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A Subcarrier-Aware Approach for Robust Respiratory Monitoring with Commodity Wi-Fi

Pei Tang, Yunpeng Ge, Ivan Wang-Hei Ho

arXiv:2608.25612v1eess.SP

TL;DR

Conventional Wi-Fi respiratory sensing treats CSI subcarriers uniformly even though their breathing responses differ, limiting characterization of respiratory signals and pauses. This paper models subcarrier-dependent sensitivity, selects informative subcarriers through unsupervised clustering, and develops pause-aware estimation. The framework reports 97% breathing-rate accuracy, a 0.45 bpm MAE reduction versus baselines, and 88% pause-condition accuracy with a 1.33 bpm MAE reduction.

  • Problem

    Conventional CSI models assume identical subcarrier responses, while respiratory pauses violate continuous sinusoidal assumptions and remain insufficiently characterized.

  • Method

    The framework models heterogeneous subcarrier sensitivity, uses unsupervised clustering for informative subcarrier selection, and applies threshold-based pause detection.

  • Results

    97% breathing-rate estimation accuracy and a 0.45 bpm MAE reduction versus baselines were achieved; pause conditions yielded 88% accuracy and a 1.33 bpm MAE reduction.

  • Takeaways & Limitations

    The framework supports robust regular-breathing estimation and apnea-related pause detection for contact-free IoT healthcare monitoring.

  • Takeaways & Limitations

    The framework assumes a single stationary breathing source, simplified breathing dynamics, and empirically derived thresholds that may require recalibration across deployment environments.

Abstract

from arXiv · show

Wi-Fi sensing has emerged as a promising modality for contact-free respiratory monitoring in home healthcare due to its ubiquity. However, conventional approaches typically treat Channel State Information (CSI) subcarriers uniformly, neglecting their heterogeneous responses to breathing motions. To address this limitation, we propose a subcarrier-aware sensing framework that characterizes subcarrier-dependent respiratory sensitivities and exploits them for informative subcarrier selection. Based on the statistical properties of breathing-sensitive subcarriers, we further develop an unsupervised clustering-based breathing estimation method for robust respiratory monitoring. Experimental results show that the proposed method achieves 97% breathing rate estimation accuracy and reduces the mean absolute error (MAE) by 0.45 breaths per minute (bpm) compared with baseline methods. Furthermore, we extend the analysis to breathing-pause detection, which derives an amplitude-attenuation-based threshold mechanism. Under breathing pauses, the proposed method achieves an MAE of 1.6 bpm in breathing rate estimation. These results demonstrate the robustness and effectiveness of the proposed framework across different scenarios and its potential for contactless home healthcare monitoring.

I. INTRODUCTION

Contact-based respiratory monitoring is accurate but obtrusive, motivating contactless Wi-Fi sensing. The paper addresses subcarrier heterogeneity and breathing pauses through a subcarrier-aware framework for robust monitoring.

  • Contact-based respiratory sensors remain clinically accurate but are obtrusive, tethered, and unsuitable for continuous home monitoring.
  • Wi-Fi sensing offers ubiquitous, cost-effective, and minimally intrusive respiratory monitoring using CSI measurements of chest displacement.
  • Conventional CSI methods treat subcarriers uniformly, despite frequency-selective multipath producing heterogeneous responses to the same breathing motion.
  • Breathing pauses abruptly attenuate respiratory signals and violate continuous sinusoidal assumptions, while their impact on rate estimation remains insufficiently characterized.
  • The proposed framework models subcarrier-dependent sensitivity, selects informative subcarriers through unsupervised clustering, and extends sensing to pause scenarios.

III. MATHEMATICAL MODEL

The mathematical model explains why CSI subcarriers respond differently to breathing and motivates normalization for selecting informative signals. It distinguishes breathing-sensitive periodic responses from insensitive near-constant responses.

  • A. Subcarrier-Dependent CSI Model for Breathing Sensing: Dynamic multipath reflections and frequency-selective propagation cause different CSI subcarriers to exhibit varying sensitivities to breathing-induced chest movements.
  • A. Subcarrier-Dependent CSI Model for Breathing Sensing: The model separates all subcarrier responses into breathing-sensitive and breathing-insensitive sets.
  • A. Subcarrier-Dependent CSI Model for Breathing Sensing: Breathing-sensitive subcarriers show periodic chest-motion modulation, whereas insensitive subcarriers remain approximately constant apart from environmental noise.
  • A. Subcarrier-Dependent CSI Model for Breathing Sensing: Larger modulation amplitude indicates a stronger breathing signature, motivating subcarrier-aware processing.
  • B. Group-Wise Normalization: Group-wise normalization preserves sensitive periodic patterns, suppresses insensitive responses, and removes group-dependent baselines before subsequent processing.

