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Model-Driven Deep Learning with Rank-One Sensing for Efficient CSI Feedback

Shunpu Tang, Qianqian Yang, Seung-Woo Ko, Jihong Park, Kaibin Huang

arXiv:2610.11558v1eess.SP

TL;DR

CSI feedback in FDD massive MIMO must fit high-dimensional channel information through a limited uplink, while conventional and learned approaches face structural or computational limitations. The paper uses rank-one low-rank-prior sensing and synthesis, augmented by residual branches in DCRNetV2. DCRNetV2 reports competitive accuracy at much lower FLOPs and adapts to a new scenario with few fine-tuning samples.

  • Problem

    Classical random sensing may mismatch the multipath structure, requires iterative BS optimization, and is not jointly designed with reconstruction error.

    Source: D. Optimization · p. 5

  • Method

    The paper combines low-rank CSI synthesis with convolutional residual refinement, including a residual decoder that generates extra rank-one components from the same codeword.

    Source: §IV · p. 6, B. Decoder Design · p. 7

  • Results

    DCRNetV2-unified achieves competitive accuracy at much lower FLOPs and, after fine-tuning, quickly approaches TransNet on the Shenzhen CBD scenario.

    Source: E. Extension to More Scenarios · p. 12

  • Takeaways & Limitations

    UE sensing rank, BS direct and residual ranks, and bottleneck size provide adjustable parameters for balancing reconstruction accuracy and computational cost.

    Source: D. Complexity Control · p. 8

    DCRNetV2’s limited parameter count may yield slightly worse out-of-distribution NMSE than large Transformers.

    Source: E. Extension to More Scenarios · p. 12

Abstract

from arXiv · show

Downlink channel state information (CSI) feedback is essential for beamforming optimization in frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. However, the feedback overhead increases with the number of antennas and subcarriers, posing a major challenge to practical deployment. Although recent deep learning (DL)-based methods reduce this overhead by compressing CSI at the user equipment (UE) and reconstructing it at the base station (BS), most of them treat CSI as a generic image and rely on convolutional or Transformer architectures. As a result, the low-rank multipath prior is insufficiently exploited, while non-negligible computation is introduced at both the UE and the BS. To address this issue, we propose a low-rank prior (LRP)-guided CSI feedback framework that performs structured sensing and reconstruction directly over rank-one channel components. Specifically, the LRP encoder conducts learnable rank-one sensing to obtain path-aware measurements at the UE, while the LRP decoder reconstructs CSI through rank-one synthesis at the BS, avoiding the iterative recovery required by classical solvers. To compensate for finite-rank approximation residuals, we extend our previous DCRNet into DCRNetV2 by incorporating the proposed LRP backbone and gated dilated-convolutional residual branches. Experiments on multiple datasets and scenarios show that the proposed methods achieve a better accuracy-complexity tradeoff than existing model-based and DL-based baselines. In particular, standalone LRP achieves more than $10$~dB NMSE improvement over model-based baselines with much lower complexity, while DCRNetV2 achieves comparable accuracy to state-of-the-art Transformer-based methods with only about one-fifth of the complexity. The source code is available at https://github.com/tangshunpu/DCRNetV2.

I. INTRODUCTION

FDD massive MIMO requires CSI feedback over a limited uplink, but the channel’s high dimensionality makes direct feedback impractical. Prior approaches trade reconstruction accuracy against computation, while existing low-rank methods do not fully co-design sensing and reconstruction around path-wise structure.

A. Background

  • FDD massive MIMO needs accurate downlink CSI for beamforming, but high-dimensional CSI makes direct feedback impractical over the limited uplink control channel.The UE must estimate and feed back CSI because downlink-uplink channel reciprocity generally does not hold in FDD systems.Source: A. Background · p. 1

1) Model-based CSI feedback:

  • Compressed-sensing methods exploit sparsity but can degrade under model mismatch and require iterative recovery whose complexity grows with antenna and subcarrier dimensions [4], [5].OMP and ISTA/FISTA are examples of iterative sparse-recovery approaches.Source: 1) Model-based CSI feedback · p. 2

2) DL-based CSI feedback:

  • CsiNet pioneered DL-based CSI feedback with a convolutional autoencoder, achieving clear gains over classical compressed sensing; some lightweight follow-up designs reduce user-side complexity but usually limit feature extraction and reconstruction performance.Source: 2) DL-based CSI feedback · p. 2

