Estimation of Breathing Rate with Confidence Interval Using Single-Channel CW Radar
Estimation of Breathing Rate with Confidence Interval Using Single-Channel CW Radar
Nejadgholi, I.;Sadreazami, H.;Baird, Z.;Rajan, S.;Bolic, M.
2019-03-28 00:00:00
Hindawi Journal of Healthcare Engineering Volume 2019, Article ID 2658675, 14 pages https://doi.org/10.1155/2019/2658675 Research Article Estimation of Breathing Rate with Confidence Interval Using Single-Channel CW Radar 1 1 2 2 1 I. Nejadgholi, H. Sadreazami , Z. Baird, S. Rajan, and M. Bolic School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada Correspondence should be addressed to H. Sadreazami; hsadreaz@uottawa.ca Received 16 November 2018; Revised 6 February 2019; Accepted 5 March 2019; Published 28 March 2019 Guest Editor: Jilong Kuang Copyright © 2019 I. Nejadgholi et al. 0is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Breathing rate monitoring using continuous wave (CW) radar has gained much attention due to its contact-less nature and privacy-friendly characteristic. In this work, using a single-channel CW radar, a breathing rate estimation method is proposed that deals with system nonlinearity of a single-channel CW radar and realizes a reliable breathing rate estimate by including confidence intervals. To this end, time-varying dominant Doppler frequency of radar signal, in the range of breathing rate, is extracted in time-frequency domain. It is shown through simulation and mathematical modeling that the average of the dominant Doppler frequencies over time provides an estimation of breathing rate. However, this frequency is affected by noise components and random body movements over time. To address this issue, the sum of these unwanted components is extracted in time-frequency domain, and from their surrogate versions, bootstrap resamples of the measured signal are obtained. Accordingly, a 95% confidence interval is calculated for breathing rate estimation using the bootstrap approach. 0e proposed method is validated in three different postures including lying down, sitting, and standing, with or without random body movements. 0e results show that using the proposed algorithm, estimation of breathing rate is feasible using single-channel CW radar. It is also shown that even in presence of random body movements, average of absolute error of estimation for all three postures is 1.88 breath per minute, which represents 66% improvement as compared to the Fourier transform-based approach. preferred in such cases. In senior’s home, it is preferable to 1. Introduction monitor breathing without the need to wear devices. In ad- Breathing rate is one of the four vital signs. Breathing rates dition, correctional institutions are looking to adopt a non- may increase with fever, stress, or some medical conditions. obtrusive method for monitoring the vital signs of inmates, Prolonged increased breathing rate is a cause of concern; especially because it is a privacy-friendly technology compared hence, it is important to measure breathing rate. Normal to cameras. In addition, depending on the frequencies used for radars, it is possible to obtain both heart rate and breathing breathing rates for an adult person at rest ranges from 12 to 16 breaths per minute. rate using a single sensor which may not be possible with RIP. In order to measure breathing rate, one may use contact- Radar has recently attracted much attention as a based method such as respiratory inductive plethysmography promising device for breathing rate monitoring, mainly (RIP) bands. Such bands are used for sleep tests despite the because of its contact-less, privacy-friendly, and relatively discomfort to the subjects. 0ere are several instances where safe properties [1–3]. Video cameras, as an alternative such a band cannot be used. For instance, in the case of burn choice, have been used for contact-less monitoring of vital victims, it is not possible to use a band. In emergency de- signs. However, cameras invade privacy and their perfor- partments, when patients arrive, it may not be possible to use a mance is highly affected by the amount of light in the band to estimate breathing rate. Remote measurements are monitored space [4, 5] and pose of the subjects. 2 Journal of Healthcare Engineering proposed to resolve the issue of random body movements. Continuous wave (CW) radar systems have widely been used for vital sign monitoring due to their low power Self-injection-locked radar was proposed in [20] to cancel body movements. In [21], empirical mode decomposition consumption and simple radio architecture [6, 7]. 0is radar has also been used to see through-wall a human was applied to cancel only the sensor movement and not skeletal figure [8] and localize a small number of colocated the random body movements. However, all these works people [9]. In such radar systems, a single-frequency signal used both in-phase and quadrature channels and their is transmitted and signals reflected off the subjects are solutions generally resulted in an increase in system received. 0e received signal is modulated by the move- complexity, cost, and power consumption. It should be ments of the chest based on the Doppler principle. Most of noted that so far, the estimation of vital signs, where the subject is moving their body parts randomly, has not been these works have focused on the two-channel CW radar for vital sign monitoring with less attention to the effect of considered with simple-structured single-channel CW radar. random body movements. In the proposed method, we employ a single-channel CW radar to estimate the vital Velocity of movements of chest and abdomen changes periodically over time due to breathing. 