1) Proposition 1 (Preservation of Breathing Periodicity):

Group-wise normalization preserves clear breathing patterns on sensitive subcarriers while compressing insensitive subcarriers toward constant levels. The resulting normalized feature relationships distinguish sensitive subcarriers for selection.

  • Proposition 1 (Preservation of Breathing Periodicity):: Sensitive subcarriers retain their sinusoidal breathing patterns after group-wise normalization.The sinusoidal structure remains unchanged, preserving breathing periodicity.
  • Proposition 2 (Compression to Near-Constant Values):: Insensitive subcarriers are compressed to near-constant values across groups.Their small fluctuations become negligible relative to the group-dependent scale.
  • Proposition 2 (Compression to Near-Constant Values):: Group-wise normalization eliminates the group-dependent baseline while separating fluctuating sensitive curves from near-straight insensitive curves.This visual distinction supports subsequent informative-subcarrier processing.
  • C. Statistical Properties for Breathing Subcarrier Selection: Sensitive subcarriers exhibit structured normalized relationships, with breathing energy proportional to squared STD and amplitude range proportional to STD.Highly sensitive subcarriers occupy larger feature-value regions, whereas less informative clusters concentrate near the origin.

D. Information Fusion of Amplitude and Phase

The analysis characterizes how breathing pauses distort sinusoidal amplitude and frequency estimation. Amplitude follows an attenuated trend with oscillations, while frequency estimation remains primarily informed by the breathing segment.

  • 1) Proposition 5 (Amplitude Attenuation):: Fitting a sinusoid across breathing and pause intervals produces amplitude estimates approximately linear in the breathing time ratio T_b/T.Non-integer-cycle truncation adds oscillations around the linear attenuation trend.
  • 1) Proposition 5 (Amplitude Attenuation):: Simulation results show fitted amplitudes oscillate around the linear attenuation trend, with smaller oscillations for longer observation windows.Real CSI observations further support attenuation during breathing pauses.
  • 2) Frequency Estimation:: The estimated breathing frequency is predominantly determined by the breathing segment, while the pause segment contributes limited bias.The pause segment provides no frequency-selective information in the theoretical analysis.
  • 2) Frequency Estimation:: Shorter observation windows reduce the average error per minute when the pause period is fixed.This finding motivates shorter windows for breathing estimation during pause episodes.

IV. METHODOLOGY

The methodology preprocesses CSI amplitude and calibrated phase, normalizes subcarrier signals, and identifies breathing-sensitive subcarriers through four-dimensional feature clustering. It then selects optimal subcarriers using sinusoidal fit quality.

  • IV. METHODOLOGY: The pipeline extracts CSI amplitude and calibrates phase before subsequent sensing analysis.Phase processing includes unwrapping and linear trend removal across subcarriers.
  • IV. METHODOLOGY: Group-wise normalization preserves breathing periodicity in sensitive subcarriers while compressing insensitive ones toward constant values.The normalized amplitude series are then used for feature construction.
  • 2) Four-Dimensional Feature Space:: Each subcarrier is represented by a four-dimensional feature vector including autocorrelation periodicity and phase standard deviation.The feature structure enables subsequent unsupervised clustering.
  • IV. METHODOLOGY: K-means clustering with K=3 separates subcarriers into high-, medium-, and low-sensitivity groups.The cluster with the highest average breathing-band energy defines the sensitive set H_sens.
  • IV. METHODOLOGY: Within the sensitive set, the optimal subcarrier is selected by maximizing the sinusoidal fit coefficient of determination R^2.This selection is performed after fitting a sinusoidal model to each candidate subcarrier.

C. Breathing Rate Estimation via Information Fusion

Breathing-rate estimation fuses amplitude and phase information by selecting the more reliable modality for an optimally chosen subcarrier. Pause detection uses amplitude attenuation and a calibrated threshold, with shorter windows motivated for pause episodes.

