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Structured Time-Frequency Representation for Channel Prediction

Ning Yang, Yuming Xian, Tong Li, Ning Gao, Haijun Zhang

arXiv:2610.35956v1cs.ITcs.AImath.IT

TL;DR

FDD channel forecasting must infer future downlink CSI from historical uplink observations while handling both elapsed time and band separation, which input and target definitions alone do not position explicitly. FAR-CSI uses a joint time-band field and consistent routing for encoding, reconstruction, and target selection. Under matched conditions, routing reduces NMSE by 21.44% relative to generic routing, and FAR-CSI leads evaluated FDD baselines in accuracy and MRT-based spectral efficiency.

  • Problem

    FDD forecasting requires temporal extrapolation and cross-band inference, while specifying historical UL input and future DL target alone does not define their positional organization.

    Source: A. Model-Based Channel Prediction · p. 2, B. FDD Channel Forecasting · p. 4

  • Method

    FAR-CSI uses a joint time-band positional field and one structured routing rule for encoder assignment, decoder reconstruction, and future-DL target readout.

    Source: §I · p. 2

  • Results

    FAR-CSI achieves the lowest NMSE and highest MRT-based spectral efficiency among evaluated FDD baselines, maintaining its accuracy advantage across tested conditions.

    Source: §I · p. 2

  • Takeaways & Limitations

    Under matched backbone and training conditions, FDD-aware routing reduces NMSE by 21.44% relative to generic routing.

    Source: §VI · p. 10

Abstract

from arXiv · show

Accurate CSI forecasting is essential for mitigating channel aging and supporting reliable downlink transmission in high-mobility wireless systems. In FDD systems, forecasting future DL CSI from historical UL observations requires joint temporal extrapolation and cross-band inference. However, defining historical UL as the input and future DL as the target does not specify how elapsed time and UL-to-DL band separation should be represented in a pretrained predictor's positional space. FAR-CSI establishes an FDD-aware representation of channel forecasting within a joint temporal and operating-band positional field. Within this field, historical UL observations and future DL targets occupy segregated regions according to their temporal and operating-band roles, preserving the distinction between observed UL context and unobserved DL prediction targets. This representation is instantiated through a unified structured routing rule that governs encoder positional assignment, decoder-field reconstruction, and future-DL target selection, ensuring the same FDD geometry is preserved from contextual encoding to prediction readout. Under matched backbone, initialization, and training conditions, FDD-aware routing reduces NMSE by 21.44\% relative to generic routing. Across the evaluated FDD baselines, FAR-CSI achieves higher CSI prediction accuracy and MRT-based spectral efficiency, while retaining its predictive advantage across mobility conditions, prediction horizons, reduced training-data regimes, and noisy historical observations.

I. INTRODUCTION

FDD forecasting must combine temporal extrapolation with cross-band inference, yet input and target definitions alone leave their positional organization unspecified. FAR-CSI supplies a consistent time-band representation and routing rule; matched experiments report improved prediction performance across evaluated FDD baselines and conditions.

I. INTRODUCTION

  • FDD prediction couples channel evolution beyond the observed interval with cross-band inference because UL and DL occupy different frequency bands.Historical UL CSI provides partial information about the unknown DL response, while conventional DL training and feedback add overhead and delay.Source: §I · p. 1
  • Input and target definitions specify available historical CSI and required future CSI but leave their positional organization to the predictor.For pretrained patch-based reconstruction predictors, positional indices select embeddings and reconstruction locations, so FDD adaptation requires explicit assignments.Source: §I · p. 1
  • Reserving positions for historical DL and future UL preserves the full time-band grid without adding measurements or supervised targets.Consecutive indexing can preserve sequence order without preserving the designated addresses of historical UL observations and future DL targets.Source: §I · p. 2
  • FAR-CSI applies one FDD-aware routing assignment to encoder positions, masked decoder construction, and future-DL target readout using a pretrained CSI Transformer initialized from HeterCSI.The representation organizes observations, targets, and unavailable regions within a joint temporal and operating-band field.Source: §I · p. 2
  • FAR-CSI achieves the lowest NMSE and highest MRT-based spectral efficiency among evaluated FDD baselines, with accuracy advantages across tested conditions.Matched routing experiments establish a predictive benefit for the complete FDD-aware configuration.Source: §I · p. 2