3) Model-driven DL for CSI feedback:

  • Model-driven DL incorporates channel priors, yet many approaches still use iterative BS-side reconstruction and therefore retain non-negligible computational cost,.Examples include CSI-L2O and FISTA-Net.Source: 3) Model-driven DL for CSI feedback · p. 2

4) Low-rank perspective:

  • CSI is naturally low-rank or approximately low-rank because paths contribute separable delay-angular responses, but prior methods do not fully co-design path-wise sensing and reconstruction and still use iterative BS solvers, –.Earlier low-rank approaches used the property for completion, submatrix approximation, or reconstruction-side decomposition,,,,.Source: A. Background · p. 1, 4) Low-rank perspective · p. 2

C. Contributions

The paper introduces a rank-one low-rank-prior framework for CSI feedback and extends it with DCRNetV2 residual branches. It also presents a ray-tracing benchmark and reports improved accuracy-complexity tradeoffs across experiments.

C. Contributions

  • LRP performs learnable rank-one sensing at the UE and rank-one synthesis at the BS, jointly optimizing sensing and reconstruction while avoiding iterative full-matrix recovery.Its sensing uses paired delay- and angular-domain vectors to produce path-aware measurements.Source: C. Contributions · pp. 2–3
  • DCRNetV2 adds dilated-convolutional residual branches to the LRP backbone to compensate for finite-rank errors, off-grid leakage, and local cluster residuals.The rank-one path remains the dominant representation, with encoder, factored-decoder, and refinement branches supporting lightweight-to-high-accuracy variants.Source: C. Contributions · p. 3
  • Sionna-RT-Mix5 covers five outdoor urban and campus scenes with diverse LoS and NLoS conditions, and a held-out Shenzhen CBD scenario supports out-of-distribution and limited-fine-tuning evaluation.The paper also evaluates COST 2100 and real FDD massive MIMO data.Source: C. Contributions · p. 3
  • Standalone LRP improves NMSE by more than 10 dB over model-based baselines with much lower complexity, while DCRNetV2 reaches comparable accuracy to Transformer methods at about one-fifth of their FLOPs.Experiments include COST 2100, Sionna-RT-Mix5, and real FDD massive MIMO data.Source: C. Contributions · p. 3

II. SYSTEM MODEL

  • The system model collects CSI across N_c subcarriers into H, with 2N_cN_t real-valued coefficients, then transforms and truncates it in the angular-delay domain before encoding and decoding.The codeword contains M real-valued feedback symbols, with compression ratio η = M/(2N_aN_t).Source: §II · p. 3

III. LOW-RANK PRIOR-BASED CSI COMPRESSION

The LRP framework treats CSI feedback as structured sensing and reconstruction over rank-one channel components. Its low-rank prior follows from the separable delay-angular responses of multipath channels after transformation and delay-row truncation.

III. LOW-RANK PRIOR-BASED CSI COMPRESSION

  • The LRP encoder obtains a low-dimensional measurement through rank-one sensing, and its decoder reconstructs CSI from that measurement through rank-one synthesis.The framework recasts CSI feedback as structured sensing and reconstruction over the multipath prior.Source: §III · pp. 3–4, Figure 1 · p. 4

A. Low-Rank Multipath Prior

  • Under the stated far-field geometric channel assumptions, each path remains an outer product after the 2D-DFT and delay-row truncation, so the angular-delay CSI is a sum of rank-one components.The assumptions include frequency-independent path gains, a frequency-invariant array response, and separable delay and spatial responses.Source: A. Low-Rank Multipath Prior · p. 4
  • When the number of dominant paths L is much smaller than min(N_a, N_t), the angular-delay CSI is low-rank or accurately approximated by a low-rank matrix [15],.The architecture approximates it using R rank-one components, where R is a designable model rank and need not equal L.Source: A. Low-Rank Multipath Prior · p. 4

B. Rank-One Sensing-Based CSI Compression

The LRP encoder measures angular-delay CSI with learnable rank-one patterns aligned to the multipath structure, then maps measurements to a feedback codeword. At the BS, rank-one factors are synthesized and summed into a low-rank CSI reconstruction.