  • C. Breathing Rate Estimation via Information Fusion: Optimal subcarrier selection is performed separately for amplitude and phase, and their estimates are fused for robust breathing-rate estimation.The final estimate uses the modality with higher fit quality.
  • C. Breathing Rate Estimation via Information Fusion: The evaluation reports breathing-rate accuracy and mean absolute error averaged over all test samples.Estimated and ground-truth breathing rates define the reported metrics.
  • D. Detection Method of Breathing Pauses: Amplitude attenuation provides the basis for threshold-based pause detection, while frequency analysis supports breathing-rate estimation during pauses.The method adopts a 3-second sliding window because shorter windows reduce estimation error in simulations.
  • D. Detection Method of Breathing Pauses: A pause is declared when estimated amplitude falls below η·A_ref, using η=0.3 relative to a normal-breathing reference.The reference amplitude is computed from pause-free calibration data.

E. Computational Complexity and Real-Time Performance

The framework is evaluated across normal breathing, pause conditions, and deployment scenarios. It maintains strong estimation performance, while pause detection depends on an empirical amplitude threshold.

  • Computational Complexity: O(N·K·G) overall complexity is linear in the input size, dominated by group-wise normalization, feature extraction, and K-means clustering.Here, N is the number of subcarriers, K the number of clusters, and G the number of averaged time groups.
  • Real-Time Performance: 3.26 seconds of average processing time is required for one minute of CSI data, with approximately 1 ms per packet and memory below 100 MB.Measurements used MATLAB on a PC with an Intel i7-13700KF CPU and 16 GB RAM.
  • Normal Breathing: 97% average accuracy and 0.48 bpm MAE are achieved under normal breathing, outperforming the second-best algorithm by approximately 2.8% accuracy and 0.45 bpm MAE.Traditional FFT and Savitzky-Golay methods remain below 92% accuracy and above 1 bpm MAE, whereas subcarrier-aware methods exceed 94% accuracy and stay below 1 bpm MAE.
  • Public Dataset: 97% accuracy and 0.4 bpm MAE are maintained on a public amplitude-only dataset, indicating consistent performance across the collected and public datasets.Diverse is excluded because the public dataset provides only amplitude information.
  • Breathing Pauses: η=0.3 yields a favorable pause-detection trade-off, reducing FDR to 8% while maintaining MDR at approximately 8%, with both metrics below 10%.Further lowering η to 0.25 raises FDR to 9% and MDR sharply to 22%; threshold recalibration may be needed across deployment scenarios.
  • Breathing Pauses: 1.6 bpm MAE and 88% accuracy are achieved during detected breathing pauses, outperforming all baseline methods by over 9%.WiRe ranks second with 78% accuracy and 3 bpm MAE, while other methods have MAEs exceeding 5 bpm.

D. Impact of Different Postures

The method is tested across lying postures, distances, framework components, and parameter settings. Results show strong posture and distance robustness, while ablations identify adaptive subcarrier selection as especially important.

  • Impact of Different Postures: 96% average accuracy and 0.63 bpm average MAE are achieved across right-side, left-side, supine, and prone postures.The method outperforms WiRe by 1.6% accuracy and 0.24 bpm MAE.
  • Impact of Testing Distances: 84% accuracy is maintained at 20 m, compared with 65% for WiRe, while the average accuracy across methods falls below 60% at that distance.The proposed method remains above 90% accuracy within 10 m and consistently exceeds the across-method average.
  • Ablation Study: 15% accuracy is lost when one arbitrarily selected subcarrier replaces adaptive selection, compared with drops of 1.3% without normalization and 2.4% when sinusoidal fitting is replaced by FFT.Removing any framework module degrades performance.
  • Parameter Analysis: 97% accuracy is obtained with a one-second grouping window, exceeding the 94%, 89%, and 89% results for 0.4-, 2-, and 4-second windows.The one-second window is therefore used throughout the work.
  • Parameter Analysis: Removing any one of the four selected features increases MAE by over 0.13 bpm, confirming that each feature contributes meaningfully to performance.The evaluated feature set is [σ_n, E, U_n, σ_ϕ,n].
  • Parameter Analysis: η=0.3 generalizes to a new indoor environment and two new volunteers, producing FDR of 7% and MDR of 4% without recalibration.The authors still recommend recalibration when deployment scenarios differ.

APPENDIX A PROOF OF THE GROUP ERROR BEHAVIORS

The appendix explains why group-wise normalization preserves respiratory structure more effectively than global normalization and supports clustering sensitive subcarriers by normalized feature relationships.