0is time-varying signs, where the subjects are moving their body parts randomly. velocity translates into time-varying Doppler frequency of When CW radar is used, the information of micro- reflections received by the single-channel CW radar. movements of chest and abdomen are concealed in the However, other movements of the subject can contribute to phase of the received signal. For small movements, i.e., the frequency modulations around the main Doppler shift that amplitude of displacement is much smaller than the are commonly referred as micro-Doppler modulations [22]. wavelength of transmitted signal, the signal can be ap- 0ese micro-Doppler signatures in time-frequency domain have already been used to perform classification [23, 24]. proximated by its phase, referred to as linear approxi- mation [10]. On the other hand, in the case of larger 0is idea has also been used to estimate vital signs during walking [25]. displacements of chest and abdomen which depend on the anatomy of the subject and the type of breathing and To estimate the breathing rate, in this work, a sequence of dominant frequencies of the signal over time in the range of posture, the linear approximation does not hold anymore especially when the wavelength of radar is small ( <2 cm). breathing is extracted and used to estimate the breathing In this case, multiple harmonics of breathing as well as rate. 0e bootstrap resampling method is used to support the intermodulations between heart rate and breathing rate estimation with a confidence interval, since we are dealing are produced [11], which affect the accuracy of breathing with a single-channel CW radar signal in which extracted rate estimation obtained through Fourier analysis. One micro-Doppler shifts may be affected by movements of body possible solution to address the nonlinearity of a single- and null point effect. 0e paper is organized as follows. Section 2 presents the channel Doppler radar is by using a quadrature radar architecture. Since the vital sign signal is a low-frequency model of reflected radar signal from a human subject using a single-channel CW radar and presents the challenges of signal, the two output channels of the quadrature radar can be used for either complex signal demodulation [12] estimating breathing rate using Fourier transform. Section 3 or arctangent demodulation [13] to calculate the total presents the proposed estimation method and also discusses Doppler phase shift. It is known that the Doppler phase the bootstrap resampling method used to estimate confi- shift is directly proportional to the displacements of chest. dence interval of breathing rate. Section 4 presents the Besides dealing with nonlinearity of the signal, integration experimental setup and the data collection procedure. of two channels in the architecture of CW radar can offer Section 5 presents a discussion of the results. Finally, Section solutions to several challenges of vital sign monitoring 6 concludes the paper. such as null point effect and effect of random body movements [14–17]. In this work, breathing rate is estimated by using a 2. Modeling and Simulation of Single-Channel single-channel CW radar and applying time-frequency Radar Signal analysis instead of Fourier transform. 0e proposed method is evaluated in a real situation, where non- During our experiment, in order to have the entire room linearity, null point effect, and random body movements covered, the radar is mounted on the wall. Figure 1 shows a are considered. Multiple subjects are monitored in dif- scenario in which a stationary person is in front of the ferent postures, namely, lying, sitting, and standing, at radar. 0e transmitting and receiving antennas are colo- different distances from the radar with or without random cated. 0e transmitter transmits a radar signal that is a continuous wave which is intercepted by the subject. movements of body. 0ere have been few works on cancellation of random movements of body. In [18], an Movements of chest, abdomen, and heart cause Doppler shift in the frequency of the returned radar signal. At the antiphase signal generator was used to reduce the effect of random body movements. In [13], a phase-diversity receiver, the transmitted signal is delayed and correlated with the received signal. A low-pass filter is then applied to Doppler radar was introduced that utilized three anten- nas, one for transmitting and the other two for receiving. demodulate and filter out the carrier frequency of trans- 0e receiving antennas were isolated by half of a wave- mitted continuous wave. 0e baseband radar signal, s(t), length. In [19], the center estimation algorithm was can be written as [10] Journal of Healthcare Engineering 3 where J (r) is a Bessel function of the first kind and ir×sin(ϕ) ∞ inϕ n e � J (r)e with J (r) � (−1) J (r). From n�−∞ n n −n (2), it can be seen that the received radar signal is composed of multiple harmonics of breathing and heart rate as well as intermodulations of these harmonics with amplitude of J (4π/λ(r cos(θ ) + r cos(θ ))) × J (4π/λr cos(θ )) and n c c a a m h c angular frequencies of (nω + mω ). Depending on the sum b h of maximum displacements of chest and abdomen r + r , c a r sin (ω ) c b and the displacement of heart r , after some n and m, the ca r sin (ω ) h h terms in (2) will become negligible. In order to estimate the breathing rate from the re- r sin (ω ) a b ceived radar signal, the frequency where the magnitude of spectrum is maximum is found within the range of normal breathing. According to (2), the amplitude of this harmonic is J (4π/λ(r cos(θ ) + r cos(θ ))) × J (4π/λr cos(θ )), 1 c c a a 0 h c when n � 1 and m � 0 for fundamental frequency. It is noted that the amount of displacement may change the amplitude of the Bessel coefficients and number of non- negligible coefficients. Figure 1: A subject is placed in front of the radar. Chest, abdomen, According to [27], movements of chest and abdomen (r and heart move periodically. and r in (1)) can change in the range of a few millimeters in quiet breathing to a few centimeters in deep breathing, 4π depending on the age, sex, and posture of the subject under s(t) � V + K cos d(t) + d (t) + w(t), 0 N study. Figure 2 shows how significant harmonics are affected by the amount of displacement of abdomen. 