CSI-Ratio Denoising Methods

• CSI-Ratio Denoising is a method that exploits the ratio of channel state measurements from multiple antennas to cancel noise and mitigate phase distortions.
• It employs model-based and deep learning approaches, such as autoencoders and score-based networks, to improve signal reliability for sensing and communication applications.
• Practical implementations show enhanced sensing range, improved NMSE performance, and robust CSI feedback even under challenging wireless conditions.

Channel State Information (CSI) ratio denoising encompasses algorithmic and architectural strategies that improve the reliability of CSI measurements or their downstream use by exploiting statistical properties, cross-antenna correlations, learned priors, or explicit knowledge of channel-error ratios. These technologies target the inherent noise, phase distortions, and non-idealities present in practical wireless systems—ranging from WiFi-based device-free sensing to massive MIMO feedback and robust hybrid beamforming—by leveraging the ratio structure (across antennas or signal/noise) and advanced denoising paradigms, including signal-model-driven preprocessing, deep learning autoencoders, diffusion/score-based approaches, and plug-and-play denoisers. CSI-ratio denoising is central to both sensing (such as non-contact vital sign monitoring) and communication (compression, feedback, and rate maximization) tasks.

1. Foundational Principles of CSI-Ratio Denoising

CSI ratio denoising exploits the structure of measured channel coefficients—often represented as $H(f,t)$ for subcarrier $f$ at time $t$—to suppress noise, hardware-induced artifacts, and ambient interference. In systems with two (or more) receive antennas connected to a common oscillator, the ratio of their raw CSI measurements,

$$R(f,t) = \frac{\widetilde H_1(f,t)}{\widetilde H_2(f,t)},$$

permits exact cancellation of time-varying phase offsets and most amplitude distortions, since these affect both antennas equally. This leaves a signal $R(f,t)$ in which the residual noise is substantially reduced, and dynamic channel fluctuations due to e.g., human micro-motions or environmental changes remain highly salient. The denoising step, fundamental to this method, is thus effectively performed by the division operation at the signal level, prior to any higher-level temporal or spectral analysis (Zeng et al., 2019).

Recently, deep learning frameworks have extended the denoising concept beyond pairwise antenna ratios to statistical or data-driven priors, autoencoder bottlenecks, or diffusion-driven score matching functions, thus enabling denoising in the presence of arbitrary noise models, partial observations, and complex channel distributions (Rizzello et al., 2021, Chen et al., 2022, Li et al., 10 Nov 2025).

2. System Models and Noise Sources

The typical CSI measurement model incorporates several sources of corruption:

• Additive Noise: Modeled as Gaussian perturbations, e.g.,

$$\widetilde H = H + N,\quad N\sim\mathcal{CN}(0,\sigma^2 I),$$

capturing estimation errors, quantization, and thermal effects.

• Time-Varying Phase Offsets: Due to lack of transceiver synchronization, represented as multiplicative rotations $e^{-j\theta_{\rm off}(t)}$ in the baseband signal.
• Multipath Effects: Superposition of multiple paths, separating into static $H_s(f)$ and dynamic $A e^{-j 2\pi d(t)/\lambda}$ components.

In WiFi-based device-free sensing, direct use of single-antenna CSI suffers from such noise, rendering fine-movement detection impractical. However, forming the antenna ratio nulls common-phase and amplitude errors, stabilizing the usable phase information (Zeng et al., 2019). In MIMO feedback and hybrid beamforming, noise manifests as unknown error-levels, typically parameterized by a "CSI ratio" $\delta_E^2$ quantifying the SNR of the observed versus true CSI (Li et al., 10 Nov 2025).

3. Algorithmic and Deep Learning Approaches

3.1 Signal-Processing with CSI Ratios

In respiration sensing, the CSI ratio $R(f,t)$ is mapped into amplitude/phase (or I/Q) projections, enabling robust detection of periodic micro-movements. The optimal combination axis $\theta^\star$ is determined by maximizing the breathing-to-noise ratio (BNR) after projecting onto a trace

$y_\theta(t) = \Re\{R(t) e^{-j\theta}\}.$

Subcarriers with suboptimal BNR are suppressed, and cross-carrier fusion yields enhanced detection and robustness to posture and range, with ambient and device noise significantly attenuated by the division and filtration operations (Zeng et al., 2019).

3.2 Autoencoder-Based Unsupervised Denoising

Autoencoder frameworks for FDD feedback (e.g., "Learning the CSI Denoising and Feedback Without Supervision") use a convolutional encoder–decoder with a tight latent bottleneck. The encoder $f_\theta$ compresses observed real–imag CSI tensors, and the decoder $g_\phi$ reconstructs the channel. Training proceeds solely with noisy uplink data, minimizing mean-squared error (MSE) between reconstructed and observed noisy input,

$$\mathcal{L}(\theta,\phi) = \mathbb{E}_{\widetilde H_{\rm UL}} \|g_\phi(f_\theta(\widetilde H_{\rm UL})) - \widetilde H_{\rm UL}\|_F^2,$$

with the compression bottleneck acting as an implicit denoiser. The encoder can be offloaded to the mobile terminal, requiring no terminal-side training, and the resulting codewords efficiently transmitted to the base station for high-fidelity downlink CSI recovery (Rizzello et al., 2021).

