Wi-Fi Channel State Information

• Wi-Fi CSI is a multidimensional descriptor that encodes amplitude and phase responses across antennas and subcarriers, reflecting environmental dynamics.
• Signal processing techniques such as phase estimation and Doppler analysis enable real-time activity recognition and precise localization.
• Machine learning and compression methods, including PCA and autoencoders, reduce data dimensionality for applications in healthcare, security, and IoT forensics.

Wi-Fi Channel State Information (CSI) is a multidimensional, physical-layer descriptor that encapsulates the complex baseband channel responses for each transmit–receive antenna pair and for each OFDM subcarrier in a Wi-Fi system. CSI encodes amplitude and phase information impacted by propagation effects such as multi-path, Doppler shifts, shadowing, and environmental changes. Because CSI measurements are highly sensitive to both static and dynamic alterations in the environment—including subtle human activity—they underpin numerous advances in wireless sensing, localization, device identification, privacy-aware healthcare monitoring, and secure key generation.

1. Mathematical Formulation and Statistical Properties

CSI is represented for the i-th receiver antenna and j-th subcarrier as a complex value:

$h_{ij} = |h_{ij}|e^{-j\phi_{ij}}$

where $|h_{ij}|$ is the channel amplitude and $\phi_{ij}$ is the signal phase. Collectively, the CSI for an OFDM Wi-Fi packet forms a tensor indexed over time, antennas, and subcarriers (Tan et al., 2017).

Statistical characterization begins by converting CSI complex vectors to amplitudes:

$$A_{k,n} = \sqrt{ \operatorname{Re}(\text{CSI}_{k,n})^2 + \operatorname{Im}(\text{CSI}_{k,n})^2 }$$

followed by normalization, e.g.,

$$\overline{A}_{k,n} = \frac{A_{k,n}}{N \cdot \sum_n}$$

or min–max mapping to $[0, 1]$. CSI evolution over time is modeled as a random process with (zero-mean) Gaussian increments:

$A_{k,n} = A_{k-1,n} + \Delta_{k,n}$

where $\Delta_{k,n}$ are i.i.d. increments; histogram and autocorrelation analyses show the increments are approximately Gaussian and nearly memoryless, whereas raw amplitudes possess temporal correlation (Tonini, 5 Nov 2024).

Quantization is then applied for algorithmic processing, either on amplitudes or their increments, facilitating representations as efficient finite-integer vectors.

2. Signal Processing and Subspace Tracking

Advanced CSI processing exploits not only amplitude but also phase and Doppler (frequency shift) components. Essential steps include:

• Phase Estimation: Tracking the time evolution of phase across subcarriers enables non-contact detection of small displacements, such as respiratory oscillations (0.5–2 cm causing $\sim0.25$–$1$ radian phase changes at 2.4 GHz) (Tan et al., 2017).
• Frequency/Doppler Analysis: Frequency shifts in CSI reflect macroscopic human motions. Techniques such as Short-Time Fourier Transform (STFT), Discrete Wavelet Transform (DWT), and Cross Ambiguity Function (CAF) are used for Doppler extraction, allowing filtering of stationary channels and highlighting moving or vital signs.

Subspace tracking formalizes the problem by decomposing the CSI tensor $H$ into a dynamic, human-modulated signal part $S$ and an additive noise part $N$:

$H = S + N$

Signal and noise subspaces are found via covariance analysis and eigendecomposition:

$$R = E\{H H^H\} = [U^s\; U^n] \begin{bmatrix} \Delta^s & 0 \ 0 & \Delta^n \end{bmatrix} [U^s \; U^n]^H$$

and the dynamics (e.g., differential unitarity $\hat{u}_i[k] = u_i^H[k] u_i[k-1]$) capture temporal variation specifically induced by human activities (Alloulah et al., 2018).

Recursive (forgetting-factor) and sliding-window (batch) estimators are employed for real-time covariance updates, trading off reactivity against noise robustness.