0e same effect d(t) � d cos θ + d (t) + d cos θ + d (t) + d (t), 0 c C 0 a A H can also be seen through different amount of movements of the chest. To depict Figure 2, (1) is used to simulate breathing d (t) + d (t) � r cos θ + r cos θ × sin ω t + ϕ , C A c c a a b 0b movements, d (t) + d (t), and radar signal, s(t), where C A each row shows a different scenario. In all the cases, the d (t) � r cos θ × sin ω t + ϕ , H h c h 0h operating frequency of the radar is f � 24 GHz, (1) r � 0.1 mm, heart rate is 72 beats per minute and breathing rate is 18 bpm, the horizontal distance of the subject from the where V is the DC voltage, K is the gain of the radar, and radar is d � 2.5 m, the distance between chest and abdomen d(t) is the distance of the subject from the radar at time t. 0 is d � 0.5 m, and the height of radar receiver (in Figure 1) is Wavelength of the CW radar is λ � C/f , where f is the ca c c H � 2 m. In addition, the maximum displacement of chest is frequency of transmitted signal and C is the speed of light. In r � 1 mm and maximum displacement of abdomen is (1), d (t), d (t), and d (t) represent the periodic dis- c C A H 1 mm, 5 mm, 20 mm, and 50 mm from top to the bottom, placements of chest, abdomen, and heart, respectively. d (t) respectively. White noise is added to the received radar denotes the random body movements that appear as phase signal with signal-to-noise ratio (SNR) of 20 dB. As observed noise in the received radar signal. r , r , and r are the c a h from the right column of this figure, the strength of amplitude of the displacement of chest, abdomen, and heart, breathing harmonic at breathing rate is ((ω × 60)/2π) bpm ω and ω are the angular frequencies of breathing and heart b b h and also the other significant harmonics are affected as the beat, respectively. Also, ϕ and ϕ are the initial phase of 0b 0h displacement of abdomen changes. Further investigation periodic movements of breathing and heart at t � 0. For the shows that the estimation (rate of the strongest peak at the sake of simplicity, it is assumed that abdomen and chest are range of breathing) can significantly be impacted by the moving with the same rate and initial phase as mentioned in noise. [26]. In addition, the white noise, w(t), is added to the Figure 3 shows the results of a simulation when Fourier received signal and (1) is written in terms of Bessel functions transform is used for estimation, the breathing rate esti- as described in the following equation: mation is sensitive to the distance of the subject from radar 4π (4π/λ) d +d (t) d and the displacement of the chest. In this simulation, ( 0 N ) ⎡ ⎣ 0 s(t) � V + K × Re e J r cos θ 0 n c c λ for two arbitrary distances, 100 noisy versions of the radar n�−∞ signal are generated using (1) and values given in Table 1. in(ω t+ϕ ) b b 0e frequency of strongest peak in the range of breathing + r cos θ e a a (6 to 24 bpm) is taken as the estimate of breathing. For each distance (d ), the average of estimations μ and ∞ 0 rate est 4π in ω t+ϕ ( h h) ⎤ ⎦ 95% standard interval of these estimations [μ − · J r cos θ e + w(t), rate est m h c Z σ ,μ + Z σ ] are shown in Figure 3 for a range m�−∞ α rate rate α rate est est est of displacements of abdomen, where Z is the Z-score of (2) 4 Journal of Healthcare Engineering –3 ×10 2 400 0 200 –2 –1 05 10 05 10 0 50 100 150 200 –3 ×10 5 1 0 0 200 –5 –1 0 05 10 05 10 0 50 100 150 200 0.02 1 200 0 0 –0.02 –1 0 05 10 0 50 100 150 200 05 10 0.05 1 0 0 50 –0.05 –1 0 05 10 05 10 0 50 100 150 200 Time (sec) Time (sec) Rate (bpm) (a) (b) (c) Figure 2: Effect of displacement of abdomen on the strength of the breathing harmonic and the other nonnegligible harmonics in simulated radar signal. Values used for simulation are shown in Table 1, r � 1 mm, 5 mm, 20 mm, 50 mm from top to the bottom, respectively. (a) Breathing signal. (b) Radar signal. (c) Chirp transform of radar. α � 0.05. It can be seen from the figure that the width of [28]. For a given s(t), the windowed Fourier transform standard interval of estimation highly depends on the dis- (WFT), S(f, t) is constructed as follows: placement of body due to breathing and the distance of the iut (3) S(f, t) � s(u)g (f− u)e du, subject from the radar. 0is shows that these two examples 2π 0 are selected to show that the estimation of breathing fre- where s(u) is Fourier transform of s(t) and g (u) is Fourier quency using Fourier transform with a single-channel CW radar may be problematic. It is also noted that in Figure 3, transform of the Gaussian window defined as only additive noise is considered, yet random movements of − t/f /2 ( 0) ���� � g(t) � e , (4) body may affect this estimation, even more dramatically. 2πf 0e most common approach used in estimating breathing rate is the Fourier transform, which is mostly where f is a resolution parameter that identifies the trade- suitable to analyze stationary signals having the same fre- off between time and frequency resolutions. In order to quency content over time. Most of the literature focuses only estimate the changing frequency of signal over time, for each on choosing the peak of the spectrum within the breathing time sample t , the frequency in which amplitude of S(f, t ) n n frequency range using the standard discrete Fourier trans- is maximum is found, i.e., dominant frequency at time t . In form. However, when random movements are present, this work, the sequence of these frequencies ](t) is extracted peaks due to breathing frequency may not be prominent, from the radar signal over time. It is noted that when ](t) is and hence estimation may either be biased or totally wrong. extracted from the range of normal breathing, it represents In this work, modifications to the Fourier transform such as micro-Doppler frequency of the signal over time and is windowed Fourier transform, chirp Fourier transform, and related to time-varying velocity of chest and abdomen. micro-Doppler series acquired from the radar return are At this stage, the phase of s(t) in the range of breathing employed to estimate the changing frequency of signal over frequency is calculated by setting n � 1 and m � 0 in (2) and time. is written as 4π Φ (t) � d + d (t) + ω t + ϕ , (5) s,Breathing 0 N,Breathing b 0b 3. Methods and Materials 3.1. Estimation of Breathing Rate Using Time-Frequency where d represents all random body movements N,Breathing Analysis. 