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Prior-Aided Masked Vector Quantization CSI Feedback for FDD Massive MIMO Systems

Yi Song, Tianyu Yang, Kangda Zhi, Shuangyang Li, Fangzhou Wu, Songyan Xue, Giuseppe Caire

arXiv:2609.17769v1cs.ITmath.IT

TL;DR

FDD massive MIMO requires the UE to feed back downlink CSI over a limited uplink budget, making accurate reconstruction a compression challenge. PM-VQ uses the average angle–delay power map to select and quantize latent tokens, with one model supporting multiple feedback dimensions. In the evaluated diffuse regime, it achieves the lowest NMSE across tested SNR levels and feedback dimensions.

Abstract

from arXiv · show

Downlink channel state information (CSI) feedback is a key bottleneck in frequency-division duplex (FDD) massive MIMO systems, as the user equipment (UE) must convey its estimated channel to the base station (BS) over a limited uplink (UL) budget. To improve CSI reconstruction accuracy under tight feedback constraints, we propose prior-aided masked vector quantization (PM-VQ), a learning-based separate source--channel coding (SSCC) feedback scheme conditioned on the average angle--delay power map---a compact representation of the channel second-order statistics available at both the UE and the BS. In PM-VQ, a prior-aided encoder maps the CSI to latent tokens, and a spatially-adaptive masking module (SAMM) scores and selects the most informative tokens within the feedback budget. The selected tokens are vector-quantized and fed back together with their positions, while an adaptive de-masking module (ADM) completes the latent representation at the BS before prior-conditioned decoding. To support variable-rate compression, a single model is trained over a range of selected-token counts, enabling operation across multiple feedback dimensions without retraining. We evaluate PM-VQ against three representative baselines on a Sionna-generated 3GPP TR~38.901 UMa dataset, focusing on the most challenging diffuse regime where channel energy is spread across many angle--delay coefficients. Simulation results show that PM-VQ achieves the lowest NMSE across all tested SNR levels and feedback dimensions in this regime. Moreover, the angle--delay power-map prior remains beneficial even when estimated from only a few channel realizations.

I. INTRODUCTION

The paper addresses one-shot FDD CSI compression under a limited uplink budget, where feedback overhead trades off against reconstruction accuracy. It motivates a practical source encoder that uses channel statistics and adapts which latent components receive the budget.

I. INTRODUCTION

  • FDD CSI feedback must balance uplink overhead against reconstruction accuracy, because the BS cannot infer the downlink channel through reciprocity.The UE estimates and compresses CSI for feedback over the uplink.Source: §I · p. 1

A. Uplink Feedback Strategies

  • SSCC fits digital feedback links and separates source coding from channel coding, while practical SSCC can suffer decoding cliffs and added latency.JSCC avoids an explicit bit interface and often degrades more gracefully with uplink SNR, but its mappings are difficult to design.Source: A. Uplink Feedback Strategies · pp. 1–2

B. Related Work

  • Remote rate–distortion theory offers structural guidance, but its asymptotic block-coding assumptions do not directly specify a practical one-shot CSI encoder.The paper frames the open question as designing a trainable variable-rate encoder that exploits channel statistics on realistic data.Source: B. Related Work · pp. 2–3
  • Prior learning-based schemes often neither prioritize informative latent components nor exploit channel statistics, and many require fixed rates or use narrow channel-profile evaluations.Existing variable-rate methods typically use feature orderings fixed across channel realizations.Source: B. Related Work · p. 3

C. Contributions

The paper proposes PM-VQ, which uses channel statistics to condition compression and reconstruction and selectively transmits latent tokens. Its system model assumes known downlink CSI at the UE and represents the channel in the angle–delay domain.

C. Contributions

  • PM-VQ uses the average angle–delay power map to guide non-uniform latent-token selection, while conditioning the encoder, token scoring, and decoder on that prior.SAMM selects informative tokens and ADM completes missing latent positions at the BS.Source: C. Contributions · p. 3
  • A single trained model supports multiple feedback dimensions by varying the number of transmitted tokens, with selection adapted to each CSI sample.The evaluation uses a geometrically diverse Sionna-generated 3GPP TR 38.901 UMa dataset and focuses on diffuse channels; PM-VQ has the best NMSE across tested SNRs and feedback dimensions there.Source: C. Contributions · p. 3

