NEFT: Efficient Near-Field Transformer for XL-MIMO

• NEFT is a unified Transformer framework for efficient near-field CSI feedback in XL-MIMO systems, integrating a hierarchical Vision Transformer to capture spherical-wave propagation.
• It directly learns the near-field channel characteristics without relying on hand-crafted sparse representations, achieving 15–21 dB NMSE improvements over CNN-based baselines.
• The framework offers deployment-aware variants—NEFT-Compact, NEFT-Hybrid, and NEFT-Edge—that leverage knowledge distillation and reduced computational overhead for practical edge applications.

Searching arXiv for the cited NEFT paper and closely related work to ground the article. Near-Field Efficient Feedback Transformer (NEFT) is a unified Transformer framework for efficient near-field channel state information (CSI) feedback in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. It was introduced for single-cell FDD downlink CSI compression and reconstruction in the near-field regime, where the plane-wave assumption breaks down and spherical-wave propagation induces distance-dependent amplitude and nonlinear phase across antennas (Li et al., 16 Sep 2025). NEFT is built on a hierarchical Vision Transformer backbone operating on a reshaped CSI tensor, and is extended with lightweight variants tailored to deployment constraints: NEFT-Compact uses multi-level knowledge distillation, while NEFT-Hybrid and NEFT-Edge target encoder- and edge-constrained scenarios through attention-free encoding and knowledge distillation (Li et al., 16 Sep 2025). In reported simulations, NEFT achieves a 15--21 dB improvement in normalized mean-squared error (NMSE) over representative baselines, and its lightweight variants reduce total FLOPs by 25--36% with negligible to modest accuracy loss (Li et al., 16 Sep 2025).

1. Near-field XL-MIMO setting and CSI feedback formulation

NEFT is formulated for XL-MIMO systems operating in the electromagnetic near-field. The boundary between near-field and far-field is characterized by the Rayleigh distance

$R_R = \frac{2D^2}{\lambda},$

where $D$ is the array aperture and $\lambda$ is the wavelength (Li et al., 16 Sep 2025). As $D$ grows, users at typical cell distances can fall within the Fresnel region, where wavefronts are spherical rather than planar and the conventional far-field angular sparsity model is no longer appropriate (Li et al., 16 Sep 2025).

The underlying communication model is a single-cell FDD downlink with a base station (BS) using a large ULA with $N_1$ antennas and a user equipment (UE) with $N_2$ antennas. The received signal is

$y = \mathbf{H}\mathbf{v}x + n,$

where $x$ is the transmitted symbol, $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$ is the precoder, $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$ is the channel, and $D$0 is noise (Li et al., 16 Sep 2025). For the narrowband near-field line-of-sight (LoS) geometric model used in the paper, the channel coefficient between the $D$1-th BS antenna and $D$2-th UE antenna is expressed as

$D$3

with

$D$4

where $D$5 is the distance from the first UE antenna to the first BS antenna, $D$6 is the angle-of-departure, $D$7 is the relative angle between UE and BS, and $D$8, $D$9 with inter-element spacing $\lambda$0 (Li et al., 16 Sep 2025).

In the reported experiments, the BS ULA has $\lambda$1 and the UE is single-antenna with $\lambda$2 (Li et al., 16 Sep 2025). The complex channel vector is reshaped into a $\lambda$3 tensor, where the two channels correspond to the real and imaginary parts, normalized to $\lambda$4 (Li et al., 16 Sep 2025). This tensor is the encoder input $\lambda$5. The encoder produces a $\lambda$6-dimensional feedback codeword

$\lambda$7

and the decoder reconstructs

$\lambda$8

with $\lambda$9 and compression ratio

$D$0

The paper studies $D$1 (Li et al., 16 Sep 2025).

