Dual-ImRUNet: Ultra-Low-Rate CSI Feedback

• The paper presents Dual-ImRUNet, a method that uses uplink-assisted BCE and IFA modules to robustly compress downlink CSI at ultra-low feedback rates.
• It leverages a transformer-based autoencoder that exploits angular-delay sparsity and bi-directional uplink/downlink correlations for precise eigenvector recovery.
• Simulation results show Dual-ImRUNet achieves approximately 0.85 SGCS with only 6 bits per eigenvector set, reducing overhead by 85% relative to prior methods.

Searching arXiv for the specified paper and closely related implicit CSI feedback work. Dual-ImRUNet is an uplink-assisted implicit channel state information (CSI) feedback framework for massive MIMO systems that targets ultra-low feedback rates while preserving robustness across diverse environments. It was introduced to address two limitations identified in prior deep learning-based implicit CSI feedback methods: performance degradation in ultra-low-rate regimes and inadaptability under environmental variation. The framework combines two plug-in preprocessing modules—Bi-Directional Correlation Enhancement (BCE) and Input Format Alignment (IFA)—with a transformer-based autoencoder that exploits angular-delay domain sparsity and bi-directional uplink/downlink correlation. In simulation, it achieves approximately the same SGCS as the state-of-the-art Ubi-ImCsiNet at substantially lower rate, including SGCS $\approx 0.85$ at only $6$ bits of feedback, corresponding to an $85\%$ reduction in overhead relative to the cited baseline (Liu et al., 16 Jul 2025).

1. Problem setting and design objective

Dual-ImRUNet is situated in the setting of deep learning-based implicit CSI feedback for FDD massive MIMO. The core objective is to compress downlink CSI into an ultra-low-rate codeword while allowing the base station to reconstruct an accurate downlink representation with the aid of uplink CSI side information (Liu et al., 16 Jul 2025).

The framework operates on the downlink eigenvector matrix $W_{DL}$ of size $N_s \times N_{Tx}$, where each row $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$ satisfies

$$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$

The use of eigenvector matrices rather than raw channel coefficients reflects the implicit CSI feedback paradigm encoded in the source paper. The decoder further leverages processed uplink CSI, specifically through aligned uplink magnitudes, to support downlink recovery under stringent rate constraints (Liu et al., 16 Jul 2025).

A central design premise is that in FDD systems, uplink and downlink channel matrices share angles and delays, but their eigenvectors may differ because of arbitrary phase rotations or basis choices within eigenspaces. This non-uniqueness reduces the direct utility of uplink side information unless the representations are explicitly normalized or aligned. Dual-ImRUNet addresses this with BCE and IFA before the neural compression stage. This suggests that the architecture is not merely a compact autoencoder, but a hybrid signal-processing and representation-learning pipeline designed to make cross-link side information usable at very low rate.

2. End-to-end processing pipeline

Dual-ImRUNet consists of three building blocks: the BCE module, the IFA module, and a transformer-based autoencoder for extreme compression and uplink-aided reconstruction (Liu et al., 16 Jul 2025). The complete signal flow is asymmetric across the user equipment (UE) and base station (BS), but the preprocessing stages are mirrored.

At the UE, the pipeline begins with $W_{DL}$. BCE is first applied:

$W_{BCE,DL} = f_{BCE}(W_{DL}),$

with the stated purpose of rotating each eigenvector into its eigenspace so as to maximize correlation with uplink. IFA is then applied:

$$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$

which aligns sparse angular-delay patterns to a common benchmark $6$0 without extra transmission overhead; $6$1 captures circular shifts. The aligned matrix is encoded as

$6$2

and the codeword is quantized to $6$3 bits per element. The feedback link carries only this ultra-low-rate codeword, with the paper giving a total of $6$4 bits as an example (Liu et al., 16 Jul 2025).

At the BS, uplink CSI is processed analogously:

$6$5

and control bits $6$6 are extracted. The decoder reconstructs

$6$7

where the aligned uplink magnitude is explicitly injected. Inverse IFA is then applied:

$6$8

Because BCE does not change eigenvalues, $6$9 yields the final recovered eigenvectors (Liu et al., 16 Jul 2025).

This decomposition is architecturally significant because the ultra-low-rate burden is imposed only after correlation enhancement and format alignment. A plausible implication is that the neural network is relieved from learning invariances that can instead be enforced analytically by the preprocessing modules.

3. Bi-Directional Correlation Enhancement

The BCE module is motivated by the observation that, although uplink and downlink channels share geometric structure, the eigenvectors $85\%$0 and $85\%$1 can differ by arbitrary phase rotations or by basis choices within eigenspaces. According to the source description, this non-uniqueness degrades the usefulness of $85\%$2 as side information unless it is corrected (Liu et al., 16 Jul 2025).

