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TensorBeat: Tensor Decomposition for Monitoring Multi-Person Breathing Beats with Commodity WiFi

Xuyu Wang, Chao Yang, Shiwen Mao

arXiv:1702.02046v1cs.CE

TL;DR

Existing approaches often require wearable or specialized equipment, and multi-person breathing estimation remains challenging. TensorBeat uses CSI phase differences and tensor decomposition with commodity WiFi to estimate multiple people’s breathing rates; experiments report satisfactory performance across three indoor environments.

  • Problem

    Contact-free, long-term breathing monitoring is needed because existing approaches can require wearable or specialized equipment, while multi-person estimation remains challenging.

    Source: §1 · p. 2

  • Method

    TensorBeat creates a CSI tensor from antenna-pair phase differences and uses CP decomposition, stable signal matching, and peak detection to estimate multiple people’s breathing rates.

    Source: §1 · p. 2

  • Results

    Across three indoor environments, extensive experiments indicate that TensorBeat achieves satisfactory performance for multiple-person breathing estimation.

    Source: §1 · p. 3, §6 · p. 26

  • Takeaways & Limitations

    The study supports using CSI phase differences with tensor decomposition for multi-person breathing estimation on commodity WiFi.

    Source: §1 · p. 2, §6 · p. 26

    The Hankelization proof assumes noise is negligible.

    Source: §3.2.2 · p. 10

Abstract

from arXiv · show

Breathing signal monitoring can provide important clues for human's physical health problems. Comparing to existing techniques that require wearable devices and special equipment, a more desirable approach is to provide contact-free and long-term breathing rate monitoring by exploiting wireless signals. In this paper, we propose TensorBeat, a system to employ channel state information (CSI) phase difference data to intelligently estimate breathing rates for multiple persons with commodity WiFi devices. The main idea is to leverage the tensor decomposition technique to handle the CSI phase difference data. The proposed TensorBeat scheme first obtains CSI phase difference data between pairs of antennas at the WiFi receiver to create CSI tensor data. Then Canonical Polyadic (CP) decomposition is applied to obtain the desired breathing signals. A stable signal matching algorithm is developed to find the decomposed signal pairs, and a peak detection method is applied to estimate the breathing rates for multiple persons. Our experimental study shows that TensorBeat can achieve high accuracy under different environments for multi-person breathing rate monitoring.

1. INTRODUCTION

TensorBeat targets contact-free, long-term multi-person breathing monitoring using commodity WiFi. It processes CSI phase differences with tensor decomposition and reports high accuracy and success rates across varied indoor environments.

1. INTRODUCTION

  • Prior work had not fully exploited CSI phase because transmitter–receiver asynchrony causes random phase fluctuation, while multi-person breathing estimation remained challenging.Source: §1 · p. 2
  • TensorBeat forms a three-dimensional CSI tensor from antenna-pair phase differences, applies CP decomposition, matches randomly indexed signals with stable roommate matching, then detects peaks per person.The pipeline preprocesses phase data through calibration and Hankelization before decomposition.Source: §1 · pp. 2–3
  • For stationary people, phase difference is reported as stable, preserves breathing periodicity, and is more robust than amplitude under link attenuation, obstacles, and multipath.Source: §1 · p. 2
  • Five persons monitored over six months across a computer laboratory, through-wall scenario, and long corridor yielded high accuracy, high success rates, and robustness across environmental parameters.The evaluation used commodity 5 GHz WiFi devices.Source: §1 · p. 3
  • The authors identify two firsts: phase difference for multi-person breathing-rate estimation and tensor decomposition for RF-sensing vital-sign monitoring.Source: §1 · p. 3

2. PRELIMINARIES AND PHASE DIFFERENCE INFORMATION

The section introduces tensor and CSI preliminaries, then motivates antenna-pair phase differences as a more stable signal for breathing estimation. It also explains why mixed multi-person breathing signals challenge direct peak and FFT-based estimation.