3. Machine Learning, Feature Extraction, and Compression

CSI’s high dimensionality and rich structure, spanning hundreds to thousands of subcarriers and MIMO spatial streams, necessitates dimensionality reduction and featurization strategies:

• Traditional Compression: Principal Component Analysis (PCA) retains a small number of main components explaining the majority of variance. Scalar quantization (e.g., Lloyd-Max) on these projections achieves substantial bit rate reductions with minimal information loss (e.g., two PCA components quantized to 3 bits sufficed for 2% F1-score degradation in presence detection) (Cerutti et al., 6 May 2025).
• Vector Quantization: Whole-CSI vectors are mapped to a codebook centroid. Deep learning–driven autoencoders and variational autoencoders (VAEs) enable learned, low-bit, nonlinear embeddings supportive of ultra-high compression ratios (up to 16000:1) with limited sensing loss, albeit with greater computational requirements.
• Deep Learning for CSI Feedback: For MIMO beamforming, autoencoders (e.g., EFNet) compress series of CSI matrices for feedback, reducing overhead by 80.77% and increasing net throughput by over 30% compared to 802.11ac, while preserving beamforming fidelity through channel attention modules and quantization (Qi et al., 8 Jul 2024). Temporal correlation in CSI can be exploited by feedback of angle differences rather than full parameters, guided by unified or parallel vector quantization and refined with DL-based temporal prediction (SimVP), optimizing both accuracy and overhead (Shin et al., 29 May 2025).
• Classifier Integration: Convolutional neural networks (CNNs), often in hybrid architectures with LSTM or RL policies, enable both activity (e.g., gesture, fall detection) and device (micro-CSI RF fingerprinting) identification at high accuracy, even under complex multipath and NLoS conditions (Kong et al., 11 Nov 2024).

4. Applications: Sensing, Authentication, Forensics, and Security

CSI-based methods are applied across multiple domains:

• Healthcare Monitoring: Through-wall vital sign measurement (by analyzing phase) and robust fall/activity detection (leveraging Doppler and matrix factorization, e.g., CAF, SVD, SRC classifiers, and sequential inference with HMMs) are demonstrated at residential scale (Tan et al., 2017).
• Human Sensing in Legacy Networks: Exploiting multiple links in non-dedicated (legacy) networks with RL-based link selection maximizes sensing accuracy by pruning irrelevant channels, achieving up to 96.5% accuracy in daily activity recognition, outperforming naive all-link or heuristically chosen link approaches while maintaining low computational latency (Guo et al., 2021).
• Localization and Positioning: CSI fingerprints (e.g., magnitude images or quantized vector sequences) are mapped to grid classes or continuous coordinates (regression) via CNNs or binary sequence matching. Binary-encoded “fingerprints” and Hamming/Manhattan distances enable sub-centimeter MAEs with storage requirements several orders of magnitude smaller than for classical ML models (Bölat, 2021, Tang et al., 3 Dec 2024).
• Copresence/Authentication and Security: CSI’s spatial decorrelation is leveraged for copresence verification (Next2You; EER < 4%) and secure key generation, wherein the min-entropy of jointly observed CSI ensures resilience against adversaries, and majority-vote binning plus Cascade error reconciliation yields secure bit rates of 1.2–1.6 bits/packet, realizing unique 128-bit keys in 20 s with device shaking (Fomichev et al., 2021, Avrahami et al., 2023).
• IoT Forensics and Storage: CSI enables a new category of forensic evidence, capturing occupancy and event detection in ambient networks. Tools like CSI Sniffer and ZTECSITool integrate directly in commercial devices, utilize amplitude-only features or higher-resolution (16-bit; up to 512 subcarriers, Wi-Fi 6), support lossy compression/scalar quantization (down to 5–8 bits), and offer graphical real-time visualizations for post hoc event investigation (Palmese et al., 2023, Wang et al., 20 Jun 2025). PCA+SQ and VAEs enable forensic-viable storage reduction with negligible sensing loss, enhancing the usability of long-term CSI logs (Cerutti et al., 6 May 2025).