For each subband $85\%$3, let

$85\%$4

be the SVD. The principal eigenspace $85\%$5 is spanned by the columns of $85\%$6 corresponding to the largest eigenvalue $85\%$7. Any eigenvector $85\%$8 solves

$85\%$9

BCE introduces a reference vector

$W_{DL}$0

described as the first row of $W_{DL}$1 and used as a correlated proxy. The transformed eigenvector is obtained by the optimization

$W_{DL}$2

For a one-dimensional eigenspace, the paper gives the closed-form projection

$W_{DL}$3

For higher multiplicity, $W_{DL}$4 is replaced by the projector onto $W_{DL}$5 formed by its orthonormal basis (Liu et al., 16 Jul 2025).

The reported effect is a dramatic increase in the Pearson correlation of magnitudes $W_{DL}$6, visible as a right-shift in the CDF of $W_{DL}$7. This reinforced correlation enables the decoder to use uplink magnitudes for accurate downlink recovery with only a few bits of feedback. Within the logic of the framework, BCE is therefore the mechanism that converts reciprocity in angles and delays into a representation compatible with implicit CSI feedback under severe quantization.

4. Input Format Alignment and environmental robustness

IFA is introduced to address distribution mismatch across environments. The source paper states that deep networks trained on one environment, with its associated angular-delay sparsity patterns, suffer when tested in others. IFA attempts to maintain consistent data distributions at encoder and decoder sides without extra transmission overhead (Liu et al., 16 Jul 2025).

The module first performs angular-delay sparsification through a two-dimensional DFT:

$W_{DL}$8

where $W_{DL}$9 and $N_s \times N_{Tx}$0 are unitary DFT matrices. A prestored benchmark pair, denoted $N_s \times N_{Tx}$1, provides a canonical LoS-like pattern shared at both UE and BS (Liu et al., 16 Jul 2025).

Alignment is implemented through circular shifts chosen to maximize the Pearson correlation between benchmark and observed row and column sums of the magnitude pattern. For rows,

$N_s \times N_{Tx}$2

and the optimal shift is

$N_s \times N_{Tx}$3

An analogous search is performed over columns to obtain $N_s \times N_{Tx}$4. The aligned representation is then

$N_s \times N_{Tx}$5

and $N_s \times N_{Tx}$6 is stored as control bits consisting of only a few indices (Liu et al., 16 Jul 2025).

The source explicitly states that this induces no extra rate. At the BS, the same shift search on uplink yields $N_s \times N_{Tx}$7, which is used both to align $N_s \times N_{Tx}$8 and to invert the shift on $N_s \times N_{Tx}$9. The original format is recovered by inverse DFT. In the paper’s interpretation, this allows environmental variation in sparse support location to be normalized into a common input distribution. This suggests that IFA acts as a domain-alignment layer operating in the angular-delay domain rather than in learned latent space.

5. Neural architecture and training criterion

After IFA, the complex matrix $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$0 is split into real and imaginary parts and concatenated along the subband axis, yielding a real feature map of size $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$1 (Liu et al., 16 Jul 2025). This input representation feeds a lightweight encoder-decoder network that combines transformer and convolutional components.

The encoder contains two “Single TransNet Encoder Layers,” described as full-attention transformer blocks as in TransNet. A fully connected layer reduces the feature dimension to $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$2 real values, after which a uniform quantizer with $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$3 bits per element produces the codeword $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$4 of length $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$5 bits. The paper gives the example $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$6 and $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$7, yielding a total codeword length of $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$8 bits (Liu et al., 16 Jul 2025).

The decoder first expands the received $w_{s,DL} \in \mathbb{C}^{N_{Tx}\times 1}$9-element codeword through a fully connected layer back to the transformer input dimension. A “conjugation layer” then injects the aligned uplink magnitude $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$0 and merges it with the reshaped downlink feature maps. Five residual blocks, each composed of two $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$1 convolutions with channels $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$2, refine the feature maps by exploiting local spatial correlation and uplink magnitude. A further $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$3 convolution reduces channels from $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$4, followed by reshaping to separate real and imaginary parts. Two “Single TransNet Decoder Layers” then apply self-attention and cross-attention for fine reconstruction, and a final reshape recovers $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$5 (Liu et al., 16 Jul 2025).

Training maximizes the average squared generalized cosine similarity (SGCS) over subbands:

$$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$6

Equivalently, the loss is

$$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$7

The description states that no additional regularization was used beyond weight decay in Adam (Liu et al., 16 Jul 2025). The reliance on SGCS rather than elementwise distortion indicates that the optimization target is aligned with eigenvector directional fidelity rather than raw Euclidean reconstruction.