2.1. Tensor Decomposition Preliminaries

  • A tensor is a multidimensional array whose dimensions are modes; tensor decomposition can extract latent features, and CP is selected for its unique solution.The passage notes that higher-order tensors face computational challenges as their order increases.Source: §2.1 · pp. 3–4

2.2. Channel State Information Preliminaries

  • CSI provides subcarrier-level channel information, but the Intel 5300 driver supplies CSI for only 30 of 56 subcarriers on a 20 MHz channel.Source: §2.2 · p. 5
  • Reflections from multiple people’s chests, usually treated as harmful multipath, can be used to estimate their breathing rates simultaneously.Source: §2.2 · p. 5

2.3. Phase Difference Information

  • Measured CSI phase is random across packets, while prior calibration techniques yield stable phase or zero-mean phase difference that the paper says is not useful for breathing estimation.The proposed phase-difference approach relies on shared errors across adjacent antennas being removed.Source: §2.3 · pp. 5–6
  • Phase differences from 500 packets cluster between 330° and 340°, while single-antenna phases are nearly uniform across 0°–360°.The paper attributes the greater stability to shared phase-error terms canceling between adjacent antennas.Source: §2.3 · p. 6, Figure 1 · p. 7
  • Independent chest movements make the aggregate multi-person breathing signal insufficiently periodic for direct peak-to-peak detection.The passage contrasts this with the noticeable periodicity of a single-person signal.Source: §2.3 · p. 6
  • For three people, the FFT curve shows only two peaks and misses the third rate, whereas the single-person estimate is 0.2 Hz.The paper says FFT needs a larger window for improved frequency resolution.Source: §2.3 · p. 7

3.1. TensorBeat System Architecture

TensorBeat builds a CSI tensor from WiFi phase differences and decomposes it to estimate multiple people’s breathing signals. Its pipeline matches decomposed signals into person-specific pairs before estimating breathing rates.

3.1. TensorBeat System Architecture

  • TensorBeat forms a CSI tensor from phase differences across 60 subcarriers and two antenna pairs, using Hankel matrices to expand the data into three dimensions.The design relies on stable phase differences from consecutive packets in stationary settings to extract periodic breathing signals.Source: §3.1 · p. 7
  • TensorBeat’s higher-dimensional CSI representation is intended to separate different breathing signals into distinct clusters.The paper compares this strategy to kernel methods such as SVM and to multiple hidden layers in deep learning.Source: §3.1 · pp. 7–8
  • The system extracts CSI phase differences, calibrates and Hankelizes them, applies CP decomposition, matches signal pairs, then estimates each person’s rate by peak detection.The matching preference lists use DTW values computed from autocorrelation signals.Source: §3.1 · pp. 8–9

3.2. Data Preprocessing

Preprocessing removes unwanted components from CSI phase differences and converts the calibrated data into Hankel matrices for tensor construction. The Hankel rank provides a way to estimate the number of breathing signals when noise is negligible.

3.2.1. Data Calibration.

  • Calibration removes the DC component with a Hampel-filter trend subtraction and reduces high-frequency noise before rate estimation.The trend filter uses a 150-sample window and 0.001 threshold; a 6-sample window and 0.01 threshold reduce high-frequency noise.Source: §3.2.1 · pp. 9–10
  • The calibration example shows DC components and high-frequency noise removed, leaving similar low-noise subcarrier signals across 600 packets.The calibrated signals are then used to estimate multiple people’s breathing rates.Source: §3.2.1 · p. 10, Figure 5 · p. 10

3.2.2. Hankelization.

  • Hankelization maps calibrated phase differences from each subcarrier into matrices, which are combined across 60 subcarriers to form a three-dimensional CSI tensor.For N packets, the matrix dimensions satisfy N = I + J − 1; the experiments use N = 599 and I = J = 300.Source: §3.2.2 · p. 10
  • When noise is negligible, a Hankel matrix generated by R breathing signals has rank 2R, indicating that 2R components are needed to separate them.With noise, the first 2R weighted components remain stronger than the rest when signal-to-noise ratio is not very low, supporting separation from white noise.Source: §3.2.2 · pp. 10–12

3.3. Canonical Polyadic Decomposition

TensorBeat approximates the CSI tensor with rank-one components using CP decomposition and estimates its factor matrices with alternating least squares. The paper argues that this decomposition is unique for its constructed tensor, while the resulting signals require matching because their indices are random.

