WiFo-CF: Wireless Foundation CSI Feedback

• The paper introduces WiFo-CF, a paradigm-shifting model for CSI feedback that replaces fixed deep learning pipelines with one pretrained solution for heterogeneous configurations.
• It employs a Mixture of Shared and Routed Expert (S-R MoE) architecture with multi-user, multi-rate self-supervision to enhance both in-distribution and zero-shot out-of-distribution performance.
• Empirical results show WiFo-CF achieving superior NMSE performance (around -4.9 dB in-distribution) and effective support for variable bit rates, enabling improved spectral efficiency.

WiFo-CF is a wireless foundation model for channel state information (CSI) feedback that is designed to replace fixed-configuration deep learning pipelines with a single pretrained model accommodating heterogeneous channel dimensions, feedback rates, and data distributions. Its defining elements are a multi-user, multi-rate self-supervised pre-training strategy, a Mixture of Shared and Routed Expert (S-R MoE) architecture, and large-scale pretraining on the heterogeneous LH-CDF dataset. In the reported evaluations, WiFo-CF achieves the best average in-distribution normalized mean-squared error (NMSE), strong zero-shot out-of-distribution performance across simulated and real-world scenarios, and transferable representations for downstream CSI-based indoor localization (Xuanyu et al., 6 Aug 2025).

1. Problem formulation and signal model

WiFo-CF addresses three recurrent limitations of earlier deep learning CSI feedback systems: fixed input shape, limited generalization, and rigid feedback rate. Earlier encoder–decoder designs are described as being tied to a particular CSI tensor size, typically trained for a single antenna geometry, one OFDM grid, one compression ratio, and one data distribution. WiFo-CF is explicitly formulated to handle heterogeneity along channel dimensions, feedback rates, and data distributions within one framework (Xuanyu et al., 6 Aug 2025).

The system model is an FDD MU-MISO OFDM link in which a base station with $N_t$ antennas serves $K$ single-antenna users over $N_c$ subcarriers with spacing $\Delta f$. On subcarrier $n$, the transmit signal is

$x_n = V_n s_n,$

and the received signal for user $k$ is

$$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$

with $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$. For illustration, the paper gives zero-forcing precoding

$V_n = \gamma H_n^H (H_n H_n^H)^{-1},$

while emphasizing that precoder details are orthogonal to the CSI feedback problem itself (Xuanyu et al., 6 Aug 2025).

Each user estimates a complex CSI matrix $K$0, which WiFo-CF converts into a real-valued two-channel tensor $K$1 containing real and imaginary parts. The encoder compresses CSI into a latent vector

$K$2

followed by non-uniform $K$3-law quantization,

$K$4

and $K$5-bit uniform quantization over $K$6, giving a bit budget

$K$7

The decoder reconstructs multi-user CSI jointly from the dequantized latents:

$K$8

Two rate-related quantities are central. The compression ratio is

$K$9

and the effective spectral efficiency is defined as

$N_c$0

thereby incorporating feedback latency through uplink rate $N_c$1, bandwidth $N_c$2, and coherence time $N_c$3. Reconstruction quality is measured by

$N_c$4

reported in dB as $N_c$5 (Xuanyu et al., 6 Aug 2025).

2. Architecture and representation learning mechanism

WiFo-CF uses a multi-user scalable autoencoder (MUAE). The user equipment side employs identical encoders, while the base station hosts a single high-capacity decoder that jointly reconstructs multi-user CSI and exploits inter-user correlations. This asymmetric allocation matches the deployment assumption that user equipment is resource-constrained and the base station is compute-rich (Xuanyu et al., 6 Aug 2025).

CSI embedding begins with a non-overlapping 2D convolution on $N_c$6:

$N_c$7

with patch size $N_c$8 along antennas and frequency. The resulting tensor is flattened into $N_c$9 tokens. Absolute sinusoidal positional encoding is then added:

$\Delta f$0

with

$\Delta f$1

The encoder stacks Transformer blocks with RMSNorm and sparse MoE feedforward layers:

$\Delta f$2

$\Delta f$3

The MoE layer is defined by

$\Delta f$4

where $\Delta f$5 is the gating network, $\Delta f$6 selects the top-$\Delta f$7 experts, and $\Delta f$8 denotes expert $\Delta f$9 (Xuanyu et al., 6 Aug 2025).