5. Experimental Testbeds, Datasets, and Standardization

Comprehensive evaluation of CSI methods requires precise, phase-coherent datasets and flexible test environments:

• Testbeds: Distributed SDR testbeds with custom 802.11a software stacks (e.g., CP-aware denoising, per-OFDM symbol estimation via weighted averaging) enable passive, real-traffic CSI collection from unmodified COTS devices with full control over the estimation algorithm, facilitating robust machine-learning-driven localization and CSI quality enhancement (Zumegen et al., 10 Dec 2024).
• Dataset Initiatives: Modern public datasets cover Wi-Fi 6/802.11ax (up to 8192 points/packet) (Cominelli et al., 2023), 80 MHz 802.11ac with domain diversity and annotated NLOS/semi-anechoic measurements (Meneghello et al., 2023), and synchronized video/3D ground truth. Phase-coherent multi-antenna datasets (ESPARGOS) support advanced research in channel charting, providing access to calibrated CSI, RSSI, and external position data synchronized to <ms accuracy (Euchner et al., 29 Aug 2024).
• Dataset Design Implications: Empirical findings show that MIMO diversity and high spectral resolution are more beneficial to activity classification accuracy than increased bandwidth, and that training/testing in new environments (“domain shift”) introduces generalization challenges that motivate benchmark standardization efforts (Cominelli et al., 2023).

6. Algorithmic and Theoretical Foundations

CSI-based sensing exploits both the physics of propagation and information-theoretic/statistical principles:

• Information-Theoretic Structure: Deep learning methods reveal non-linear dependencies in remote CSI that are invisible to classical correlation analysis—mutual information approaches indicate that, despite vanishing linear correlation, the information content of a remote CSI sample approaches the entropy of the target, supporting remote beamforming and scheduling via DNNs (Jiang et al., 2018).
• Distance Metrics: For environment and movement recognition, explicit, interpretable measures (weighted Hamming distance) between quantized CSI vectors complement or rival “black-box” ML approaches, enabling algorithmic classifiers with provable performance under quantifiable channel variations (Tonini, 5 Nov 2024).
• Sequential Feedback and Error Correction: In DL-based feedback designs, joint vector quantization, recurrent prediction, and periodic difference encoding (with proper angular periodicity handling) enable feedback that robustly tracks the temporal evolution of beamforming parameters, minimizing error propagation and overhead (Shin et al., 29 May 2025).

7. Challenges and Forward Directions

Despite advances, several open challenges persist:

• Generalization and Robustness: Domain shift (environment/person/hardware variability), multi-user interference, temporal misalignment, and handling low data-rate signals remain limiting factors for universal algorithm design and deployment (Tan et al., 2017, Meneghello et al., 2023).
• Real-Time Constraints: Balancing algorithmic complexity (especially with deep models or RL frameworks) against the latency and resource constraints of embedded and IoT devices is an ongoing area of system-level research (Guo et al., 2021, Cerutti et al., 6 May 2025).
• Standardization and Benchmarks: The field’s fragmentation—with a plethora of device types, non-standard extraction tools, and evaluation metrics—motivates the need for widely-accepted datasets, open-source tools, and reporting standards (Cominelli et al., 2023, Wang et al., 20 Jun 2025).
• Future Integration: Prospective directions include tight integration of sensing and communication (JCAS, vehicular cooperative perception), advanced waveform optimization, privacy-preserving analytics, adversarial robustness for device authentication, and plug-and-play adaptation in forensic and healthcare IoT deployments (Tonini, 5 Nov 2024, Tan et al., 2017, Palmese et al., 2023).

In summary, Wi-Fi CSI offers a physically grounded, measurement-rich substrate for pervasive and unobtrusive sensing. Its exploitation for activity recognition, localization, device identification, copresence detection, and secure key generation is technically mature and validated by substantial experimental, statistical, and algorithmic research. Continued progress will depend on scalable, robust, and standardized tools and methodologies that bridge the gap between controlled experiments and complex, variable real-world deployments.