0e signal model described in (1) represents a having the same velocity unlike the breathing-related nonstationary signal that can be analyzed in time-frequency Doppler and thus is detected in the range of the breath- domain by applying Fourier transform in sufficiently narrow ing frequency. By definition, ](t) � (Φ (t))/2π [28], where time windows, where the signal may be assumed stationary Φ (t) is the phase derivative of s(t) with respect to time t. Journal of Healthcare Engineering 5 0 5 10 15 20 25 30 35 40 45 50 Displacement of abdomen (mm) Mean of estimation Upper limit of 95% standard interval Lower limit of 95% standard interval (a) 0 5 10 15 20 25 30 35 40 45 50 Displacement of abdomen (mm) Mean of estimation Upper limit of 95% standard interval Lower limit of 95% standard interval (b) Figure 3: Estimated breathing rates vs displacement of the abdomen r . Sensitivity of the estimated breathing rates to displacement of abdomen and distance of the subject from radar is shown, when Fourier transform of the signal is used to estimate breathing rate from noisy simulated signals (parameters are given in Table 1). (a) d � 2.5 (m). (b) d �1 m. 0 0 Table 1: Values used for simulation in Figures 2 and 3. It is noted that bpm stands for breath per minute. Variable H (m) d (m) Breathing rate (bpm) Heart rate (beat/minute) r (mm) r (mm) r (mm) d (m) λ (mm) 0 c h a ac Value in Figure 2 2 2.5 18 72 1 0.1 (1, 5, 20, 50) 0.5 12.5 Value in Figure 3 2 2.5 18 72 1 0.1 (1–50) 0.5 12.5 0e dominant frequency of s(t) in the range of breathing can breathing. In view of this, ](t) is assumed to be a linear then be written as combination of breathing rate and low-frequency harmonics of noise and random movements, and f can be estimated 4π b ] (t) � d (t) + f , (6) s,Breathing N,Breathing b via calculating the mean of ](t) over a specified time window of radar signal. where d (t) denotes the speed at which the random Figure 4 shows the micro-Doppler sequence extracted N,Breathing body movements occur. Since 4π/λ is about 1000 for the for the simulated radar signals shown in Figure 2. In simu- radar in our experiments, very slow movements of body lations, d is not included assuming that random body parts may give rise to high Doppler frequencies and thus movement is too slow to be detected at low frequencies may not be detected as a strong harmonic in the range of of breathing range. Yet, additive noise w(t) is considered. Fourier transform estimation (bpm) Fourier transform estimation (bpm) 6 Journal of Healthcare Engineering 0123456789 10 0123456789 10 0123456789 10 0123456789 10 Time (sec) Figure 4: Micro-Doppler sequence extracted for simulated radar signal shown in Figure 2. From this figure, the average and standard deviation of the measured signal and calculates the confidence interval the extracted sequences are found to be 17.15 ± 0.16 bpm, for each estimated parameter by assessing how noise dis- 17.60 ± 0.26 bpm, 17.23 ± 2.39 bpm, and 17.41 ± 0.7 bpm, tribution can affect the estimated parameter [31–33]. from top to bottom, respectively. However, the dominant In our experiments, random body movements and in- termodulations are hidden in the phase of the residuals. frequencies in the range of breathing in frequency domain (calculated from right column of Figure 2) are 17.81 bpm, 0us, in order to make the bootstrap method resamples, the 18.28 bpm, 6.56 bpm, and 17.81 bpm, respectively. 0e actual residuals are first calculated and the phase of the residuals is breathing rate for all these simulated signals is 18 bpm. 0ese randomized to build multiple versions of possible random estimations indicate that the average of micro-Doppler se- intermodulations and body movements. 0ese noisy ver- quence is a more accurate way of breathing rate estimation sions of residuals are referred as “surrogates” and have been using a single-channel CW radar. In addition, it is observed introduced in order to build noisy versions of a signal with from this figure that for the third simulated signal, where the same energy and frequency spectrum [34]. r + r � 21 mm, the estimation in frequency domain is in- In order to calculate the residuals, for each time sample t, a C accurate since the harmonic of breathing is very weak. In this the frequency associated with maximum amplitude of case, the standard deviation of the extracted micro-Doppler S(f, t) is found, i.e., micro-Doppler frequency ](t) at time t. 0e average of ](t) is taken as the estimate of breathing as sequence is larger than the other cases. 0us, the standard deviation of the extracted micro-Doppler is used to calculate described in Section 3.1. In order to reconstruct the the confidence interval of estimation as a measure of confi- breathing component in the time domain, the phase and dence of the estimation in Section 3.3. amplitude of S(](t), t) are obtained. 