A. Model-Based Channel Prediction

  • Model-based predictors use channel dynamics or propagation parameters, while neural and FDD-oriented methods learn temporal or cross-band relationships.Model-based accuracy depends on dynamics or propagation-component recovery; neural predictors and newer operators address temporal modeling, cross-band mapping, efficiency, and adaptability, but do not necessarily explicitly assign unavailable time-band regions.Source: A. Model-Based Channel Prediction · p. 2, B. Task-Specific Neural Prediction · pp. 2–3

B. Task-Specific Neural Prediction

  • Limited labeled FDD pairs and noisy historical observations make predictive information less reliable, motivating pretrained channel knowledge alongside explicit time-band role preservation.The task-specific neural methods include UL-to-DL mapping and joint historical-UL-to-future-DL prediction [12],.Source: B. Task-Specific Neural Prediction · p. 3

C. Pretrained Representation Learning

Pretrained CSI representations provide reusable channel knowledge, but do not alone specify how historical UL observations and future DL targets occupy a forecasting field. FAR-CSI addresses that organization for the joint time-band task.

C. Pretrained Representation Learning

  • Pretrained channel representations support reconstruction and temporal, frequency, or spatial modeling, but forecasting still must connect them to available observations and prediction targets.Masked autoencoding reconstructs missing content from visible observations; related approaches include CSI-MAE, LWM, LWM-Temporal, BERT4MIMO, and wireless foundation models –.Source: C. Pretrained Representation Learning · p. 3
  • LLM4CP adapts a GPT-2 backbone for historical-UL-to-future-DL prediction, but its input-to-output mapping does not use a common time-band reconstruction field with consistent observation and target addresses.Its channel-specific modules bridge CSI structure and a language-pretrained backbone, while native sequence positions do not specify the full historical/future and UL/DL arrangement.Source: C. Pretrained Representation Learning · p. 3
  • WiFo and HeterCSI learn directly from CSI, including heterogeneous channel dimensions, but broad CSI input support does not itself assign positions to a fixed FDD task,.HeterCSI uses three-dimensional time-frequency-antenna patches, scale-aware batching, and double masking.Source: C. Pretrained Representation Learning · p. 3

A. FDD Channel Representation

B. FDD Channel Forecasting

Historical-UL-to-future-DL forecasting is a mapping from observed UL CSI to predicted future DL CSI, combining temporal extrapolation and cross-band inference. Its objective minimizes normalized reconstruction error over future-DL channel tensors.

B. FDD Channel Forecasting

  • Historical-UL-to-future-DL forecasting combines temporal extrapolation with cross-band inference across distinct operating frequencies.The predictor maps historical UL CSI to predicted future DL CSI.Source: B. FDD Channel Forecasting · p. 4
  • The forecasting problem is to fit predictor parameters so temporal evolution and the relationship between UL and DL channels are recovered from historical UL observations.Temporal dependence concerns channel evolution beyond the observation interval; cross-band dependence relates responses at distinct operating frequencies.Source: B. FDD Channel Forecasting · p. 4

C. Forecasting Objective

  • The objective minimizes normalized reconstruction error over paired samples of future-DL channel tensors.The ratio-of-sums error normalizes accumulated complex-valued reconstruction error by target-channel energy, yielding an energy-weighted measure.Source: C. Forecasting Objective · p. 4
  • NMSE reports the same criterion on an evaluation set, and lower NMSE means closer reproduction of the complex-valued future DL channel.The criterion evaluates prediction against the future-DL target tensors.Source: C. Forecasting Objective · p. 4

IV. FAR-CSI

FAR-CSI organizes historical UL observations and future DL targets in a joint time-band field, retaining positions for unavailable regions. Its framework routes patch representations through encoding and reconstruction to future-DL readout.

