaces or scatterers.Source: Figure 1 · p. 5, §III · p. 5
  • A Gaussian covariance is parameterized using a rotation matrix and scaling matrix to keep it positive semi-definite during optimization.Projection uses a local affine approximation to obtain the projected covariance and center.Source: §III · p. 5
  • Overlapping projected Gaussians are depth-sorted and accumulated by front-to-back alpha blending, with the rendered attribute formed from their contributions.The projection and blending pipeline is differentiable, allowing Gaussian parameters to be optimized against observations.Source: §III · p. 5

IV. MIMO-GS RENDERING FRAMEWORK

MIMO-GS represents the channel scene with paired receive and transmit Gaussians and renders a long-term beam-pair power map at a UE location. A shared gain network models how each primitive’s power varies with UE location.

IV. MIMO-GS RENDERING FRAMEWORK

  • MIMO-GS outputs a beam-pair power map by combining channel-scene representation, dual-sided projection, and beam-pair splatting.Each map entry is jointly indexed by a receive and transmit beam, so both sides must be projected.Source: §IV · p. 5

A. Channel Scene Representation

  • Each MIMO-GS primitive pairs receive and transmit Gaussians whose means set the two beam associations and whose shared weight represents static component strength.The means are effective geometric parameters, not physical scatterer locations; distinct means allow a mixture of primitives to represent multipath propagation.Source: A. Channel Scene Representation · pp. 5–6
  • A shared gain network scales each primitive’s static weight using its location-dependent visibility, which can change abruptly across blockage boundaries.The network takes primitive and UE locations as input and returns one scalar per primitive.Source: A. Channel Scene Representation · p. 6
  • Fourier-feature positional encoding is applied to coordinate inputs to represent abrupt power changes that raw-coordinate neural networks tend to smooth.The features use encoded primitive and UE positions, including their relative displacement from the receive Gaussian mean.Source: A. Channel Scene Representation · p. 6
  • The gain network’s nonnegative output modulates the static primitive weight before projection and splatting distribute its contribution across beam pairs.The network maps the constructed location-conditioned feature vector to a dynamic gain factor.Source: A. Channel Scene Representation · p. 6

B. Dual-Sided Projection onto Beam Domains

MIMO-GS projects each primitive from the UE and BS onto separate receive and transmit beam domains. The projected Gaussian spreads determine each side’s beam associations.

B. Dual-Sided Projection onto Beam Domains

  • Two geometric projections map each primitive’s receive Gaussian from the UE and its transmit Gaussian from the BS onto their respective beam domains.The beam coordinates use the UE and BS array frames, whose orientations are assumed fixed and known.Source: B. Dual-Sided Projection onto Beam… · p. 6
  • Each side’s projected covariance represents the Gaussian’s spatial spread in beam coordinates, so broader Gaussians can cover more beams.The covariance is projected using a local affine approximation around the Gaussian mean.Source: B. Dual-Sided Projection onto Beam… · pp. 6–7
  • Receive and transmit association weights are evaluated at their respective DFT beam centers and normalized separately over beam indices.The two associations are formed independently; the paired primitive parameters describe effective beam-pair support rather than a single physical interaction point.Source: B. Dual-Sided Projection onto Beam… · p. 7

C. Beam Pair Splatting for Rendering

Beam-pair splatting allocates each primitive’s location-dependent power across receive–transmit beam pairs and sums contributions into a power map. It uses direct summation rather than depth-ordered optical blending.

C. Beam Pair Splatting for Rendering

  • Each primitive’s contribution is allocated across beam pairs using its location-dependent gain and the receive and transmit association weights.The two association weights define a separable allocation over receive and transmit beam indices.Source: C. Beam Pair Splatting for Rendering · p. 7
  • The main rendering equation accumulates Gaussian contributions over receive–transmit DFT beam pairs to produce the beam-pair power map.It replaces splatting over image pixels with splatting over beam pairs.Source: C. Beam Pair Splatting for Rendering · p. 7
  • MIMO-GS directly sums nonnegative primitive contributions because beam-pair power has no universal depth ordering for optical alpha blending.Visibility and blockage are instead absorbed into the learned location-dependent gain.Source: C. Beam Pair Splatting for Rendering · p. 7
  • The renderer models aggregate beamspace power induced by coherent multipath without resolving individual complex path coefficients.Each projected primitive contributes a learnable nonnegative amount over the beam-pair grid.Source: C. Beam Pair Splatting for Rendering · p. 7

D. Training and Inference

MIMO-GS is optimized from observed UE locations by minimizing reconstruction loss, with differentiable rendering operations enabling joint parameter updates. After training, it renders a beam-pair map at a target UE location.