0e reconstructed signal is subtracted from the original one, where the re- mainder (residual) is related to radar reflections from other 3.2.ConstructingBootstrapResamples. It is noted that we are parts of body or signals related to intermodulations of only interested in the dominant frequency at the range of breathing and heart harmonics. Accordingly, a bootstrap breathing. However, estimation of this frequency is affected resample of the radar signal is built through reconstructing by random body movements and intermodulations amongst the residuals with randomized phase and adding them to the breathing frequency, heart rate and other frequencies related breathing component extracted from the signal. to body movements. 0e contributions due to body In order to estimate the bootstrap statistics from the movements can be estimated via constructing the breathing constructed bootstrap samples, micro-Doppler frequency of signal based on the estimated breathing rate, subtracting it each bootstrap resample is estimated and Student’s t is score from the original radar signal and calculating the residual. calculated (described in Section 3.3), with respect to the In order to examine how noise and intermodulations estimation calculated from the original signal [33]. In order affect the estimation of micro-Doppler frequency, the to calculate micro-Doppler frequencies, WFT uses multiple bootstrap resampling method is employed. 0e bootstrap windows of signal similar to the block bootstrap method resampling was first introduced in [29] and has been [35–37]. WFT uses overlapping blocks of the signal with the modified and used in several applications since then. For same length and is desired for block bootstrap for time series instance, in [30], bootstrap has been used for confidence as it results in lower variance in estimators [38]. In view of interval estimation using percentile-t method. It should be this, in this work, a double-loop bootstrap method is used in noted that the bootstrap method estimates the residuals and order to generate bootstrap resamples and provide bootstrap resamples it many times to build multiple noisy versions of statistics with higher accuracies [39]. (bpm) (bpm) (bpm) (bpm) Journal of Healthcare Engineering 7 3.3. Estimation of Confidence Interval. In the following, different steps for estimating the confidence interval of breathing rate are presented. (1) A 15-second long radar signal s(t) is taken and preprocessed using a Butter-worth filter with cut-off frequencies of 0.05 Hz and 5 Hz. (2) Using the WFT method, time-frequency represen- tation of s (t) of the preprocessed s(t) is con- structed. Micro-Doppler frequency over time ](t) is extracted in the range of breathing [0.1−0.5] Hz. Breathing rate f , i.e., the average of ](t), is esti- Figure 5: Experiment setup. mated and standard deviation of ](t), σ , is calculated. in this experiment was a 24.125 GHz CW single-channel (3) Using phase and amplitude of S (](t), t), the Doppler radar prototype model built by K&G Spectrum in breathing model, s (t, f ) in the time domain is F b Gatineau, Canada, equipped with four adjacent transmit/ constructed and sum of the components related to receive antenna pairs each with 20 × 70 degree beamwidth. It random movements and intermodulations, ε(t), is should be noted that all four transmitter antennas simul- calculated. taneously transmitted the signal and only one receiver an- tenna received it at any point in time. A Bosch NE1368 s (t) � s t, f + ε(t). (7) F F b vandal-proof wide angle camera was also used in the ex- periments for recording baseline activity and posture in- (4) A surrogate sample of ε (t) is obtained by ran- formation. 0e bed was constructed of concrete support domizing the phase of ε(t) in the frequency domain blocks and oriented strand board, and a cotton filled mat- and the residuals in time domain are reconstructed. A tress was placed on top of the board. 0e door of the room bootstrap sample of the radar signal is constructed as was closed, and only the test subject was present in the room. ∗ ∗ s (t) � s t, f + ε (t). (8) A Braebon model number 0528 piezoelectric respiratory F F b effort sensor was fitted to the subject’s chest at sternum level ∗ ∗ for monitoring breathing activity and three Ambu Blue-T (5) 0e micro-Doppler frequency, ] (t) of s (t) in the ECG sensors were adhered to the subject’s left and right range of breathing is extracted. 0e bootstrap sta- wrists and left ankle for monitoring the ECG signal. All data tistics for this particular bootstrap sample can then were streamed to two computers situated outside of the be calculated as room for recording. Radar data and ECG/breathing belt data f − f ∗ were streamed via USB and Bluetooth, respectively, to b b (9) T � , σ Computer 1, and camera data were streamed via Ethernet to Computer 2. 0ree subjects, one male (22 years old, 164 cm ∗ ∗ where f and σ are the mean and standard de- height, 60 kg weight) and two females (24, 155 cm, 50 kg and viation of ] (t). 36, 160 cm, 70 kg), participated in data collection. 0e fol- lowing test protocol was followed by all subjects with breaks (6) Steps 4 and 5 are repeated B times. in between each test: (7) 0e bootstrap estimates are sorted as ∗1 ∗2 ∗B (1) Breathing normally and remaining still for T < T < · · · < T , and 100(1−α)% confidence interval is computed as 3 minutes: ∗U ∗L T σ + f , T σ + f , (10) (i) Standing in front of bed and facing radar b b (ii) Sitting on the edge of the bed and facing radar with hands resting on knees where U � B− [Bα/2] + 1 and L � Bα/2. (iii) Lying on bed in left lateral recumbent position and facing radar 4. Experiment Setup and Data Collection (2) Breathing normally and moving head shoulders and torso randomly for 3 minutes: 0e data in this experiment were collected in a simulated prison cell at Carleton University, Ottawa, Canada, after (i) Standing in front of bed and facing radar obtaining the appropriate ethics approval. 