The decoder first upsamples each user code into a full token sequence, then adds both absolute positional embeddings and a user-identity embedding:

$n$0

All user sequences are concatenated and jointly decoded, which is a structural device for modeling inter-user CSI correlation. Dynamic-rate feedback is supported because the bit width $n$1 is configurable per user, and joint decoding allows higher-precision users to assist lower-precision users through shared latent structure (Xuanyu et al., 6 Aug 2025).

The defining architectural component is the S-R MoE:

$n$2

Shared experts are always active and model global CSI priors; routed experts are sparsely activated and model user- or domain-specific factors. The paper attributes natural support for variable $n$3 to this design, without padding or retraining. To prevent routing collapse, WiFo-CF adds a Switch-Transformer-style load-balancing term

$n$4

and pretraining uses

$n$5

with $n$6 (Xuanyu et al., 6 Aug 2025).

The reported model variants are as follows.

Variant	Architecture	Parameters
Small	encoder depth 2 / width 64 / heads 8; decoder depth 2 / width 64 / heads 8; experts 1 shared − 1 activated − 31 routed	$n$7 M inference / $n$8 M training
Base	$n$9 encoder; $x_n = V_n s_n,$0 decoder; experts 1−3−31	$x_n = V_n s_n,$1 M / $x_n = V_n s_n,$2 M
Large	$x_n = V_n s_n,$3 encoder; $x_n = V_n s_n,$4 decoder; experts 1−7−31	$x_n = V_n s_n,$5 M / $x_n = V_n s_n,$6 M

3. Heterogeneous pretraining on LH-CDF

WiFo-CF is pretrained on LH-CDF, described as the first large-scale heterogeneous channel feedback dataset. LH-CDF combines three generation paradigms: statistical channels from QuaDRiGa, ray-tracing channels from DeepMIMO and SynthSoM, and real-world measurements from Argos and Dichasus. The dataset spans frequencies from $x_n = V_n s_n,$7 to $x_n = V_n s_n,$8 GHz in QuaDRiGa, $x_n = V_n s_n,$9–$k$0 and $k$1–$k$2 GHz in DeepMIMO, $k$3 GHz in SynthSoM, $k$4 GHz in Argos, and $k$5–$k$6 GHz in Dichasus, with base-station antenna counts from $k$7 to $k$8, user antenna counts from $k$9 to $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$0, subcarrier counts from $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$1 to $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$2, and mobility ranges from $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$3 to $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$4 km/h (Xuanyu et al., 6 Aug 2025).

The total scale is reported as over $$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$5 million samples. The pretraining set contains QuaDRiGa Q1–Q8 ($$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$6k), DeepMIMO D1–D2 ($$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$7k), and Argos A1–A6 ($$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$8k). Zero-shot evaluation uses QuaDRiGa Q9–Q16 ($$y_{k,n} = h_{k,n}^H v_{k,n} s_{k,n} + \sum_{i\neq k} h_{k,n}^H v_{i,n} s_{i,n} + n_{k,n},$$9k), DeepMIMO D3–D4 ($n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$0k), SynthSoM S1–S2 ($n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$1k), Argos A7–A8 ($n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$2k), and Dichasus H1–H2 ($n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$3k) (Xuanyu et al., 6 Aug 2025).

Pretraining is self-supervised, multi-user, and multi-rate. For each batch, the number of users is randomly sampled as $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$4, and the bit width is randomly sampled as $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$5 per user. The model then performs encoding, $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$6-law quantization, dequantization, and joint decoding for all users. The reported hyperparameters are batch size $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$7, $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$8 pretraining epochs, learning rate in $n_{k,n} \sim \mathcal{CN}(0,\sigma^2)$9, patch size $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$0, and fixed $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$1, optimized with Adam and cosine annealing (Xuanyu et al., 6 Aug 2025).