B. Rank-One Sensing-Based CSI Compression

  • Rank-one sensing acts like matched filtering: each branch measures alignment between CSI and a delay-angular pattern, yielding path-aware measurements.The rank-one operator is formed from paired sensing vectors along the row and column dimensions.Source: B. Rank-One Sensing-Based CSI… · pp. 4–5
  • A lightweight learned projection maps stacked complex measurements, represented by concatenated real and imaginary parts, to the feedback codeword.The encoder embeds the low-rank prior in its measurement structure rather than relying on generic neural layers to learn it implicitly.Source: B. Rank-One Sensing-Based CSI… · p. 5

C. Low-Rank Multipath Reconstruction

  • At the BS, the decoder maps the codeword to delay- and angular-domain factors, forms rank-one outer products, and sums branches into the CSI reconstruction.The decoder generates rank-one factors instead of directly producing all complex CSI coefficients with neural-network layers.Source: C. Low-Rank Multipath Reconstruction · p. 5
  • The decoder rank R is a reconstruction hyperparameter, not the number of physical propagation paths; its branches jointly approximate dominant CSI structure.A separate scalar gain is not introduced because each component’s complex coefficient is absorbed into its factors.Source: C. Low-Rank Multipath Reconstruction · p. 5

1 UE side: rank-one sensing

The UE-side rank-one sensing procedure includes a matched-filtering coefficient computation.

1 UE side: rank-one sensing

  • The UE-side procedure computes a matched-filtering coefficient.This is listed as step 3 of the rank-one sensing process.Source: §1 · p. 5

8 Send z to the BS over the feedback link

The framework jointly trains structured sensing and reconstruction rather than using fixed random sensing with per-sample iterative recovery. The BS synthesis stage uses a linear projection to obtain rank-one factors.

9 BS side: low-rank synthesis

  • The BS-side low-rank synthesis applies a linear projection to obtain rank-one factors within the structured encoder-decoder design.The structured parameters include the rank-one sensing vectors.Source: §9 · p. 5, D. Optimization · p. 5

D. Optimization

  • Classical recovery uses fixed random sensing and nuclear-norm regularization, but may mismatch CSI structure, require iterative BS optimization, and separate sensing from reconstruction design.These issues motivate jointly optimizing sensing and reconstruction against empirical reconstruction error.Source: D. Optimization · p. 5
  • DCRNetV2’s final estimate sums direct low-rank reconstruction and factored residual reconstruction after the encoder branches are fused.The branches are decoded separately at the BS.Source: Figure 2 · p. 6
  • Mini-batch stochastic-gradient training adapts rank-one sensing vectors to practical CSI statistics and couples them to the synthesis decoder through one reconstruction objective.Measurements are thereby encouraged to preserve CSI features useful for final reconstruction rather than being designed independently of recovery.Source: D. Optimization · pp. 5–6

E. Complexity Analysis

LRP uses rank-one sensing and synthesis to limit computation, while DCRNetV2 adds parallel convolutional processing to complement global low-rank features with local channel detail.

E. Complexity Analysis

  • LRP complexity is O(Renc(NaNt + M)) at the UE and O(R[M(Na + Nt) + NaNt]) at the BS, avoiding explicit O(N_t^2) matrix reconstruction.The decoder cost includes the linear factor projection and synthesis of R rank-one outer products.Source: E. Complexity Analysis · p. 6
  • By using lightweight rank-one sensing and avoiding explicit matrix reconstruction, LRP has much lower complexity than conventional convolutional autoencoder feedback and suits resource-constrained users.The UE sensing stage consists of rank-one sensing followed by a linear projection.Source: E. Complexity Analysis · p. 6

IV. DESIGN OF DCRNETV2

  • DCRNetV2 processes angular-delay CSI with parallel LRP and convolutional branches, preserving global low-rank features while refining local correlations.The branches are fused at the encoder output and decoded separately at the BS.Source: §IV · p. 6, A. Encoder Design · p. 7

A. Encoder Design

  • The DCR encoder uses asymmetric 1 × k and k × 1 convolutions and dilated paths to capture angular and delay correlations across broader multipath clusters.It operates alongside LRP before compression because details lost during global projection cannot be recovered later from the codeword.Source: A. Encoder Design · p. 7
  • A learnable scalar gate controls the convolutional residual’s contribution to the feedback vector, while concatenation and an MLP learn interactions between branch codewords.Small initialization of the gate and fusion output keeps the initial codeword close to the LRP codeword.Source: A. Encoder Design · p. 7

B. Decoder Design

The decoder addresses fixed-rank representation bottlenecks with a lower-cost residual rank tail, then refines full-domain CSI using parallel convolutional paths.