0e room mea- (ii) Sitting on the edge of the bed and facing radar sured 3.35 × 3.15 × 2.95 m, and radar was mounted 2.70 m with hands resting on knees above floor level in one corner, a tripod mounted camera (iii) Lying on bed in left lateral recumbent position was kept in an adjacent corner, a bed was present along one facing radar of the walls opposite to the radar, and a prison-type stainless steel toilet and sink (one joint structure) was kept close to the A total 18 minutes recording for each subject was wall that was opposite to the radar (Figure 5). 0e radar used collected. 8 Journal of Healthcare Engineering calculated from RIP signal is 15.6 bpm, and this, such a 5. Results narrow confidence interval, confirms that the estimation As mentioned in [27], posture of the subject may have a is accurate. substantial effect on the amount of movement of chest and abdomen. In this Section, three postures are investigated, 5.2.Posture:Sitting. Similarly for the case of a subject sitting namely, lying down, sitting, and standing, and the results are on a bed, breathing is regular, and the radar signal contains presented. In addition, the proposed method discussed in harmonics other than the breathing frequency. 0e time- Section 3.3 is compared to the other breathing rate esti- frequency representation and frequency content of the radar mation methods using CW radar in the literature. In the signal are obtained. 0e dominant peak in the frequency ubiquitous method of estimating breathing rate, the fre- domain is found to be 18.5 bpm. 0e sequence of micro- quency with the maximum energy (dominant frequency) in Doppler frequencies is then extracted from WFT, and their the frequency spectrum of the signal in the range of average is found to be 16.77 bpm. 0e residuals are then breathing is considered. In order to estimate breathing calculated, and its phase is randomized to generate a noise frequency, the signal is first preprocessed according to Step 1 time series with the same energy. Finally, bootstrap of the proposed procedure described in Section 3.3. A resamples are constructed. 0e upper and lower bootstrap Hamming window is then applied to the signal, and the ∗L ∗U statistics are calculated as T � −0.35 and T � 0.90, re- chirp transform of the signal is obtained in the range of spectively, resulting in a 95% confidence interval of (0–4) Hz. It has been shown that the chirp transform results (16.3, 18.0) bpm, while the reference estimation calculated in more accurate estimations than regular DFT, since it from RIP signal is 15.68 bpm. benefits from improved frequency resolution in the range of frequency of interest [40, 41]. 5.3. Standing. When the subject is standing, the abdomen moves without any restriction which may have an influence 5.1. Lying Down. In the case of a lying down subject, it is on the magnitude of periodic breathing movement seen by observed for most cases that the breathing frequency estimated the radar. In addition, while standing, the body slightly from the received radar signal is close to that obtained from moves back and forth in order to keep the balance. In this the RIP signal and the number of significant harmonics related case, the radar recording is very different from RIP signal. to random body movements or intermodulations is minimum. WFT and chirp transform of the radar signal are obtained, Figure 6 shows 15 seconds of the recorded signal when showing that the frequency content of the signal changes Subject 1 is lying down on the bed, relaxing and breathing dramatically over time, and thus, a strong dominant peak normally. It is observed from the RIP signal the subject’s may not be found in the range of breathing rate in the breathing pattern is regular and almost periodic. In this frequency domain. 0e breathing rate is estimated by example, the radar signal is similar to RIP signal, similar to extracting the micro-Doppler frequencies to be 14.73 bpm, the simulated signal in the first row of Figure 2. while the estimation from frequency domain is 24 bpm. It is Figure 7 shows WFTas well as frequency spectrum of the noted that the energy of residuals is much higher than that of radar signal. It can be seen from this figure that both Fourier the breathing signal, since it contains intermodulations of transform and WFT exhibit a single significant harmonic at large movements of abdomen and the other body move- the rate of breathing. Micro-Doppler frequency of radar ments. 0e bootstrap statistics are calculated and the upper signal is the dominant frequency in the range of breathing, as ∗U and lower limits of T-score are found to be T � 0.86 and shown in Figure 6. 0e average of micro-Doppler fre- ∗L T � −0.18, respectively, resulting in a 95% confidence quencies is calculated as 15.97 bpm and considered to be the interval of (14.32, 18.63) bpm. 0e reference estimation estimation of breathing rate. It is noted that the breathing calculated from RIP signal is 16.03 bpm. rate calculated from the frequency spectrum (Figure 7(b)) is 16.6 bpm. 0e micro-Doppler frequencies are extracted from the time-frequency domain using WFT, as shown in 5.4. Random Body Movements. Random body movements Figure 7(a), and then, the signal is converted back to the time with linear velocity of V translate into Doppler frequency of domain in order to obtain the breathing model shown in 2V/λ in the received radar signal. For instance, if a part of Figure 6. Finally, the residual signal is calculated by sub- body moves with the velocity of 0.1 m/s, it leads to a Doppler tracting the radar signal from its reconstructed version. frequency of 16 Hz. In view of this, these movements may be As discussed in Section 3, 200 bootstrap resamples of ignored when looking at WFTof the radar signal in the range the signal are constructed. Micro-Doppler frequency of of breathing and may not affect the extracted micro-Doppler each bootstrap sample as well as the bootstrap statistic T series. Figure 9 shows the effect of random body movements is calculated. Figure 8 shows the density function of the in the radar signal. It is seen from this figure that the received bootstrap statistics obtained from 200 resamples. In this radar signal is very different from the breathing signal, and est figure, T � 0 is the T-score related to the original sig- random body movements are present as high frequency ∗L ∗U nal, whereas T � −0.44 and T � 0.27 specify the lower artifacts. Figure 10 shows WFT and chirp transform of the and upper limits of 95% confidence interval of this esti- radar signal. 