3.3. Canonical Polyadic Decomposition

  • CP decomposition approximates the CSI tensor as a sum of 2R rank-one tensors, with factor vectors spanning its three dimensions.The component count follows from the Hankel-rank result that R breathing signals yield 2R components.Source: §3.3 · p. 12
  • With 2R components specified, TensorBeat applies alternating least squares to minimize squared reconstruction error by iteratively solving for factor matrices.Fixing two matrices makes each update a linear least-squares problem.Source: §3.3 · p. 12
  • For the proposed CSI tensor χ with rank 2R, CP decomposition is unique; TensorBeat uses matrix A = [a1, a2, …, a2R] as decomposed signals to estimate multiple breathing rates.For three people (R = 3), decomposition yields six signals, with similar pairs 1 and 2, 3 and 5, and 4 and 6. The output signals are randomly indexed, so the system must identify each person’s signal pair.Source: §3.3 · p. 13

3.4. Signal Matching Algorithm

TensorBeat pairs the randomly indexed CP-decomposed signals by comparing their autocorrelations with dynamic time warping (DTW) and applying stable roommate matching. Autocorrelation strengthens periodicity, while DTW accommodates shifts between signals.

3.4. Signal Matching Algorithm

  • The matching algorithm pairs the 2R randomly indexed decomposed signals by strengthening periodicity with autocorrelation, measuring pairwise similarity with DTW, and applying stable roommate matching.DTW values define each signal’s preference list for other signals.Source: §3.4 · p. 13, §3.4.2 · p. 16

3.4.1. Autocorrelation and Dynamic Time Warping.

  • Autocorrelation makes decomposed signals more clearly periodic and increases their length from 300 to 600 samples, aiding peak detection and reducing phase shifts.The method is used because decomposed signals may have phase shifts and nonalignment.Source: §3.4.1 · p. 14
  • DTW aligns time series to measure their distance despite shifts, unlike pointwise Euclidean distance; downsampling reduces its computational cost.The computed DTW value has time complexity O(N'^2).Source: §3.4.1 · p. 15
  • For downsampled autocorrelation signals, the 4–6 pair has DTW 3.65 versus 13.7 for the 4–3 pair, making 4 and 6 more likely to belong to the same person.The paper also notes that center regions have higher similarity than boundaries, reducing phase-shift effects.Source: §3.4.1 · pp. 15–16, Figure 8 · p. 16

3.4.2. Stable Roommate Matching.

  • Signals rank all others by inverse DTW distance, and stable roommate matching seeks pairs without a mutually preferred alternative.The algorithm uses proposal and rejection steps, with a second cycle-processing step for more challenging cases; its complexity is O(R^2).Source: §3.4.2 · pp. 16, 18

3.5. Breathing Rate Estimation

TensorBeat fuses matched decomposed signal pairs and uses their autocorrelation peaks to estimate each person’s breathing rate. This avoids FFT’s window-size trade-off and uses smoothed curves to simplify peak detection.

3.5.2. Peak Detection.

  • Peak detection is chosen over FFT because FFT’s frequency resolution depends on window size, which trades accuracy against time-domain resolution.The paper also notes FFT’s limitations for multi-person scenarios.Source: §3.5.2 · p. 18
  • Averaging each matched signal pair reduces variance while preserving its period, and autocorrelation increases the data length from 300 to 600, adding peaks for estimation.The fusion results show three smoothly decomposed signals with different periods.Source: §3.5.2 · p. 18, Figure 9 · p. 19, Figure 10 · p. 19
  • A 7-sample moving window identifies peaks in each fused signal’s autocorrelation; the median peak-to-peak interval gives period T_i, and breathing rate is 60/T_i.The method relies on Hankel-matrix and CP-decomposition smoothing to reduce fake peaks.Source: §3.5.2 · p. 19

4. EXPERIMENTAL STUDY

TensorBeat was evaluated with up to five stationary people over six months in laboratory, through-wall, and corridor settings. Results show accurate single-person estimates across settings, with multi-person performance varying by participant count, sampling rate, window size, and positioning.