A. Framework Overview

  • The joint time-band field distinguishes historical from future time and UL from DL; historical UL is observed, future DL is the target, and the other regions retain positions without measurements.The routing assignment governs encoder positional embeddings, decoder placement of contextualized observations, and prediction readout.Source: A. Framework Overview · p. 4

B. CSI Patch Representation

  • Normalization uses only observed UL history and retains scale factors to restore predictions to the original amplitude domain.The observed history is partitioned into non-overlapping patches across time, frequency, and antenna dimensions, subject to divisibility assumptions on patch sizes.Source: B. CSI Patch Representation · pp. 4–5

A. Framework Overview

  • The framework normalizes historical UL CSI, divides it into local time-frequency-antenna patches, routes observations and unobserved locations into a shared field, and selects future-DL reconstruction outputs.Selected outputs are unpatched and restored to the physical CSI amplitude scale.Source: A. Framework Overview · p. 4, Figure 1 · p. 5

B. CSI Patch Representation

  • Patch embeddings represent observed CSI content, while the routing rule assigns each token its position in the complete FDD forecasting field.The shared assignment determines encoder positions, decoder-input arrangement, and target readout.Source: B. CSI Patch Representation · p. 5

C. FDD-Aware Structured Routing

FAR-CSI uses a joint time-band field to represent historical UL observations and future DL targets alongside the two unobserved regions. The field preserves their distinct temporal and operating-band roles.

C. FDD-Aware Structured Routing

  • The field represents the historical-UL-to-future-DL forecast on a two-by-two time-band grid, including historical DL and future UL regions that are neither observations nor targets.These unobserved regions retain addresses in the shared field.Source: 1) Joint Time-Band Forecasting Field · p. 5
  • The unobserved regions preserve the complete time-band layout without supplying channel measurements or direct prediction targets.Source: 1) Joint Time-Band Forecasting Field · p. 5
  • Only historical-UL positions contain observations; the decoder mask-initializes other positions, and future-DL positions are the prediction targets.Source: 1) Joint Time-Band Forecasting Field · p. 5

2) Observation and Target Assignment:

Observation and target patches receive distinct addresses in the shared time-band field rather than consecutive sequence positions. Remaining positions preserve the field while staying masked and outside the loss.

2) Observation and Target Assignment:

  • Global time-band addresses depend on each patch’s temporal and frequency coordinates, preserving distinct offsets rather than its order among observed tokens.The assigned addresses determine which pretrained positional embeddings the encoder uses and where the decoder places observations and targets.Source: 2) Observation and Target Assignment · p. 6
  • The observation and target address sets are disjoint, while consecutive sequence positions do not generally preserve their designated locations in the field.Source: 2) Observation and Target Assignment · p. 6
  • Non-observation positions are mask-initialized, but loss is applied only to target positions; auxiliary positions preserve layout without adding observations or targets.Source: 2) Observation and Target Assignment · p. 6

3) Consistent Routing Across Prediction:

FAR-CSI carries the same time-band routing from encoder positional assignment through decoder reconstruction to future-DL readout. Contextualized observed tokens are placed in their assigned decoder positions, and reconstructed target patches form the forecast.

3) Consistent Routing Across Prediction:

D. Structured Contextual Reconstruction

  • Encoder-contextualized tokens are projected into decoder space and placed at their observation addresses; other field locations receive mask tokens and decoder positional embeddings.The complete field includes both future-DL targets and remaining masked positions.Source: D. Structured Contextual Reconstruction · p. 6
  • The prediction head converts decoder outputs at target positions into complex patches, which are assembled as normalized future-DL CSI and restored to the observed-history scale.Source: D. Structured Contextual Reconstruction · p. 6

E. Training Objective

FAR-CSI fine-tunes a pretrained HeterCSI checkpoint for FDD forecasting, using physical-domain ratio-of-sums loss on future-DL targets. The evaluation uses a specified channel-prediction benchmark and fixed training, validation, and test splits.