II. SYSTEM MODEL

  • The system model assumes the UE has acquired its downlink channel perfectly and studies one-shot CSI compression under a limited uplink feedback budget.This isolates feedback from pilot design and channel estimation.Source: §II · p. 4

A. Angle–Delay CSI Representation

  • The angle–delay representation applies unitary DFTs to map frequencies to delays and BS antennas to angles, exposing sparse structure while preserving channel energy.The channel tensor stacks the angle–delay CSI across UE antennas.Source: A. Angle–Delay CSI Representation · p. 4

B. Prior Information: Average Angle–Delay Power Map

The average angle–delay power map approximates channel second-order statistics and is available at both UE and BS from historical CSI buffers. PM-VQ uses this prior across its encoder, token selection, and decoder to support selective feedback.

B. Prior Information: Average Angle–Delay Power Map

  • The average angle–delay power map approximates the channel’s dominant second-order structure without requiring the full covariance matrix.The angle–delay DFT approximately decorrelates coefficients in sparse multipath channels, making per-coefficient power informative.Source: B. Prior Information: Average… · p. 4
  • Averaging independent small-scale realizations estimates the slowly varying angle–delay power spectrum, and UE and BS can compute it locally from historical CSI buffers.The paper assumes the resulting estimates are consistent because the buffers reflect correlated realizations sharing large-scale statistics.Source: B. Prior Information: Average… · p. 4

III. PROPOSED PRIOR-AIDED MASKED VECTOR QUANTIZATION CSI FEEDBACK SCHEME

  • PM-VQ addresses fixed-rate, data-only compression by using one trained model across feedback dimensions, scoring tokens, and incorporating a prior assumed available at both ends.The prior is injected at multiple points in the encoder, SAMM, and decoder.Source: §III · p. 5
  • The pipeline conditions the encoder, token scoring, and decoder on the prior, then selects, scales, and vector-quantizes tokens for feedback with their positions.At the BS, ADM completes masked latent positions from received codewords before prior-conditioned CSI reconstruction.Source: §III · p. 5

A. Asymmetric Prior-Aided U-Net Backbone

The asymmetric prior-aided U-Net uses multi-scale processing to capture global channel structure and recover local detail without sending UE-side intermediate features. The input representation keeps instantaneous CSI distinct from the slowly varying prior.

A. Asymmetric Prior-Aided U-Net Backbone

  • A U-Net-like backbone captures global channel structure at its bottleneck and restores fine angle–delay detail through multi-scale decoding.The design is motivated by localized channel clusters and a power map that indicates likely path locations.Source: A. Asymmetric Prior-Aided U-Net Backbone · p. 6
  • The BS replaces unavailable encoder skip features with multi-scale features extracted from the prior, conveying structural information without additional feedback.The UE transmits no intermediate features.Source: A. Asymmetric Prior-Aided U-Net Backbone · p. 6

B. Input Representation

  • The input X stacks the real and imaginary parts of instantaneous angle–delay CSI, while the aligned power map represents slowly varying second-order geometry.The channel and prior are reshaped to the same layout.Source: B. Input Representation · p. 6

C. Prior-Aided Encoder with Gated Fusion

The encoder fuses CSI features with a gated angle–delay prior, then prior-aware masking selects latent tokens and score-scaled vector quantization makes selection trainable end-to-end.

C. Prior-Aided Encoder with Gated Fusion

  • Gated fusion combines CSI features with a resized angle–delay prior at every encoder resolution, letting each stage control prior strength without overwhelming instantaneous CSI.Identity and normalized feature terms preserve amplitude information and stabilize activations.Source: C. Prior-Aided Encoder with Gated Fusion · p. 6

D. Spatially-Adaptive Masking Module

  • SAMM uses prior-conditioned scores to keep the k most informative latent tokens, allocating each realization’s feedback budget content-adaptively.SPADE modulates feature statistics according to dominant angle–delay clusters.Source: D. Spatially-Adaptive Masking Module · p. 6

E. Score-Scaled Vector Quantization

  • Score-scaling selected, LayerNorm-normalized tokens puts SAMM scores on the forward path, allowing reconstruction loss to train token selection end-to-end.The straight-through estimator passes gradients through the non-differentiable codeword assignment.Source: E. Score-Scaled Vector Quantization · p. 7

F. Feedback Budget and Number of Kept Tokens

The feedback budget determines how many latent tokens can be retained, accounting for both codeword indices and the positions needed to identify selected tokens.