3.3 Plug-and-Play Denoisers and One-for-All Models

CSI-PPPNet demonstrates a linear-compression plus DL-denoiser approach, where the projection $A$ at the user equipment (UE) produces compressed noisy CSI $y = Ah+n$. The BS reconstitutes CSI with plug-and-play priors: alternating between a least-squares gradient step and a fixed CNN denoiser $D_\sigma$, trained agnostic to $A$ or compression ratio. This results in a one-for-all architecture capable of handling variable compression rates and matrix projections without retraining, supporting resource-constrained UEs and diverse deployment scenarios (Chen et al., 2022).

3.4 Score-Based Denoising Networks

Score-based CSI denoising (as instantiated in DeBERT) leverages a noise-conditional score network (DSN) that directly estimates the gradient of the log-likelihood (score) of the imperfect CSI conditioned on known error level $\delta_E^2$:

$$\nabla_{\widetilde H} \log p(\widetilde H|H, \delta_E^2) = -\frac{\widetilde H - H}{\delta_E^2}.$$

DeBERT utilizes a BERT-style transformer, conditioned on $\delta_E^2$, to generate a denoising direction and per-stream step size, supporting robust, single-step recovery across a wide dynamic range of SNR/error regimes with no performance collapse at SNR extremes (Li et al., 10 Nov 2025).

4. Practical Implementations and Performance

Key implementation steps vary according to end-use and system scenario, but core elements include:

• Antenna ratio computation for immediate denoising in sensing; explicit amplitude/phase or I/Q projection with dynamic axis selection for maximizing SNR (Zeng et al., 2019).
• Autoencoder training on noisy uplink CSI only (no clean ground truth needed), with encoder/decoder split, codeword quantization, and efficient binary feedback (Rizzello et al., 2021).
• Universal CNN denoiser trained for additive noise removal, insensitive to compression ratio or projection specifics, yielding strong NMSE and cosine similarity at low storage cost (Chen et al., 2022).
• Transformer-based score network (DeBERT) mapping noisy CSI and explicit error-levels to denoised outputs via supervised multitask loss, maintaining normalized reconstruction error (NRE) below 0.1 across $[-10,10]$ dB noise levels and recovering beamforming sum-rates within 5% of the perfect-CSI oracle, even at challenging error regimes (Li et al., 10 Nov 2025).

The following table summarizes performance highlights for representative CSI-ratio denoising techniques:

Approach	Scenario	Key Metric	Typical Gain / Result
CSI Ratio + I/Q Projection	Respiration Sensing	Sensing Range	Extends detection from ∼3m→8–9m
Autoencoder Denoising	FDD Feedback	Median NMSE	$-15.6$ dB vs $-10$ dB (IDFT baseline)
Plug-and-Play CNN Denoiser	Massive MIMO	NMSE (CR=1/4)	$-16.32$ dB vs $-10.42$ dB (TVAL3)
Score-Based DeBERT	HBF/DeepMIMO	NRE, Sum-Rate	$<0.1$ NRE; $\leq 5\%$ rate loss at $-10$ dB

5. Applications Across Communication and Sensing

• Device-Free Sensing: CSI ratio denoising enables real-time, through-wall respiration and device-free presence detection at distances up to 8–9 meters, outperforming single-antenna amplitude/phase approaches by a factor of $>2$ in range and an order-of-magnitude in error rates (Zeng et al., 2019).
• Massive MIMO Feedback: Autoencoder and plug-and-play denoising frameworks provide scalable, quantization-robust CSI feedback and recovery, achieving high CSI reconstruction accuracy and near-optimal downlink rates under strict compression and feedback constraints (Rizzello et al., 2021, Chen et al., 2022).
• Hybrid Beamforming: Score-based denoisers like DeBERT enable reliable channel recovery under arbitrary error variances, ensuring hybrid beamforming systems retain peak spectral efficiency independent of CSI imperfection (Li et al., 10 Nov 2025).

6. Limitations, Comparative Analysis, and Future Directions

CSI-ratio denoising is highly effective for hardware/oscillator-coupled antenna arrays and scenarios where common-mode noise dominates. For fully spatially separated or independently clocked nodes, the ratio assumption and corresponding denoising effect may not hold. Plug-and-play and score-based frameworks address broader noise models but can incur increased computational demand at the base station or require pretraining on large, representative datasets.

Autoencoder systems with offloaded encoders are sensitive to mismatch between uplink and downlink distributions if the channel environment becomes nonisomorphic (e.g., due to different scattering geometries), potentially reducing denoising efficacy (Rizzello et al., 2021). One-for-all models may be suboptimal compared to retrained baselines when the statistics of the downlink depart from those seen during denoiser training (Chen et al., 2022).

A continuing research focus is the integration of explicit channel-model knowledge, adaptive denoising conditioned on real-time noise estimates, and the incorporation of higher-order or temporal context—potentially via graph neural networks or advanced transformer architectures—to further improve robustness, scalability, and applicability in rapidly evolving wireless environments (Li et al., 10 Nov 2025).

• FarSense: pushing the range limit of WiFi-based respiration sensing with CSI ratio of two antennas (Zeng et al., 2019)
• Learning the CSI denoising and feedback without supervision (Rizzello et al., 2021)
• CSI-PPPNet: a one-sided one-for-all deep learning framework for massive MIMO CSI feedback (Chen et al., 2022)
• GNN-enabled robust hybrid beamforming with score-based CSI generation and denoising (Li et al., 10 Nov 2025)