D. Training and Inference

  • The differentiable gain, projection, association, and splatting operations allow joint optimization of Gaussian and gain-network parameters against reconstruction loss.Training renders maps at observed UE locations from the observation set.Source: D. Training and Inference · p. 7
  • Adaptive density control clones, splits, or prunes primitives during training to refine the scene representation.Densification targets large positional gradients; splitting addresses primitives spanning many DFT beams, while pruning removes low-contribution primitives.Source: D. Training and Inference · p. 8
  • At an arbitrary UE location, the trained renderer computes primitive gains, projects both Gaussians, and splats their associations into a beam-pair power map.The framework’s paired projections preserve receive–transmit coupling that one-sided RF renderers do not provide.Source: D. Training and Inference · p. 8

V. BEAM MANAGEMENT WITH RENDERED MAPS

MIMO-GS supports multiuser beam management by rendering the beam-pair powers needed to account for interference, replacing per-user sounding with a rendering pass while leaving transmission and scheduling unchanged.

V. BEAM MANAGEMENT WITH RENDERED MAPS

  • As arrays grow, narrower beams lengthen CSI-RS sweeps, and overhead also grows with the number of users served.The BS sweeps CSI-RS resources and UEs measure and report them in 5G NR.Source: §V · p. 8

A. Multiuser Transmission in the Beam Domain

  • The scheduler needs every beam’s power at every user, because other users’ beams contribute user- and beam-specific interference.A best-beam index alone does not provide the information needed to determine each user’s rate.Source: A. Multiuser Transmission in the Beam… · p. 8
  • Under BDMA, users occupy distinct DFT transmit beams, each carrying one stream, and the BS uses beam-domain statistical CSI rather than instantaneous CSI.The required statistical CSI is the beam pair power map.Source: A. Multiuser Transmission in the Beam… · p. 8
  • Once the scene is trained, MIMO-GS renders that map from each user’s reported position, replacing per-user sounding while leaving transmission and scheduling unchanged.Conventional acquisition sounds each user on every beam over many coherence intervals; the rendered map also supports scheduling a user at initial access without a measurement history.Source: A. Multiuser Transmission in the Beam… · p. 8
  • Configuring only the scheduled beams costs |S|τ_RS rather than N_tτ_RS for a full-codebook sweep, assuming |S|τ_RS < T_B.Reporting and control signaling overheads are outside the comparison.Source: A. Multiuser Transmission in the Beam… · p. 8

B. Scheduling on the Rendered Map

Scheduling uses the rendered map’s expected powers to evaluate interference-aware user–beam assignments, rather than mapping position directly to a beam decision.

B. Scheduling on the Rendered Map

  • Expected powers replace instantaneous powers in the scheduling objective, and predicted receive beams maximize over the beam the UE will later select.Substituting expected powers into SINR approximates ergodic rate; that approximation is used only to choose users and beams.Source: B. Scheduling on the Rendered Map · p. 9
  • Path gain estimated from reported position puts rendered powers on the common scale needed to compare them with noise and one another, without measuring candidate users.The scheduling objective uses the expected powers supplied by the map.Source: B. Scheduling on the Rendered Map · p. 9
  • The scheduler greedily adds the user–free-beam pair that most increases F, then revisits assigned beams until no move improves F or the user limit is reached.It may schedule fewer than L users, assign a user a beam other than its strongest, or leave an interfering user unscheduled.Source: B. Scheduling on the Rendered Map · p. 9
  • Unlike predictors that output one beam index per user, MIMO-GS renders beam-pair powers that can be re-evaluated for another scheduling rule or codebook.The compared position- or vision-based predictors do not express another user beam’s interference; the vision-based approach also depends on optical visibility and is centered on LoS-dominated conditions.Source: B. Scheduling on the Rendered Map · p. 9

VI. NUMERICAL RESULTS

The evaluation covers a simulated urban DeepMIMO scene and a measured indoor scenario, with rendering accuracy assessed on held-out locations against several map-rendering baselines.