F. Feedback Budget and Number of Kept Tokens

  • The modeled source-coding cost includes k log2 J bits for codeword indices and an upper-bounded positional cost for selecting k of K tokens.The positional-cost bound ensures the budget constraint is respected.Source: F. Feedback Budget and Number of Kept… · p. 7
  • The UE retains the largest admissible token count under the reliable feedback-bit budget, using the modeled source-coding cost.The admissible count is determined by the budget constraint.Source: F. Feedback Budget and Number of Kept… · p. 7
  • Because both UE and BS know the budget and codebook parameters, they determine k identically, allowing one trained model to support multiple feedback budgets without retraining.The number of retained tokens varies directly with the feedback resource.Source: F. Feedback Budget and Number of Kept… · p. 7

G. Adaptive De-Masking Module

ADM reconstructs the complete latent grid from received quantized tokens, using a baseline path and learned corrections while progressively trusting inferred positions.

G. Adaptive De-Masking Module

  • ADM restores the full latent grid by placing received codewords at their positions and filling missing positions with a shared learnable mask token.A dimension-preserving baseline projection gives received codewords a direct path to the output.Source: G. Adaptive De-Masking Module · p. 7
  • Progressive reliability weighting makes received tokens dominate early completion, then gradually admits inferred positions as layers refine the grid.Missing-position reliability begins near zero and increases toward one across layers.Source: G. Adaptive De-Masking Module · p. 8
  • ADM adds learned corrections with separate strengths for received and missing positions, applying stronger correction to positions that must be inferred.The baseline-plus-correction design preserves received information rather than reconstructing it from scratch.Source: G. Adaptive De-Masking Module · pp. 7–8

H. Prior-Conditioned Decoder

The BS decodes the completed latent into the angle–delay image using a prior-conditioned expanding path, with shared-prior features replacing unavailable UE-side skips.

H. Prior-Conditioned Decoder

  • The decoder maps the completed latent to the angle–delay image through a U-Net expanding path with a bottleneck multi-head self-attention block.Prior-conditioned upsampling blocks restore the original resolution.Source: H. Prior-Conditioned Decoder · p. 8
  • Multi-scale features from a BS-side prior encoder replace encoder skip connections because UE-side intermediate features cannot reach the BS without extra feedback overhead.The prior skip features carry high-resolution structure about likely angle–delay support.Source: H. Prior-Conditioned Decoder · p. 8
  • Each upsampling block merges prior skip features with decoder state and uses SPADE-modulated convolutions, conditioning reconstruction on information available at the BS.The decoder uses the same prior as the encoder and SAMM.Source: H. Prior-Conditioned Decoder · p. 8

I. Training Objective

The modules are trained jointly with a four-term objective that balances CSI reconstruction, vector-quantization commitment, latent completion, and code usage. Training also weights missing latent positions more heavily and encourages broad codebook use.

I. Training Objective

  • Joint end-to-end training uses reconstruction, VQ commitment, ADM latent-completion, and code-usage regularization losses.The objective combines all four terms in a single training objective.Source: §I · p. 9
  • The reconstruction loss is normalized MSE between reconstructed and ground-truth angle–delay images.Source: §I · p. 9
  • Exponential-moving-average updates of codewords replace the usual codebook loss and stabilize the codebook during training.The commitment loss pulls each selected token toward its assigned codeword.Source: §I · p. 9
  • ADM is supervised by comparing recovered and encoder latents, with greater weight assigned to masked positions than received positions.This lets ADM preserve received tokens while focusing effort on missing positions.Source: §I · p. 9
  • A soft-assignment KL penalty against uniform codeword usage maximizes usage entropy and helps prevent codebook collapse.The assignments approximate token-to-codeword probabilities and are averaged over the batch to estimate usage.Source: §I · p. 9

IV. DATASET GENERATION

The study uses a Sionna-generated 3GPP UMa dataset and compares learned and training-free feedback baselines under matched feedback budgets. The learned JSCC and SSCC baselines use TransNet, but differ in what they transmit and how their models are trained.