6. Evaluation protocol and reported performance

The reported simulations use a ray-tracing simulator over $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$8 real-world city maps at $$H_{s,DL}^H H_{s,DL} w_{s,DL} = \lambda_{s,DL} w_{s,DL}, \qquad \|w_{s,DL}\|_2 = 1.$$9 downlink and $W_{DL}$0 uplink, with center gap $W_{DL}$1. The array and frequency configuration is $W_{DL}$2, $W_{DL}$3, $W_{DL}$4 subbands, and $W_{DL}$5 carriers. The training, validation, and test split is $W_{DL}$6k/$W_{DL}$7k/$W_{DL}$8k samples, and the test set includes $W_{DL}$9k samples each from $W_{BCE,DL} = f_{BCE}(W_{DL}),$0 unseen environments (Liu et al., 16 Jul 2025).

The performance metrics are SGCS, total feedback bits per sample, and model complexity in parameters and FLOPs. The key comparative claims reported in the source are summarized below.

Aspect	Dual-ImRUNet	Comparator / context
SGCS at ultra-low rate	$W_{BCE,DL} = f_{BCE}(W_{DL}),$1 at $W_{BCE,DL} = f_{BCE}(W_{DL}),$2 bits	Ubi-ImCsiNet requires $W_{BCE,DL} = f_{BCE}(W_{DL}),$3 bits for the same performance
Unseen-environment generalization	SGCS $W_{BCE,DL} = f_{BCE}(W_{DL}),$4 across $W_{BCE,DL} = f_{BCE}(W_{DL}),$5 unseen maps at $W_{BCE,DL} = f_{BCE}(W_{DL}),$6 bits when trained on a single environment	Outperforms Ubi-ImCsiNet by $W_{BCE,DL} = f_{BCE}(W_{DL}),$7 in SGCS and matches a model trained on $W_{BCE,DL} = f_{BCE}(W_{DL}),$8 maps
Complexity at $W_{BCE,DL} = f_{BCE}(W_{DL}),$9 bits	$$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$0K parameters, $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$1M FLOPs	Ubi-ImCsiNet: $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$2M parameters, $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$3M FLOPs

These results are used in the paper to support three claims: first, that the feedback overhead can be reduced by $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$4 compared with the state-of-the-art method while maintaining the same SGCS; second, that the IFA module improves robustness to unseen propagation environments; and third, that the network is substantially lighter than the cited baseline, using $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$5 of the model size and $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$6 of the FLOPs while still achieving higher accuracy at the stated operating point (Liu et al., 16 Jul 2025).

The robustness result is especially notable because the single-environment-trained model attains SGCS $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$7 across $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$8 unseen maps at $$(W_{IFA,DL}, b_{DL}) = f_{IFA}(W_{BCE,DL}, W_{Ben,DL}),$$9 bits and reportedly matches a model trained on $6$00 maps. This suggests that the preprocessing-induced normalization of sparsity structure is a major contributor to generalization, rather than scale alone in the training corpus.

7. Interpretation, scope, and relation to implicit CSI feedback

Within the framework described in the source, Dual-ImRUNet can be understood as a structured implicit CSI feedback system in which representation ambiguity, domain shift, and compression are handled by separate mechanisms. BCE addresses eigenspace non-uniqueness and strengthens usable cross-link correlation; IFA aligns angular-delay support to a shared canonical format; the transformer-based autoencoder then performs the low-rate mapping and reconstruction with explicit uplink assistance (Liu et al., 16 Jul 2025).

A potential misconception is that the method depends solely on learned reciprocity from raw uplink CSI. The architecture as presented does not do this. Instead, it preprocesses both uplink and downlink through eigenspace projection and circular-shift alignment before the decoder injects the aligned uplink magnitude $6$01. Likewise, the claim of “no extra rate” pertains specifically to IFA: the shifts are recovered at the BS by performing the same search on uplink, rather than by transmitting additional side information (Liu et al., 16 Jul 2025).

Another possible misunderstanding is that BCE changes the physical content of the eigenstructure. The paper explicitly states that BCE does not change eigenvalues, and the recovered $6$02 therefore yields the final eigenvectors after inverse IFA. In that sense, BCE is a representation-selection procedure within the principal eigenspace rather than an alteration of the eigenspectrum itself (Liu et al., 16 Jul 2025).

In summary, the method is presented as an integration of signal-domain priors and lightweight deep architecture for robust ultra-low-rate implicit CSI feedback. Its reported contribution lies in showing that bi-directional reciprocity can be made operational at only six bits per eigenvector set by combining eigenspace-based correlation enhancement, benchmark-guided alignment of sparse angular-delay patterns, and a transformer-plus-convolution backbone tuned to SGCS optimization (Liu et al., 16 Jul 2025).