E. Training Objective

  • Training fine-tunes a pretrained HeterCSI checkpoint and optimizes physical-domain ratio-of-sums loss on future-DL targets after restoring reconstructed CSI to its original amplitude scale.Other masked locations contribute to the decoder field but receive no direct reconstruction supervision.Source: E. Training Objective · pp. 6–7

1) Dataset:

  • The benchmark uses QuaDRiGa-generated 3GPP urban-macro NLOS channels, with 16 historical UL snapshots used to predict four future snapshots.The primary task predicts future DL CSI; the complementary TDD evaluation predicts future UL CSI from historical UL CSI.Source: 1) Dataset · p. 7
  • The 9,000 development samples are split into 8,100 training and 900 validation samples, while the test set has 10,000 samples across ten velocities from 10 to 100 km/h.Validation and test identities remain fixed across evaluations; reduced-data experiments use subsets of the original training split.Source: 1) Dataset · p. 7

2) Model and Training Settings:

The evaluation fine-tunes a pretrained CSI Transformer for FDD forecasting, compares it with FDD and TDD baselines, and assesses prediction accuracy and communication utility under clean and noisy inputs.

2) Model and Training Settings:

  • FAR-CSI fine-tunes the pretrained HeterCSI CSI Transformer for FDD forecasting using an eight-block encoder and four-block decoder.All model parameters are fine-tuned; training runs for 30 epochs, with the lowest-validation-NMSE checkpoint selected from each of three independent runs.Source: 2) Model and Training Settings · p. 7

3) Baselines:

  • FDD comparisons include conventional neural predictors, LLM4CP, WiFo, and FAR-CSI; TDD comparisons also include PAD3 and a Generic CSI Transformer.The reimplemented Transformer is trained from scratch, while several other baselines use released task checkpoints or pretrained weights.Source: 3) Baselines · p. 7

4) Evaluation Protocol:

  • Evaluation measures physical-domain ratio-of-sums NMSE and MRT-based spectral efficiency at a communication SNR of 10 dB.Reduced-data tests use nested 5%, 10%, 25%, 50%, and 100% training subsets; noisy-input tests add circular complex Gaussian noise only to historical CSI, from 0 to 25 dB.Source: 4) Evaluation Protocol · pp. 7–8

B. Overall Prediction Performance

FAR-CSI outperforms evaluated FDD predictors on clean-input accuracy and MRT-based spectral efficiency. Matched routing controls and evaluations across mobility and forecast horizons show that its advantage persists across the tested conditions.

B. Overall Prediction Performance

  • FAR-CSI achieves the lowest FDD NMSE and highest MRT-based SE; it reduces NMSE by 60.6% versus LLM4CP and 67.6% versus the reimplemented Transformer.The higher MRT-based SE indicates improved beamforming performance alongside the reduction in CSI prediction error.Source: B. Overall Prediction Performance · p. 8

C. Effect of FDD-Aware Structured Routing

D. Performance Across Mobility and Forecast Horizons

E. Data Efficiency

FAR-CSI retains its FDD prediction advantage across reduced training data and noisy historical inputs. Its conclusion reports lower NMSE than generic routing and stronger overall accuracy and MRT-based utility across evaluated FDD baselines and conditions.

E. Data Efficiency

  • At every evaluated training fraction, FAR-CSI has lower NMSE than the reimplemented Transformer; with 5% of downstream data, it also beats both full-data references.LLM4CP is shown only as a separate full-data reference.Source: E. Data Efficiency · p. 9, Figure 6 · p. 10

F. Robustness to Noisy Historical CSI

VI. CONCLUSION

  • A 21.44% mean paired NMSE reduction over generic routing accompanies FAR-CSI’s strongest overall accuracy and MRT-based communication utility across evaluated FDD baselines.The conclusion says the advantage persists across mobility levels, forecast horizons, reduced-data regimes, and noisy historical observations.Source: §VI · pp. 9–10

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