This pretraining protocol is intended to expose the model simultaneously to variation in user count, quantization precision, antenna dimension, subcarrier dimension, propagation model, and domain shift. A plausible implication is that WiFo-CF’s generalization is driven not only by scale, but by deliberate co-training over multiple operational axes rather than simple dataset aggregation.

4. Empirical performance, generalization, and ablation results

On in-distribution evaluation over Q1–Q8 and D1–D2, WiFo-CF reports the best average NMSE at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$2 dB, compared with LAM at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$3 dB, CRNet at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$4 dB, CsiNet at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$5 dB, and TVAL3 at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$6 dB. Representative dataset-level results include Q1 at $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$7 dB versus $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$8 for LAM and $V_n = \gamma H_n^H (H_n H_n^H)^{-1},$9 for CRNet, and D1 at $K$00 dB versus $K$01 for LAM and $K$02 for CRNet. The paper emphasizes that a single WiFo-CF model handles all heterogeneous configurations, whereas baselines require many models, with CsiNet cited as requiring approximately $K$03 per scenario family (Xuanyu et al., 6 Aug 2025).

The multi-rate setting is evaluated through both spectral efficiency and effective spectral efficiency. The reported trend is that WiFo-CF improves spectral efficiency as $K$04 increases from $K$05 to $K$06 bits, but larger $K$07 reduces the effective communication ratio $K$08 because the uplink payload $K$09 increases. In fast time-varying or mmWave channels with small $K$10, smaller $K$11 can outperform larger $K$12 in ESE, which is the principal systems argument for multi-rate capability (Xuanyu et al., 6 Aug 2025).

Zero-shot out-of-distribution performance is a central result. On Q9–Q16, D3–D4, and S1, WiFo-CF achieves an average NMSE of $K$13 dB, while the best full-shot baseline, LAM, achieves $K$14 dB. The average gain is reported as approximately $K$15 dB despite evaluation on unseen configurations. Dataset highlights include S1 at $K$16 dB for WiFo-CF zero-shot, versus $K$17 for LAM full-shot and $K$18 for CRNet, and D4 at $K$19 dB versus $K$20 for LAM and $K$21 for CRNet (Xuanyu et al., 6 Aug 2025).

Ablation results are structured around the S-R MoE and the pretraining recipe. On Q1–Q8, the base model achieves $K$22 dB. Removing routed experts yields $K$23 dB, removing shared experts yields $K$24 dB, removing multi-user joint decoding yields $K$25 dB, and removing multi-rate training yields $K$26 dB. On Q9–Q16, the same removals degrade performance from $K$27 dB to $K$28, $K$29, $K$30, and $K$31 dB, respectively. The paper interprets these results as confirming the importance of S-R MoE, joint multi-user decoding, and multi-rate pretraining (Xuanyu et al., 6 Aug 2025).

The scaling study states that larger models and larger, more diverse datasets consistently improve both in-distribution and out-of-distribution performance. Patch size is also treated as a design variable, with $K$32 described as a robust choice that yields Q1 NMSE of $K$33 dB at moderate FLOPs (Xuanyu et al., 6 Aug 2025).

5. Transfer learning, efficiency, deployment, and limitations

WiFo-CF is also evaluated as a transferable representation model. In few-shot transfer on real-world data, the reported comparison includes zero-shot inference, full fine-tuning, frozen-backbone transfer, and training from scratch. Zero-shot WiFo-CF is stated to outperform baselines even when those baselines are trained with $K$34k labeled samples, with an average NMSE advantage of approximately $K$35 dB. The frozen backbone often surpasses full fine-tuning, which the paper attributes to highly generalizable pretrained features and reduced overfitting from fewer trainable parameters (Xuanyu et al., 6 Aug 2025).