A. Simulation Settings

  • The DeepMIMO simulation uses one fixed BS, 256 transmit beams and 16 receive beams across 7,240 locations, split into 5,792 training and 1,448 test locations.The 126 × 80 m urban region is sampled on a 1 m grid; ground-truth beam-pair maps sum path powers rather than amplitudes.Source: A. Simulation Settings · p. 9
  • Fig. 3 depicts the simulated urban scene and a measured indoor scene, with the BS or transmitter location and UE or receiver grid indicated.The indoor transmitter is in the corridor and the receiver grid is inside the room.Source: Figure 3 · p. 10
  • Training uses a weighted loss for peak normalization, beam-pair power distribution, and the strongest entries, which carry over 90% of average map power.The weights are (0.4, 0.4, 0.2), and the strongest 1/16 of entries form the restricted error set.Source: A. Simulation Settings · p. 10
  • Accuracy is evaluated by test-location NMSE; the reported figures also plot NMSE against training-set fraction and the per-location NMSE CDF.The fraction-one setting corresponds to all 5,792 training locations.Source: A. Simulation Settings · p. 10, Figure 5 · p. 10
  • MIMO-GS is compared with Sionna ray tracing, nearest neighbor, an MLP, and a CNN decoder trained on the same data with about the same parameter count.The RF rendering methods in Table I do not produce the joint map and are not compared numerically.Source: A. Simulation Settings · p. 10

B. Rendering Accuracy and Cost

MIMO-GS reproduces diverse beam-pair map structure and outperforms the compared renderers on DeepMIMO accuracy, including against ray tracing in most test locations, while rendering faster.

B. Rendering Accuracy and Cost

  • Rendered maps reproduce dominant clusters’ positions and relative strengths, along with transmit-array sidelobe stripes, across two distinct test-location profiles.One profile spreads power across several receive beams; the other concentrates on a few beam pairs with a weaker secondary component.Source: B. Rendering Accuracy and Cost · p. 10
  • 3.2 to 5.2 dB lower NMSE than CNN across training fractions, with the largest gap at the fewest observations.MIMO-GS shares primitives across locations and derives maps through projection geometry; Fig. 5(a) plots NMSE against training fraction with the test set fixed.Source: B. Rendering Accuracy and Cost · pp. 10–11
  • MIMO-GS is more accurate than ray tracing at 74.7% of locations; beyond 60 m from the BS, the gap grows to 23 dB and MIMO-GS is more accurate at over 98%.Within 60 m, the methods are within a few decibels, where direct geometry dominates the map.Source: Figure 6 · p. 11, B. Rendering Accuracy and Cost · p. 11
  • −30.8 dB median per-location NMSE for MIMO-GS compares with −28.9 dB for CNN, −27.4 dB for MLP, −18.3 dB for nearest neighbor, and −17.5 dB for ray tracing.The CNN and MLP exceed −10 dB at 1.2% and 1.5% of locations, respectively, matching MIMO-GS at 1.2%; nearest neighbor reaches 16.7% and ray tracing 40.4%.Source: B. Rendering Accuracy and Cost · p. 11
  • 0.44 ms per location for MIMO-GS versus 2.41 ms for ray tracing, making rendering about 5.5 times faster.The comparison is for a scene of 25,000 primitives, or 50,000 Gaussians, with 557k parameters.Source: Table II · p. 11, B. Rendering Accuracy and Cost · p. 11

C. Rendering on Measured Channels

On measured indoor channels, MIMO-GS captures the beam-pair structure, while rendered maps support interference-aware beam management close to the genie-aided benchmark. The learned scene can be reused across channel realizations.

C. Rendering on Measured Channels

  • On measured indoor channels, MIMO-GS attains −12.36 dB NMSE and the highest Top-K and C4 scores, capturing rapid beam-pair shifts through projection geometry.The dataset uses 60.48 GHz channels measured at 350 locations; its 63 steering-codebook beams are not mutually orthogonal.Source: C. Rendering on Measured Channels · pp. 11–12, Table III · p. 12

D. Beam Management with the Rendered Maps

VII. CONCLUSION

  • The learned scene reproduces dominant beam-pair structure in ray-traced urban and measured indoor channels, then renders maps at any location in the scene as lightweight inference reusable across channel realizations.The beam-management scheme configures CSI-RS only on scheduled beams.Source: §VII · p. 13
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