  • Group-Wise Normalization: Group-wise normalization eliminates the group-dependent baseline b_m, reducing static environmental interference without affecting breathing-induced dynamic components.It also relativizes amplitudes by removing the group-wise minimum while preserving the periodic breathing structure.
  • Normalization Comparison: Global normalization uses a denominator determined across the entire observation matrix, allowing extreme values and large-amplitude interference to compress respiration-induced fluctuations.This explains why group-wise normalization is preferred for the proposed framework.
  • Normalization Comparison: For the sensitive subcarrier, global normalization produces substantially smaller amplitude fluctuations than group-wise normalization.The comparison in Fig. A.1 is consistent with the analytical explanation for using group-wise normalization.
  • Assumptions: The theoretical analysis assumes breathing modulation dominates noise on sensitive subcarriers, noise remains small relative to insensitive-subcarrier baselines, and noise variance is consistent across subcarriers.These assumptions define the conditions under which the derived feature relationships are analyzed.
  • Feature Relationships: Sensitive subcarriers concentrate at larger normalized feature values along ˜R∝˜σ and ˜E∝˜σ^2, whereas insensitive subcarriers cluster near the origin.All normalized features lie in the [0, 1] interval, and insensitive-subcarrier features are primarily noise-driven.

B.2 Impact of Motions on Feature Relationships

Motion interference broadens the feature relationship’s variability while preserving its qualitative trend. The appendix also derives an approximately linear link between fitted amplitude and the breathing-time ratio during pauses.

  • Impact of Motions on Feature Relationships: Most subcarriers remain close to the quadratic feature trend under walking-person interference, indicating qualitative robustness of the theoretical relationship.The 90% coverage band becomes notably wider than in the quiet condition, reflecting additional variability from motion interference.
  • Theoretical Analysis of Breathing Pauses: The estimated sinusoidal amplitude exhibits an approximately linear relationship with the breathing-time ratio T_b/T when signals contain both breathing and pause periods.Oscillations arise from non-integer-cycle truncation, represented by an oscillatory correction term.
  • Theoretical Analysis of Breathing Pauses: The pause-related amplitude relationship provides the analytical basis for estimating breathing time from signals containing interruptions.The result follows from minimizing the sinusoidal-fitting objective under a normalized baseline assumption.

1) Linear Approximation with Oscillation Correction:

The analysis shows that fitted amplitude decreases approximately linearly with the fraction of the observation window containing breathing, with oscillatory correction effects. The approximation improves for longer windows, while sufficient breathing duration supports reliable estimation.

  • 1) Linear Approximation with Oscillation Correction:: The dominant amplitude behavior is linear in the breathing-time ratio T_b/T, with oscillatory correction from non-integer-cycle truncation.The approximation error is bounded by terms involving the observation and breathing durations.
  • 1) Linear Approximation with Oscillation Correction:: As the observation window length T increases, the linear amplitude approximation becomes increasingly accurate.The oscillatory correction decreases with longer windows.
  • 1) Linear Approximation with Oscillation Correction:: When the breathing duration contains an integer number of respiratory cycles, the amplitude relation simplifies and estimation error is minimized.The integer-cycle condition is T_b = n/r_b.
  • 1) Linear Approximation with Oscillation Correction:: When breathing duration approaches zero, the signal approaches a pure pause, highlighting the need for sufficient breathing duration for reliable parameter estimation.This establishes a practical boundary for fitting sinusoidal parameters.
  • 1) Linear Approximation with Oscillation Correction:: The derived attenuation relation A_hat/A ≈ T_b/T provides the theoretical basis for amplitude-threshold-based breathing-pause detection.Respiration-belt and real CSI observations approximately follow the same linear attenuation trend with oscillatory deviations.

C.2 Frequency Estimation

The frequency-estimation analysis distinguishes the roles of breathing and pause segments: breathing provides frequency-selective information, whereas pauses contribute a frequency-flat constraint. Simulations confirm that the true breathing frequency remains the dominant minimum across observation windows.

  • C.2 Frequency Estimation: The breathing frequency estimate is predominantly determined by the breathing segment, while the pause segment introduces only limited bias.This is the central conclusion of Proposition 6.
  • C.2 Frequency Estimation: During pauses, optimizing amplitude to zero makes the fitting error equal for any candidate frequency, so pauses provide no frequency-selective information.The pause segment contributes only a weak, frequency-flat constraint to the overall optimization.
  • C.2 Frequency Estimation: During breathing, the integrated squared error is minimized when the candidate frequency equals the true breathing frequency.The error grows as the candidate frequency deviates from the true frequency and oscillates because of beat-frequency effects.
  • C.2 Frequency Estimation: Across observation-window lengths, the average error per unit time has a pronounced minimum at the true breathing frequency of 0.3 Hz.The simulations also reproduce beat-frequency oscillations with local minima at integer multiples of 1/T_b from the true frequency.
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