IV. DATASET GENERATION

  • The dataset uses Sionna’s 3GPP TR 38.901 UMa NLoS model, with fixed topology and ray geometry but independently resampled phases across realizations.It contains 150,000 training samples from 7,500 locations and 15,000 test samples from 750 disjoint locations, with 20 phase realizations per location.Source: §IV · p. 10

V. BASELINE METHODS

  • The comparison includes JSCC, SSCC, and training-free compressed sensing at matched uplink feedback dimension and SNR; both learned baselines use TransNet.TransNet uses self-attention to capture long-range angle–delay dependencies.Source: §V · p. 10

A. Transformer-Based JSCC Baseline

  • The JSCC baseline maps the angle–delay channel directly to analog uplink symbols and requires a separate model for each feedback dimension and SNR.Its transformer encoder and decoder are trained jointly to minimize channel NMSE.Source: A. Transformer-Based JSCC Baseline · p. 10

B. Transformer-Based SSCC Baseline

  • The SSCC baseline scalar-quantizes a latent bitstream, trading coefficient resolution against the number of coefficients within the fixed bit budget.The experiments use a 2-bit scalar quantizer.Source: B. Transformer-Based SSCC Baseline · p. 10

C. Orthogonal Matching Pursuit under Random Projection

In the diffuse-channel evaluation, PM-VQ leads the baselines across the tested SNRs and feedback dimensions. The study also describes OMP’s random-projection recovery and the mechanisms that shape performance as the feedback budget changes.

C. Orthogonal Matching Pursuit under Random Projection

  • OMP compresses real and imaginary channel components through random measurements, then greedily recovers the channel under a sparsity constraint.Its sparsity level is set from empirical channel energy concentration; it requires neither training nor channel statistics.Source: C. Orthogonal Matching Pursuit under… · p. 11

VI. SIMULATION RESULTS

  • The evaluation uses a diffuse-channel test quartile, with PM-VQ trained across selected-token counts so one model supports multiple feedback budgets.JSCC and SSCC are trained separately for each target feedback dimension and SNR.Source: §VI · p. 11

A. NMSE versus UL SNR at a Fixed Feedback Dimension

  • Across the tested SNRs, PM-VQ achieves the lowest NMSE; its reconstructions preserve more multi-cluster structure and align clusters better than the no-prior variant.At low SNR, the prior helps when few tokens can be transmitted.Source: A. NMSE versus UL SNR at a Fixed… · p. 12, Figure 2 · p. 12
  • At fixed feedback dimension, SSCC can use higher SNR for more bits while JSCC’s fixed representation can saturate; PM-VQ adds adaptive token selection and prior conditioning.The prior is especially valuable when few tokens can be sent, while the no-prior variant can surpass learned baselines once more tokens fit the budget.Source: A. NMSE versus UL SNR at a Fixed… · p. 12

B. NMSE versus Feedback Dimension at a Fixed UL SNR

C. Ablation Study of Prior Side Information

The ablations identify decoder-skip conditioning as the largest source of prior gain, while showing that learned token selection outperforms energy-based and random alternatives, especially at intermediate feedback dimensions.

C. Ablation Study of Prior Side Information

  • Removing decoder-skip conditioning eliminates most reconstruction gain; encoder conditioning matters next, decoder-pyramid conditioning adds a smaller consistent gain, and SAMM prior input changes performance little.The ablation suggests encoder conditioning already embeds enough statistical information for SAMM to rank tokens effectively.Source: C. Ablation Study of Prior Side… · pp. 13–14, Figure 4 · p. 14
  • Retrained models preserve the same ordering: full PM-VQ has the lowest NMSE, no-prior performs worst, and decoder-skip-only recovers most of the full-prior gain.Other prior paths provide smaller but consistent improvement.Source: Figure 4 · p. 14, C. Ablation Study of Prior Side… · p. 14
  • A rough power-map estimate restores most lost performance, while modest averaging approaches a well-estimated prior; complete prior absence causes a performance loss.The results indicate that coarse angle–delay support matters most, with more accurate averaging primarily refining power values.Source: C. Ablation Study of Prior Side… · p. 14, Figure 4 · p. 14

VII. CONCLUSION

  • PM-VQ outperforms the baselines across all tested UL SNRs and feedback dimensions in the diffuse regime.The conclusion attributes most prior gain to decoder-skip conditioning and reports that coarse power-map estimates retain most of the benefit.Source: §VII · p. 14

D. Ablation Study of the Token Selection Mechanism

  • SAMM performs best across the feedback range; latent-energy selection approaches it at very low or high dimensions but falls behind most at intermediate dimensions, while random masking performs substantially worse throughout.The comparison indicates that token identities, not only their number, matter for reconstruction.Source: D. Ablation Study of the Token… · p. 14, Figure 5 · p. 15
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