B. Decoder Design

  • A fixed rank-R decoder can bottleneck rich-scattering channels with slowly decaying rank tails, while increasing R linearly raises decoder complexity.The direct decoder produces a rank-R estimate.Source: B. Decoder Design · p. 7
  • The residual decoder generates extra rank-one components from the same codeword at lower cost than enlarging the direct branch.Its shared factors and d-dimensional bottleneck cost O(Red + d(Na + Nt)) parameters, versus O(ReM(Na + Nt)) for expanding the direct branch.Source: B. Decoder Design · p. 7
  • Per-rank sigmoid gates weight the supplementary components, while a learnable scalar α controls their strength relative to the direct reconstruction.The gates can suppress or emphasize rank components, and the residual branch is initialized near zero.Source: B. Decoder Design · p. 7

C. DCR Refinement Module

  • After reconstruction, the DCR refinement module uses dilated and asymmetric kernels for local off-grid leakage and standard convolutions for short-range details.Its two paths are concatenated and fused with a 1 × 1 layer; a learnable scalar gate is initialized close to zero.Source: C. DCR Refinement Module · p. 8

D. Complexity Control

DCRNetV2 variants adjust UE sensing rank and BS direct rank, residual rank, and bottleneck size to balance accuracy and computational cost. The simulations compare CSI feedback methods and evaluate complexity, device latency and energy, and generalization.

D. Complexity Control

  • DCRNetV2 variants vary UE sensing rank Renc and BS direct rank R, residual rank Re, and bottleneck size d.Reducing Renc directly lowers UE encoder FLOPs; the residual rank expands effective rank without full high-dimensional projections.Source: D. Complexity Control · p. 8

V. SIMULATION RESULTS

  • The simulation section compares proposed methods with model-based and DL-based methods for reconstruction accuracy and computational cost.It also evaluates inference latency and energy on a mobile device and generalization on benchmark and real measured CSI datasets.Source: §V · pp. 8–9
  • Fig. 3 compares FLOPs and indoor NMSE for representative DL-based methods at η = 1/4 and η = 1/16.Source: Figure 3 · p. 9
  • Fig. 4 evaluates indoor quantization performance versus total feedback bits under different compression ratios, with FP32 points and dotted lines as unquantized references.Source: Figure 4 · p. 9

A. General Setup

  • The COST 2100 evaluations use indoor and outdoor scenarios at 5.3 GHz and 300 MHz, respectively, with 32 BS antennas and 1024 OFDM subcarriers.Training, validation, and test sets contain 100,000, 30,000, and 20,000 samples.Source: A. General Setup · p. 9
  • Proposed models are evaluated by FLOPs and trained for 1500 epochs using mean squared error and Adam, with batch size 200 and initial learning rate 2×10−3.Source: A. General Setup · p. 9

B. Baseline Methods

The comparisons show that LRP improves on model-based feedback methods at lower or comparable complexity, while DCRNetV2 extends the low-rank backbone with residual refinement to balance accuracy and computation.

C. Performance Comparison

  • At η = 1/4, LRP with Renc = 128 and R = 4 achieves −13.18 dB indoor NMSE with 0.68M FLOPs, versus FISTA’s −10.46 dB with 42.99M FLOPs.LRP consistently outperforms model-based methods in NMSE at the same or lower FLOPs across the reported COST 2100 comparisons.Source: C. Performance Comparison · p. 9
  • At η = 1/4, DCRNetV2-mini improves indoor NMSE from −28.04 dB to −31.00 dB versus DCRNet-1× while reducing FLOPs from 4.01M to 2.83M.DCRNetV2-unified reaches −32.84 dB indoor NMSE at η = 1/4, and the mini variant reaches nearly −20 dB at η = 1/8 with 1.87M FLOPs.Source: C. Performance Comparison · p. 9
  • At η = 1/4, DCRNetV2-large-I reaches −33.20 dB indoor NMSE with 7.00M FLOPs, outperforming TransNet’s −32.38 dB at one-fifth of the computation.DCRNetV2-large-O matches TransNet outdoors at −14.85 dB with 8.25M FLOPs; at η = 1/16, both large variants have comparable accuracy with nearly 10× fewer FLOPs.Source: C. Performance Comparison · p. 10

