WideNLNet-CA: Adaptive CSI Feedback

• The paper introduces a rate-adaptive deep learning framework for CSI feedback in wideband near-field XL-MIMO systems by conditioning feature selection on variable compression ratios.
• It employs a lightweight encoder–decoder with multi-stage downsampling/upsampling and efficient LightResBlocks to capture multi-scale channel features.
• Empirical results show superior NMSE performance and graceful degradation across different compression ratios while maintaining fast inference and low model storage.

WideNLNet-CA is a rate-adaptive deep learning framework for channel state information (CSI) feedback in wideband near-field extremely large-scale MIMO (XL-MIMO) systems. It is introduced for settings in which near-field spherical wave propagation and frequency-dependent beam split jointly complicate CSI representation and compression. The framework combines a lightweight encoder–decoder with multi-stage downsampling and upsampling, computationally efficient residual blocks, and a compression ratio adaptive module (CAM) that conditions feature selection on the target feedback rate. Its stated objective is to support variable compression ratios with a single model while preserving reconstruction quality, fast inference, and low model storage requirements in wideband near-field XL-MIMO feedback (Liu et al., 1 Aug 2025).

1. Signal model and wideband near-field feedback problem

The underlying system is a wideband XL-MIMO downlink with $N$ base-station antennas arranged as a ULA and $M$ OFDM subcarriers. The spatial–frequency–domain CSI is represented as

$$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$

A 2D DFT is then applied to obtain the angular-delay-domain tensor

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$

which is reshaped into a real-valued input

$$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$

by splitting the real and imaginary parts.

Two propagation effects define the problem setting. First, under spherical wavefronts, the phase at antenna $n$ on subcarrier $m$ is

$$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$

which is explicitly not linear in $n$. Second, beam split causes a frequency-dependent array response and therefore spatial dispersion across subcarriers. In combination, these effects make the CSI structure more difficult to compress with fixed-rate or narrowband-oriented feedback schemes.

The feedback compression ratio is defined as

$r = \beta = \frac{K_{\rm code}}{2NM},$

where $M$0 is the codeword dimension. A central design target of WideNLNet-CA is support for variable $M$1 with one model. This directly situates the framework in the class of rate-adaptive CSI feedback methods rather than single-compression-ratio autoencoders.

2. Encoder–decoder formulation

The encoder $M$2 maps $M$3 to a latent code through a hierarchical convolutional pipeline. It begins with an initial $M$4 convolution,

$M$5

followed by three downsampling blocks indexed by $M$6. Each block applies a strided $M$7 convolution with stride $M$8,

$M$9

and then a LightResBlock,

$$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$0

The resulting feature map $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$1 has size $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$2 and serves as the input to the CAM.

The decoder $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$3 mirrors the encoder. A $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$4 convolution first restores channels,

$$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$5

after which three upsampling blocks apply transposed convolutions with stride $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$6 and LightResBlocks. Reconstruction ends with a final $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$7 convolution and Sigmoid,

$$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$8

This encoder–decoder organization is explicitly lightweight and multi-stage. The stated rationale is that multi-stage downsampling and upsampling capture complex multi-scale channel features while keeping overhead low. A plausible implication is that the architecture is intended to preserve enough spatial–frequency structure for reconstruction without resorting to a large monolithic latent bottleneck.

3. LightResBlock and computational efficiency

The residual unit used throughout the network is the LightResBlock (LRB), which employs depthwise-separable convolutions. For input $$\tilde{\mathbf H} = [\mathbf h_1,\dots,\mathbf h_M]^H \in \mathbb{C}^{M\times N}.$$9, it is defined as

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$0

with skip connection

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$1

The design objective of the LRB is stated directly: it captures multi-scale local features while keeping parameter count low. In WideNLNet-CA, this block is used after each strided convolution in the encoder and after each transposed convolution in the decoder. The resulting pattern makes the residual path a structural component of both compression and reconstruction.

Within the framework, efficiency is therefore not only a property of model size but also of operator choice. The use of depthwise-separable convolutions places the LRB in a specifically lightweight regime, which aligns with the reported emphasis on fast inference and low model storage requirements. This suggests that WideNLNet-CA is intended for scenarios where feedback quality and deployment constraints must be balanced simultaneously.