0e peak of the signal in the frequency domain mation, respectively. 0e confidence interval is estimated occurs at 21.8 bpm, while the average of micro-Doppler to be (15.5, 16.1) bpm. 0e reference breathing rate series extracted from WFT is 17.8 bpm. From these Journal of Healthcare Engineering 9 –2 02468 10 12 14 0.4 0.2 02468 10 12 14 02468 10 12 14 0.2 –0.2 02468 10 12 14 0.2 –0.2 02468 10 12 14 Time (sec) Figure 6: From top to bottom: RIP signal, received radar signal, micro-Doppler frequencies extracted from WFT, breathing model, and residuals, when Subject 1 is lying down. 12 0.8 0.6 0.4 0.2 0 50 100 150 200 Rate (bpm) 20 40 60 80 100 120 140 160 180 200 220 240 Rate (bpm) (a) (b) Figure 7: WFT and chirp transform of the radar signal, shown in Figure 6, when the subject is lying down on a bed. ∗U 50 0e upper and lower T-score are calculated as T � 1.2 and ∗L T � −1.3, respectively, resulting in 95% confidence in- est T terval of (14.40, 20.97) bpm. 0e reference breathing rate calculated from RIP is 16.03 bpm. Breathing rate estimation results obtained using the proposed method as well as the reference value calculated ∗U ∗L from RIP and that obtained using the FFT-based method (estimated, actual, FFT) bpm, for three subject in three different postures, namely, lying down, sitting, and standing, are listed in Table 2. –1 –0.5 0 0.5 1 It is known that breathing rate increases by age [42, 43]. Bootstrap statistics From Table 2, the actual breathing rates for different pos- tures show that the older subject have consistently higher Figure 8: Bootstrap statistics for 200 bootstrap resamples con- breathing rate. It is also known that the breathing rate of structed from the radar signal shown in Figure 6. overweight people is generally higher than the other people. Yet, the weight of all three subjects is considered normal and figures, it can be observed that random body movements cannot be a discriminative feature in analyzing their give rise to very strong residuals. Phase of this residual signal breathing rate. In addition, women tend to breath faster than is randomized to generate other possible random move- men [44, 45]. 0is is in accordance with the actual breathing ments that could be added to the breathing signal. 0e rate of subjects. As seen from this table, the first two female bootstrap statistics are calculated and shown in Figure 11. subjects have higher breathing rates than the third (male) Time (s) Frequency Mic. Dop. Res. (v) Model (v) (bpm) Radar (v) RIP (v) Normalized PSD 10 Journal of Healthcare Engineering –2 0 2 4 6 8 10 12 14 0.5 –0.5 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0.1 –0.1 0 2 4 6 8 10 12 14 0.5 –0.5 0 2 4 6 8 10 12 14 Time (sec) Figure 9: From top to bottom: RIP signal, received radar signal, micro-Doppler frequencies extracted from WFT, breathing model, and residuals, when Subject 1 is sitting on the bed and moves head, torso, and arms randomly. 12 0.8 0.6 0.4 0.2 2 0 50 100 150 200 Rate (bpm) 20 40 60 80 100 120 140 160 180 200 220 240 Rate (bpm) (a) (b) Figure 10: WFT and chirp transform of the radar signal, shown in Figure 9. breathing rate calculated from RIP signal for a 6-minute experiment. In this experiment, the subject is lying down on a bed and stays stationary for the first 3 minutes. In the last 3 minutes, the subject moves her arms, head, and shoulders est randomly. It is observed from this figure that estimated 40 breathing rate matches the estimation obtained from breathing belt. Table 3 summarizes all the estimation results. In this table, results are in the form of (mean± standard ∗L 20 ∗U deviation) of absolute errors between the estimated pa- rameters and the reference estimation calculated from RIP signal. All the values are given in terms of breath per minute –1.5 –1 –0.5 0 0.5 along with the number of outliers. It is noted that an element Bootstrap statistic of a vector is called an outlier, if removing it decreases the Figure 11: Bootstrap statistics corresponds to the radar signal in mean of the vector by 5%. Figure 9. In Table 3, breathing estimation obtained from chirp transform of the signal is compared with the average of micro-Doppler frequencies for different postures with or one. Height of the subjects has no considerable influence on without random body movements. In all the cases, WFT is their breathing rates. applied with f � 2. It is seen from this table that the accuracy of estimation is improved when using the proposed method instead of chirp transform of the signal. 