A central design choice is that NEFT does not rely on frequency-domain wideband tensors or polar-/angle--distance-domain sparsity. Instead, it is designed to learn near-field spherical-wave phase and amplitude structure directly from the reshaped spatial tensor (Li et al., 16 Sep 2025). This distinguishes it from other near-field CSI feedback approaches that first impose a hand-crafted sparse representation. A plausible implication is that NEFT prioritizes end-to-end representation learning over explicit physical reparameterization.

2. Hierarchical Vision Transformer architecture

NEFT is built on a hierarchical Vision Transformer encoder-decoder. The input is the $D$2 CSI tensor (Li et al., 16 Sep 2025). In stage-0 patch embedding, the input is partitioned into $D$3 non-overlapping patches of size $D$4, and each patch is linearly projected to embedding dimension $D$5, producing a feature map of size $D$6 with sequence length $D$7 (Li et al., 16 Sep 2025).

The encoder stage-1 contains a Transformer block with multi-head global self-attention (MSA) and MLP (Li et al., 16 Sep 2025). Patch merging is then performed through a $D$8 convolution, aggregating four neighboring tokens into one, reducing spatial resolution from $D$9 to $N_1$0 and doubling channels to $N_1$1, corresponding to sequence length $N_1$2 (Li et al., 16 Sep 2025). The bottleneck tensor is flattened into the feedback codeword; its dimension is

$N_1$3

which equals $N_1$4 under direct floating-point feedback (Li et al., 16 Sep 2025).

The decoder mirrors the hierarchy through transposed-convolution upsampling, denoted as patch division. It maps $N_1$5 with kernel $N_1$6 and stride $N_1$7, and then $N_1$8 with $N_1$9, $N_2$0 (Li et al., 16 Sep 2025). Transformer blocks with global attention are applied at the corresponding decoder stages to reconstruct long-range dependencies and fine-grained local patterns (Li et al., 16 Sep 2025). Positional information is handled through a relative position bias $N_2$1 in attention; global attention does not rely on window shifting (Li et al., 16 Sep 2025).

The self-attention computation is given for feature $N_2$2 as

$N_2$3

$N_2$4

$N_2$5

For global attention and windowed attention, the paper gives

$N_2$6

$N_2$7

where $N_2$8 is feature map size, $N_2$9 is the number of channels, and $y = \mathbf{H}\mathbf{v}x + n,$0 is window size (Li et al., 16 Sep 2025). By operating at smaller sequence lengths with larger patches, NEFT retains global attention at feasible cost. With typical parameters $y = \mathbf{H}\mathbf{v}x + n,$1, the aggregated operations are reported as approximately $y = \mathbf{H}\mathbf{v}x + n,$2 for NEFT versus $y = \mathbf{H}\mathbf{v}x + n,$3 for W-MSA, corresponding to about $y = \mathbf{H}\mathbf{v}x + n,$4 of the windowed-attention cost (Li et al., 16 Sep 2025).

This architectural choice should not be confused with attention decompositions such as FMMformer, which split attention into near-field banded and far-field low-rank components for linear-complexity sequence modeling (Nguyen et al., 2021). NEFT uses global MSA directly, but makes it efficient by aggressively reducing token count through patching and hierarchy rather than by replacing the attention operator itself (Li et al., 16 Sep 2025).

3. Lightweight variants and deployment-oriented design

NEFT was presented as a family rather than a single model. The principal variants are NEFT-Compact, NEFT-Hybrid, and NEFT-Edge, each corresponding to a different deployment constraint (Li et al., 16 Sep 2025).

NEFT-Compact is a student Transformer trained by multi-level knowledge distillation from the full NEFT teacher (Li et al., 16 Sep 2025). The student reduces token and channel dimensions as well as MLP projection size, while the distillation process aligns three internal signals: reconstruction outputs (RA), attention maps (AA), and encoder codewords (CA) (Li et al., 16 Sep 2025). The associated losses are

$y = \mathbf{H}\mathbf{v}x + n,$5

$y = \mathbf{H}\mathbf{v}x + n,$6

$y = \mathbf{H}\mathbf{v}x + n,$7

with overall objective

$y = \mathbf{H}\mathbf{v}x + n,$8

where $y = \mathbf{H}\mathbf{v}x + n,$9, $x$0, and $x$1 (Li et al., 16 Sep 2025).