4.1. Experiment Configuration

  • Experiments used up to five stationary people over six months in a laboratory, through-wall, and corridor scenarios; multi-person trials were conducted in the laboratory.Single-person ground truth used a NEULOG Respiration device; multi-person ground truth used a metronome smartphone application with 1 bpm accuracy.Source: §4.1 · p. 20, Figure 11 · p. 21

4.2. Performance of Breathing Estimation

  • Maximum single-person estimation error was below 0.9 bpm across all three scenarios; median-test errors were below 0.19 bpm in the laboratory, 0.25 bpm in the corridor, and 0.35 bpm through-wall.Laboratory performance was better, which the authors attribute to its smaller space and stronger breathing signal than in the longer-distance or wall settings.Source: §4.2 · pp. 20–21, Figure 12 · p. 21
  • About 96% of single-person test data, 93% of two- and three-person data, and 62% of five-person data had estimation error below 0.5 bpm.Performance generally worsened as the number of breathing signals increased; the authors attribute this to greater distortion in the mixed received signal.Source: §4.2 · p. 22, Figure 13 · p. 22
  • The five-person success rate was about 82.4%, and success rates decreased as participant count increased.The metric counts repeated experiments in which the maximum breathing-rate error is below 2 bpm; low SNR and overlapping breathing rates are discussed as challenges.Source: §4.1 · p. 20, §4.2 · p. 22, Figure 14 · p. 23
  • With four people and a 30 s window, success rates were approximately 70% at 5 Hz and 90% at 30 Hz; performance stabilized above 20 Hz.The authors therefore selected 20 Hz for their experiments.Source: §4.2 · pp. 22–23, Figure 15 · p. 23
  • For four people at 20 Hz, increasing the Hankel-matrix window from 15 s to 30 s greatly increased success rate, with little change from 30 s to 45 s.The authors selected a 30 s window for TensorBeat experiments.Source: §4.2 · p. 23, Figure 16 · p. 24
  • For two or three people, LOS and NLOS performance was nearly the same; success rate fell quickly with more people blocking one another in a line.The authors attribute the decline to weaker breathing signals when more people block the path; Fig. 17 also compares scattered positioning.Source: §4.2 · pp. 23–24, Figure 17 · p. 24

5. RELATED WORK

Related work spans wearable and smart-device sensing, radar and WiFi vital-sign systems, and CSI-based localization and activity recognition. TensorBeat positions CSI phase differences and tensor decomposition as new tools for multi-person breathing estimation.

5. RELATED WORK

  • Wearable and smart-device vital-sign methods require body-attached sensors or nearby phones, limiting their use for remote monitoring.Examples include capnometers, pulse oximeters, and smartphone-based sensing.Source: §5 · p. 25
  • Radar systems can monitor vital signs, but cited examples require custom, high-frequency hardware; WiFi RSS systems have line-of-sight, range, or antenna constraints, while prior CSI-amplitude work was limited to at most two sleepers.The cited examples include Vital-Radio, UbiBreathe, mmVital, and CSI-amplitude monitoring.Source: §5 · p. 25
  • CSI has supported indoor localization and activity recognition, but the authors identify few prior uses of CSI phase differences for detecting multiple people’s behavior simultaneously.The cited applications include CSI fingerprinting, angle-of-arrival estimation, and activity recognition.Source: §5 · p. 25
  • The authors claim TensorBeat is the first to use CSI phase differences for multi-person breathing-rate estimation and tensor decomposition for RF vital-sign sensing.They note tensor decomposition could also be applied to indoor localization and human activity recognition.Source: §5 · p. 26

6. CONCLUSIONS

TensorBeat estimates multiple people’s breathing beats with commodity WiFi by applying tensor decomposition to CSI phase differences. Experiments across three indoor environments showed satisfactory multi-person breathing-estimation performance.

6. CONCLUSIONS

  • TensorBeat combines CSI phase-difference data with preprocessing, CP decomposition, signal matching, and peak detection to estimate multiple people’s breathing beats.The authors report validation in three indoor environments and satisfactory multi-person estimation performance.Source: §6 · p. 26
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