4. Compression Ratio Adaptive Module

The compression ratio adaptive module is the mechanism that makes WideNLNet-CA rate-adaptive. Starting from encoder output $$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$2, the model applies a $$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$3 convolution to obtain $$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$4. At each spatial location, a feature vector $$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$5 is processed by a feature-importance estimator

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$6

implemented via four fully connected layers with intermediate adaptation conditioned on the target channel count

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$7

The adaptation mechanism is itself explicit. At adaptation module $$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$8, the modulation is

$$\mathbf H = \mathbf F_d^H\,\tilde{\mathbf H}\,\mathbf F_a \in \mathbb{C}^{M\times N},$$9

These cascaded modulations operate on the FC stages and yield the final per-channel importance map

$$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$0

Feature selection proceeds in two stages. First, $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$1 is aggregated spatially to obtain global channel scores $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$2. Then the top $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$3 channels are selected to form a binary mask $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$4. The feature modulation and masking are

$$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$5

which yields exactly $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$6 active feature maps as the codeword $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$7.

The significance of CAM is that a single WideNLNet-CA instance supports multiple $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$8 through conditioning on $$\mathbf H_{\mathrm{ts}}\in\mathbb R^{N\times M\times 2}$$9. The framework does not claim to remove the rate–distortion trade-off. On the contrary, its stated trade-off is that lower CR, corresponding to smaller $n$0, leads to fewer channels selected and higher NMSE; the role of CAM is to ensure graceful degradation rather than invariance across compression ratios.

5. Training protocol and implementation configuration

Training minimizes the mean squared error over a training set of size $n$1: $n$2 Multi-rate training is performed by selecting a random $n$3 for each batch and setting $n$4 accordingly. No additional regularization terms were required beyond batch normalization and weight decay inherent in Adam.

The implementation details are fully specified. The dataset consists of 45,000 spherical-model channels, divided into 35,000 training samples, 5,000 validation samples, and 5,000 test samples. The configuration uses $n$5, a $n$6 carrier, and $n$7 bandwidth. Optimization uses Adam with learning rate $n$8, batch size $n$9, and $m$0 epochs. Feature depths are $m$1, $m$2, CAM depth $m$3, and latent $m$4. The implementation framework is PyTorch on an NVIDIA RTX 4090 GPU and an Intel Xeon w7-3465X CPU.

These details indicate that WideNLNet-CA is trained as a single shared model across multiple feedback rates rather than as a collection of separately optimized single-rate models. A plausible implication is that the CAM is not an auxiliary add-on but the primary mechanism through which rate adaptivity is learned during optimization.

6. Empirical behavior, comparative results, and significance

The reported evaluation emphasizes reconstruction accuracy, bandwidth robustness, and deployment efficiency (Liu et al., 1 Aug 2025). At compression ratio $m$5, WideNLNet-CA achieves $m$6, compared with ExtendNLNet at approximately $m$7 and BSPD at greater than $m$8. Cosine similarity remains greater than $m$9 even at high compression. Under bandwidth variation at $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$0, as $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$1 increases from $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$2 to $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$3, WideNLNet-CA degrades by less than $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$4 NMSE, whereas baselines lose more than $$\phi_{l,m}^{(n)}=-\tfrac{2\pi}{\lambda_m}(r_{l}^{(n)}-r_l),$$5.

The reported complexity and latency results are as follows:

Method	Parameters	Inference time
BSPD	1.07 M	130 ms
ExtendNLNet / ENL	8.39 M	2.51 ms
WideNLNet / WNL	1.47 M	1.57 ms
WideNLNet-CA / WNL-CA	1.52 M	1.64 ms

Only WideNLNet-CA is stated to use one model for all compression ratios. This is significant because the rate-adaptive claim is tied not merely to reconstruction quality but also to model consolidation. The framework’s contribution is therefore twofold: it introduces a rate-conditioned feature-importance mechanism and demonstrates that this mechanism can operate with minimal additional overhead relative to WideNLNet, while maintaining what the source describes as flexible, accurate, and efficient CSI feedback with state-of-the-art performance.

A common misunderstanding would be to interpret rate adaptivity as implying compression-invariant accuracy. The reported trade-off rejects that interpretation: lower compression ratios correspond to fewer selected channels and higher NMSE. The empirical claim is instead that the degradation is graceful, and that this occurs within a single trained model across a broad range of feedback rates.