NEFT-Hybrid replaces the Transformer encoder with a lightweight CNN stack, while retaining a Transformer decoder (Li et al., 16 Sep 2025). The paper motivates this change by noting encoder-side local correlations, described as diagonal attention, and targets asymmetric deployment in which the UE encoder is the main computational bottleneck (Li et al., 16 Sep 2025). The encoder consists of a three-stage CNN with $x$2 convolutions, batch normalization, and ReLU; each stage halves spatial resolution and doubles channels, producing a compact $x$3 representation (Li et al., 16 Sep 2025). The per-layer convolutional complexity is given as

$x$4

The paper states that this reduces encoder FLOPs by up to approximately $x$5 compared to a Transformer encoder, and reports encoder-side reductions up to $x$6 across scenarios (Li et al., 16 Sep 2025).

NEFT-Edge is a distilled student of NEFT-Hybrid with reduced dimensions while preserving the hybrid structure (Li et al., 16 Sep 2025). It is intended for IoT and edge deployments with tighter resource budgets (Li et al., 16 Sep 2025).

At compression ratio $x$7, the paper reports the following experimental figures (Li et al., 16 Sep 2025):

Model	Params / FLOPs	NMSE
NEFT	551,740 params; 6.35M FLOPs	−31.14 dB
NEFT-Compact	439,220 params; 4.70M FLOPs	−30.13 dB
NEFT-Hybrid	427,841 params; 4.07M FLOPs	−26.12 dB
NEFT-Edge	300,340 params; 2.61M FLOPs	−24.24 dB

For the same setting, NEFT-Compact reduces parameters by $x$8 and FLOPs by $x$9 relative to NEFT, with NMSE degradation of about $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$0 dB (Li et al., 16 Sep 2025). NEFT-Edge reduces parameters by $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$1 relative to Hybrid, reduces total FLOPs by $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$2, and reduces encoder FLOPs by $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$3 (Li et al., 16 Sep 2025). Similar reductions are reported at $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$4 and $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$5, with Compact and Edge reducing total FLOPs by $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$6--$\mathbf{v} \in \mathbb{C}^{N_1\times 1}$7 and Hybrid lowering encoder complexity by up to $\mathbf{v} \in \mathbb{C}^{N_1\times 1}$8 (Li et al., 16 Sep 2025).

These variants formalize NEFT as a deployment spectrum rather than a fixed architecture. The full model targets maximal reconstruction performance, while Compact, Hybrid, and Edge progressively trade representational capacity for lower total or encoder-side complexity.

4. Training objectives, optimization, and feedback pipeline

The primary reconstruction metric is NMSE,

$\mathbf{v} \in \mathbb{C}^{N_1\times 1}$9

reported in decibels as

$\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$0

The paper also reports cosine similarity,

$\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$1

These metrics are used to evaluate the fidelity of CSI reconstruction after feedback compression (Li et al., 16 Sep 2025).

The training dataset is generated using LoS near-field channels with Rayleigh distance $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$2 and uniform sampling of $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$3 and $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$4 (Li et al., 16 Sep 2025). The dataset contains $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$5k training samples, $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$6k validation samples, and $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$7k test samples (Li et al., 16 Sep 2025). Optimization uses AdamW for $\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$8 epochs with cosine-annealed learning rate

$\mathbf{H} \in \mathbb{C}^{N_2\times N_1}$9

where $D$00, $D$01, and $D$02 (Li et al., 16 Sep 2025). Early stopping is applied if NMSE fails to improve by at least $D$03 dB over $D$04 epochs (Li et al., 16 Sep 2025). During knowledge-distillation training, the learning rate is increased to $D$05 (Li et al., 16 Sep 2025). The implementation environment is PyTorch 2.6.0, CUDA 12.4, and an RTX 4080 GPU; the details section additionally lists an i7-13700K (Li et al., 16 Sep 2025).