D. Ablation Studies

  • Adding the decoder-side DCR branch improves NMSE from −21.62 dB to −29.34 dB at 3.84M FLOPs, while adding the encoder branch without decoder residual reaches −32.00 dB.The ablation attributes the LRP backbone to dominant low-rank structure and residual branches to channel details outside that subspace.Source: D. Ablation Studies · p. 10, Table IV · p. 10
  • Adding the LRP path improves NMSE for both CsiNet and Conv5-MLP backbones across compression ratios, with gains ranging from 1.03 dB to 5.66 dB.For CsiNet the gains are 5.66 dB at η = 1/4 and 1.78 dB at η = 1/16; for Conv5-MLP they are 1.03 dB and 4.22 dB, respectively.Source: Table V · p. 10, D. Ablation Studies · p. 11

E. Extension to More Scenarios

The proposed methods are evaluated on ray-tracing scenes, an out-of-distribution Shenzhen scenario, and real measured CSI. DCRNetV2 is competitive across these settings, with its limited parameter count noted as a boundary for out-of-distribution NMSE.

E. Extension to More Scenarios

  • The Sionna-RT-Mix5 benchmark combines five outdoor scenes, while Shenzhen CBD is held out for testing; the scenes span varied LoS and NLoS propagation characteristics.The five scenes include Paris, Florence, Munich, ZJU, and SUTD.Source: E. Extension to More Scenarios · p. 11
  • DCRNetV2-unified achieves the best NMSE at η = 1/4 in all five Sionna-RT-Mix5 scenes and is competitive with TransNet in the remaining cases.The models are trained on all five scenes and evaluated on each scene’s test set.Source: E. Extension to More Scenarios · p. 11
  • On Shenzhen CBD, DCRNetV2-unified is second-best without fine-tuning, less than 1 dB worse than TransNet, and quickly approaches it after fine-tuning.The models are pretrained on Sionna-RT-Mix5 and tested on 40,000 Shenzhen samples before fine-tuning.Source: E. Extension to More Scenarios · pp. 11–12, Figure 7 · p. 12
  • On real Renew-group FDD data, DCRNetV2-unified achieves the best NMSE at every tested compression ratio and leads the second-best method by 2.11 dB at η = 1/16.At η = 1/32, it improves over DCRNet-1× by 2.87 dB with comparable FLOPs.Source: Table VII · p. 12, E. Extension to More Scenarios · p. 12

VI. CONCLUSION

  • The conclusion identifies near-field wideband channels as a limitation because angle–distance–frequency coupling may weaken the spatial–frequency separability assumed by LRP’s rank-one paths.The paper proposes frequency-dependent spherical-wave modeling and local low-rank representations over subbands and subarrays as future directions.Source: §VI · p. 12

I. RT-CSI DATASET CONFIGURATION

The RT-CSI dataset combines multiple outdoor and campus settings with a held-out Shenzhen stress case. Visualizations show how rank-one responses accumulate channel structure and how DCRNetV2 reduces localized reconstruction errors relative to LRP.

I. RT-CSI DATASET CONFIGURATION

  • The RT-CSI benchmark uses five non-Shenzhen scenes for training and evaluation, with Shenzhen Futian CBD held out as a dense high-rise test scenario.The campus scenes constrain BS placement to campus bounds; Shenzhen uses 10 BSs and a fixed test set of 40,000 UE-BS channel samples.Source: §I · p. 14

II. VISUALIZATIONS

  • The full LRP reconstruction preserves main delay-domain energy concentrations and angular distribution, while selected rank-one responses exhibit distinct delay–angular patterns.The responses are interpreted as measuring alignment between the channel and learnable separable patterns.Source: §II · p. 14, Figure 8 · p. 15
  • Across four samples, sums of more LRP responses recover additional energy concentrations and weaker details; the top 64 and 128 responses better reproduce the first sample’s main horizontal delay-domain clusters than the top 4 and 16.The responses contribute complementary channel information.Source: §II · pp. 14–15, Figure 9 · p. 16
  • DCRNetV2 reduces localized errors remaining in LRP reconstructions, including small-delay errors in sample (a) and middle-delay errors in sample (b).Residual errors remain visible for both methods as η decreases.Source: §II · p. 15, Figure 10 · p. 17
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