For CSI-based indoor localization, WiFo-CF’s encoder representations are used as features for coordinate regression. Encoded features yield more than $K$36 lower localization error than raw CSI, and the compressed and quantized features also provide substantial gains at much lower dimension. This situates WiFo-CF not only as a feedback model, but also as a reusable channel representation learner (Xuanyu et al., 6 Aug 2025).

Compute and latency are reported in both sparse and dense terms. WiFo-CF-Small attains NMSE of $K$37 dB at $K$38 MFLOPs, $K$39 ms inference, and $K$40 M inference parameters. The sparse design reduces FLOPs by more than $K$41 relative to its dense counterpart while maintaining accuracy; the dense small model is listed at $K$42 MFLOPs and $K$43 ms. Baseline figures are LAM at $K$44 MFLOPs and $K$45 dB, CRNet at $K$46 MFLOPs and $K$47 dB, and CsiNet at $K$48 MFLOPs and $K$49 dB. The training platform is reported as $K$50 NVIDIA RTX 4090 GPUs, $K$51 Intel Xeon Platinum 8358P CPUs, and $K$52 GB RAM (Xuanyu et al., 6 Aug 2025).

The deployment model is asymmetric. The encoders are described as identical and lightweight for user equipment deployment, while the heavier decoder runs at the base station. Per-user bit widths $K$53 are signaled to the base station, and size-agnostic down/up-sampling allows a single pretrained model to serve multiple cells and devices. The practical guidance given is to normalize magnitude to $K$54 before $K$55-law quantization, use Conv2d patch embedding with $K$56 as a strong default, and begin domain adaptation with frozen-backbone fine-tuning of the output head before escalating to full fine-tuning if necessary (Xuanyu et al., 6 Aug 2025).

The paper also enumerates several limitations. Foundation pretraining depends on large, diverse datasets such as LH-CDF, and collecting real CSI raises privacy and logistics concerns. Routing stability depends on well-tuned gating and load balancing, and extreme domain shifts may challenge the S-R MoE router. The decoder is compute-heavier than the encoder, so further efficiency work such as quantization-aware inference and expert pruning is identified as beneficial. Future directions include online or federated updates, per-cell personalization, explicit rate–distortion objectives, mutual-information regularization, and more explicit physics-informed priors (Xuanyu et al., 6 Aug 2025).

6. Relation to the broader WiFo literature and nomenclature

WiFo-CF belongs to a broader family of wireless foundation models. The paper explicitly states that the wireless foundation model concept, “as in WiFo and LWM,” is extended to CSI feedback by pretraining on large, heterogeneous channel corpora to learn universal channel compression and reconstruction priors (Xuanyu et al., 6 Aug 2025). The immediate precursor is WiFo, introduced as the first space-time-frequency wireless foundation model for time-frequency channel prediction, where time extrapolation and cross-frequency prediction are unified as masked reconstruction on heterogeneous CSI tensors (Liu et al., 2024).

The term itself is not entirely uniform across later WiFo literature. In WiFo-2, “WiFo-CF” refers to a downstream CSI feedback capability in which WiFo-2 is used on the receiver side to denoise or refine CSI reconstructed by a standard compression network under a fixed $K$57 compression ratio, rather than to an end-to-end variable-rate feedback model (Liu et al., 27 Nov 2025). In WiFo-M$K$58, by contrast, the summary states that the paper does not explicitly define a module named “WiFo-CF,” and instead interprets the phrase as “WiFo Channel Feature forecasting” in the context of multimodal sensing and CSI-aligned latent prediction (Zhang et al., 14 Jan 2026).

This terminological variation has two consequences. First, “WiFo-CF” in the strict bibliographic sense denotes the model introduced in “WiFo-CF: Wireless Foundation Model for CSI Feedback” (Xuanyu et al., 6 Aug 2025). Second, later usage sometimes broadens the label to mean CSI-feedback capability or channel-feature forecasting inside other WiFo-derived systems. The most precise usage therefore depends on context, but within the CSI feedback literature the canonical referent is the variable-rate, heterogeneous-configuration feedback model built around multi-user self-supervision and S-R MoE (Xuanyu et al., 6 Aug 2025).