The feedback pipeline is explicit. The encoder input is the normalized $D$06 real-imaginary tensor; patch embedding yields $D$07 tokens, patch merging yields the $D$08 bottleneck, and flattening produces the feedback vector of length $D$09 (Li et al., 16 Sep 2025). The BS decoder reshapes the received vector back to the bottleneck tensor and reconstructs the CSI through hierarchical upsampling and Transformer decoding (Li et al., 16 Sep 2025). The encoder resides at the UE and the decoder at the BS (Li et al., 16 Sep 2025).

Quantization and entropy coding are not incorporated in the reported experiments; the paper trains and evaluates with continuous floating-point feedback vectors (Li et al., 16 Sep 2025). It states that uniform or nonuniform quantization and entropy coding may be added post-training in practical deployments, but these are treated as orthogonal add-ons rather than part of NEFT proper (Li et al., 16 Sep 2025). Residual or iterative refinement is likewise not used; reconstruction relies on the hierarchical ViT decoder (Li et al., 16 Sep 2025).

5. Experimental evaluation and ablation results

The reported baselines are CsiNet, a CNN encoder-decoder, and ExtendNLNet, a CNN model with Non-Local blocks (Li et al., 16 Sep 2025). SwinCFNet is discussed in the paper but is not used as a baseline in the reported tables (Li et al., 16 Sep 2025). The evaluation is performed on the narrowband near-field LoS dataset under the BS and UE configuration described above (Li et al., 16 Sep 2025).

Across all tested compression ratios, NEFT substantially outperforms the reported baselines in NMSE (Li et al., 16 Sep 2025). At $D$10, NEFT achieves $D$11 dB, compared with $D$12 dB for ExtendNLNet and $D$13 dB for CsiNet, corresponding to an improvement of approximately $D$14--$D$15 dB; the cosine similarity is reported as $D$16 (Li et al., 16 Sep 2025). At $D$17, NEFT achieves $D$18 dB, versus $D$19 dB for ExtendNLNet and $D$20 dB for CsiNet (Li et al., 16 Sep 2025). At $D$21, NEFT achieves $D$22 dB, versus $D$23 dB and $D$24 dB, respectively (Li et al., 16 Sep 2025).

NEFT-Hybrid achieves $D$25, $D$26, and $D$27 dB NMSE at $D$28, $D$29, and $D$30, respectively, while using the lowest or comparable FLOPs among the baselines and markedly reducing encoder complexity (Li et al., 16 Sep 2025). NEFT-Compact and NEFT-Edge reduce total FLOPs by $D$31--$D$32 with small NMSE degradation; the paper summarizes Compact as incurring about $D$33--$D$34 dB loss and Edge about $D$35--$D$36 dB loss depending on $D$37 (Li et al., 16 Sep 2025).

The ablation results emphasize the role of multi-level knowledge distillation. At $D$38, removing KD or using reconstruction-only losses degrades Compact from $D$39 dB to $D$40 dB for Compact-onlyRecon and to $D$41 dB for Compact-w/o-KD (Li et al., 16 Sep 2025). For Edge, the corresponding degradation is from $D$42 dB to $D$43 dB for Edge-onlyRecon and to $D$44 dB for Edge-w/o-KD (Li et al., 16 Sep 2025). The paper also reports stable convergence in the loss curves, with the student approaching teacher loss while retaining a minor capacity gap (Li et al., 16 Sep 2025).