5.5.OverallResults. Figure 12 shows the estimated breathing rate and confidence interval as well as the reference In other words, unwanted harmonics of the signal which Time (s) Frequency Mic. Dop. Res. (v) Model (v) (bpm) Radar (v) RIP (v) Normalized PSD Journal of Healthcare Engineering 11 Table 2: Breathing rate estimation using the proposed method as well as the reference value and that of the FFT-based method (estimated, actual, and FFT) bpm, for three subjects in three different postures, namely, lying down, sitting, and standing. Lying down Sitting Standing Subject 1 (36, 160 cm, 70 kg) (15.85, 15.60, 16.68) (16.77, 15.68, 18.52) (14.73, 16.03, 23.78) Subject 2 (24, 155 cm, 50 kg) (13.88, 14.42, 13.78) (14.63, 15.01, 15.19) (15.10, 15.23, 19.14) Subject 3 (22, 164 cm, 60 kg) (14.67, 13.67, 14.36) (13.94, 14.15, 14.38) (15.20, 14.26, 18.38) 0.4 Stationary Random body movements 0.2 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 Time (sec) Estimation Upper limit Lower limit Reference Figure 12: Estimation of breathing within a 95% confidence interval for a 6-minute experiment, where the subject is lying down and stationary for the first 3 minutes and moves shoulders, arms, and head randomly in the last 3 minutes. Table 3: Summary of results for different postures with or without random body movements. Absolute error with respect to reference in bpm (number of outliers) Number of Width of CI in bpm State of the subject Average of Lower limit Higher limit samples (number of outliers) Chirp transform micro-Doppler of CI of CI Lying down and stationary 50 1.32± 0.79 (1) 0.82± 0.54 (0) 0.88± 0.61 (2) 1± 0.67 (1) 0.96± 0.67 (3) Sitting and stationary 51 2.8± 2.55 (0) 1.25± 0.87 (0) 1.52± 1.37 (2) 1.76± 1.52 (0) 3.05± 2.81 (0) Standing and stationary 51 4.36± 2.78 (0) 2.24± 1.39 (0) 2.90± 2.07 (0) 3.73± 3.28 (1) 5.50± 4.92 (1) Lying down with movements 51 3.87± 2.07 (0) 2.05± 1.22 (0) 2.61± 1.96 (0) 2.65± 1.96 (0) 3.86± 3.03 (0) Sitting with movements 51 4.57± 2.60 (0) 1.76± 1.30 (0) 4.23± 2.93 (1) 2.89± 2.65 (2) 6.35± 4.99 (2) Standing with movements 51 3.99± 2.41 (0) 1.84± 1.32 (0) 3.29± 2.54 (1) 1.97± 1.60 (3) 5.26± 4.22 (0) are related to intermodulations between breathing and (3.05 bpm). In this case, slight movements of body due to heart rate and also random body movements can affect balance may introduce uncertainty to the estimation. When estimation of breathing in frequency domain. However, the subject is standing, movements of body for balancing are when the signal is analyzed in time-frequency domain, larger and abdomen moves freely. In this case, chirp harmonic of breathing can be separated from the other transform results in huge errors and, in some cases, the harmonics. estimated breathing is twice that of the reference. Although 0e most accurate estimation is obtained when the the estimation improves to absolute error of 2.24 bpm using subject is stationary and lying down on a bed. In this case, the proposed method, the width of confidence interval is 5.5 bpm, because of the significant energy of noise and even chirp transform results in an acceptable precision of measurement. Also, the estimated 95% confidence in- unwanted harmonics with respect to the breathing harmonic. terval is very narrow (almost 1 bpm), indicating that we are quite confident about the estimated breathing rate When the subject starts moving head, shoulders, and and in 95% of cases, we would find the estimation in this torso, the accuracy of estimation using chirp transform range in presence of other sources of noise and body drops severely. 0is estimation may be improved by using movements. the proposed method. Yet, the confidence interval could be In the case of sitting, the estimation may be improved by large indicating that these estimations are carried out in a using average of micro-Doppler frequencies instead of chirp noisy environment or in presence of random movements. transform. However, the 95% confidence interval is larger It is seen from the results that the proposed method is than that of the case, where the subject is lying down able to compensate for lack of quadrature channel and Estimation Radar signal 12 Journal of Healthcare Engineering estimate breathing using single-channel CW radar with an unwanted intermodulations is hidden in the phase of the average absolute error of estimation equal to 1.88 breaths per residuals. 0e results have also shown that the proposed method is able to compensate for lack of quadrature channel minute. Although this error seems high for monitoring patients, the error rate is satisfactory when the use of and can be used to estimate breathing using single-channel wearable devices or cameras is not allowed, such as con- CW radar with an average absolute error of estimation equal tinuous monitoring of breathing rate of inmates and elderly to 1.88 breaths per minute. people, during sleep or rescue operations. It should be noted that breathing rate estimation is realized based on the de- Data Availability tected motion, observed at a distance, and therefore is much 0e data used in the experiments will be made available more susceptible to noise, interference, and artifacts and is online. not expected to be as accurate at estimating breathing rate as the RIP band. Conflicts of Interest One of the limitations of the proposed method is that it is sensitive to the parameter f in (4), which controls the 0e authors declare that there are no conflicts of interest trade-off between time and frequency resolution of WFT. regarding the publication of this paper. 0is parameter has been set to f � 2, which was found by trial and error and might need to be adjusted for other radar Acknowledgments systems. In future works, ways of optimizing f needs to be investigated. 0e proposed method will also be examined in We would like to thank NSERC for funding this research other environments where interference from other moving through IDEA to Innovation and Discovery program. We objects is present in the room. would also like to thank Mr. Andre Gagnon from K&G It is noted that the system complexity, cost, and power Spectrum Inc. for providing the radar prototype and Mr. consumption of a two-channel radar are well known to be Sylvio Bisson from Correctional Service Canada for his higher than those of a single-channel radar, because a single- support of this research. channel radar requires only one receiver branch [46, 47] and does not require balancing I/Q data [48]. References [1] L. Anitori, A. de Jong, and F. Nennie, “FMCW radar for life- 6. Conclusion sign detection,” in Proceedings of the IEEE Radar Conference, pp. 1–6, Pasadena, CA, USA, May 2009. 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