Architectural ablations indicate that larger $D$45 patches and a two-stage hierarchy reduce sequence length from $D$46 to $D$47 while preserving global attention, yielding approximately $D$48 of W-MSA cost (Li et al., 16 Sep 2025). Relative position bias is reported to support spatial modeling without window shifting (Li et al., 16 Sep 2025). The paper does not directly study robustness to SNR mismatch, user mobility, or array scaling, and states that such robustness is not directly examined (Li et al., 16 Sep 2025).

6. Interpretation, practical significance, and limitations

NEFT is explicitly positioned as a practical and scalable solution for near-field CSI feedback in XL-MIMO systems (Li et al., 16 Sep 2025). Its central contribution is to reconcile global Transformer-based modeling with the computational constraints of CSI feedback, especially at the UE encoder. The full NEFT model addresses accurate reconstruction, while Hybrid and Edge directly target asymmetric hardware scenarios in which encoder-side resources are much tighter than decoder-side resources (Li et al., 16 Sep 2025).

Several practical limitations are stated. First, the training and evaluation are restricted to narrowband near-field LoS channels (Li et al., 16 Sep 2025). Performance under mixed LoS/NLoS conditions, wideband OFDM settings, or hybrid near-/far-field propagation is not validated in the paper (Li et al., 16 Sep 2025). Second, the feedback vector is continuous rather than quantized, so quantization bottlenecks and entropy coding effects are not part of the reported performance numbers (Li et al., 16 Sep 2025). Third, GPU training and inference are reported, but mobile or SoC latency and memory footprints are not measured (Li et al., 16 Sep 2025).

The paper identifies several future directions, including cross-domain adaptation such as domain randomization, mixed-precision inference, online fine-tuning, and integration with variable-length bit-level feedback (Li et al., 16 Sep 2025). This suggests that the current NEFT formulation is best interpreted as a floating-point algorithmic core that could be integrated into a fuller communication stack rather than as a complete air-interface design.

A further point of clarification concerns naming. NEFT should not be conflated with other uses of “near-field” in the Transformer literature. For example, FMMformer uses a near-/far-field attention decomposition inspired by the fast multipole method for long-sequence modeling (Nguyen et al., 2021). By contrast, NEFT’s “near-field” refers to electromagnetic propagation physics in XL-MIMO CSI, not to a banded/local attention decomposition (Li et al., 16 Sep 2025). The two works address different problem domains and employ different efficiency mechanisms.

7. Position within near-field CSI feedback research

Within near-field CSI feedback research, NEFT represents a Transformer-centered alternative to CNN-based feedback architectures such as CsiNet and ExtendNLNet, which serve as its direct baselines (Li et al., 16 Sep 2025). Its main empirical claim is that global dependency modeling on the reshaped spatial CSI tensor is especially effective for near-field spherical-wave channels, provided that the attention cost is controlled through aggressive patching and hierarchy (Li et al., 16 Sep 2025).

The paper’s scope is distinct from approaches that explicitly exploit near-field sparsity in transformed domains. For example, vector-quantized deep joint source-channel coding for XL-MIMO near-field CSI feedback has been studied using a polar-delay transform, hierarchical CNN and Transformer backbones, and discrete latent transmission over an AWGN channel (Ma et al., 12 Jan 2026). NEFT does not use polar-delay preprocessing, vector quantization, or DJSCC training; it instead learns directly from the spatial tensor and evaluates floating-point feedback (Li et al., 16 Sep 2025). This suggests a methodological contrast between representation-first and transform-first paradigms for near-field CSI compression.

In that context, NEFT can be understood as establishing that high-fidelity near-field CSI feedback is achievable with a hierarchical Vision Transformer even without explicit sparse-domain preprocessing, provided that token count is constrained and deployment-aware variants are available (Li et al., 16 Sep 2025). Its reported $D$49--$D$50 dB NMSE gains over the cited baselines and the availability of Compact, Hybrid, and Edge variants position it as a reference design for efficient near-field CSI feedback under diverse hardware constraints (Li et al., 16 Sep 2025).