Monitoring Breathing via Signal Strength in Wireless Networks

ARXIV .ORG TECHNICAL REPOR T 1 Monitor ing Breathing via Signal Strength in Wireless Networks Neal P atw ari, Joey Wilson, Sai Ananthanara yanan P .R., Sneha K. Kasera, Dw a yne W estenskow ✦ Abstract —This paper shows e xperimentally that standard wireless networks which measure receiv ed signal strength (RSS) can b e used to reliably detect human breathing and estimate the breathing rate, an application we call “BreathT aking”. We show that although an in- dividual link cannot reliably detect breathing, the collective spectral content of a network of devices reliably i ndicates the presence and rate o f breathing. We present a maximum likelihood e stimator (MLE) of breathing rate, amplitude, and phase, which uses the RSS data from many links simultaneously . We show experimental results which demonstrat e that reliable detection and frequency est imation is possib le with 30 seconds of data, within 0.3 breaths per minute (bpm) RMS error. Use of directional antennas is shown to improv e robustness to motion near the network. 1 I N T R O D U C T I O N In this paper , we explore the ability to detect and monitor breathing using the changes in received signal streng th (RSS) measured on many links in a deployed wireless network. The ability of a wireless network to make measurements that can monitor a person’s breathing ca n create new opportunities for improving patient moni- toring in health care applications. As one example, post- surgical patients can die from respiratory depression a nd airway obstr uction, which ar e unfortunately co mmon after surgery due the difficulty of correctly dosing seda - tives and pain medications administered to a patient [1]. Reliable respiration monitoring is critical to detection of these conditions [2], [ 3], [4]. Breathing monitoring a lso has application in diagnosis and tr eatment for obstr uc- tive sleep apnea, in which a person experiences periods of low breathing rate or long p a uses in breathing while sleeping [5]. Finally , breathing monitoring may have application in d etecting sudden infa nt death syndrome (SIDS), which is one of the largest causes of de ath in infants. Parents with a child at high risk f or SIDS may wish to use a baby breathing monito r to alert them in case their child’s breathing bec omes depressed or stops. W e use of measurements of RSS between many p a irs of wireless devices in a deployed network to non- invasively detect and monitor a person’s breathing, an N. Patwari is with the Department of Electrical and Computer Engineering, University of U tah, Salt Lake City, U SA. J. Wilson is with Xandem T echnol- ogy , Utah, USA. S. K. Kasera is with the School of Computing, University of Utah. S. Ananthanaraya nan is with Motorola Mobility , USA. D. Westenskow is with the Department of Anesthesiology , University of Utah. This material is based upon work supported b y the Nationa l Science Founda tion under Grant N os. #0748206 and #1035565. Contact email: npatwari@ece.utah.edu. application we call BreathT aking . While severe fa ding in mobile radio channels is expe cted, it is counterintuitive that small changes in a person’s siz e a s a result of their breathing could be detected usi ng measur ements of RSS. However , in this paper , we demonstrate that in a n otherwise stationary e nviron ment, when we use the data collected on many links between static wireless devices, breathing monitoring is not only possible, but remarkably reliable. 0.2 0.3 0.4 0.5 0.6 30 40 50 60 70 80 90 100 110 Frequency (Hz) Normalized Average PSD Norm. Avg. PSD Actual Breathing Rate Fig. 1. Nor maliz ed a verag ed power s pectral density (PSD) vs. frequency (Hz). T otal PSD is defined as the argument of (4). The peak of the PSD plot i s at 0.253 Hz (15.18 bpm), compared to the actual breathing rate of 0.250 Hz (15 bpm), shown as a v er tical dashed line . Our research on BreathT aking is motivated by exper- imental observations. W e have observed that when a person is standing on or near the line-of-sight ( LOS) of a static radio li nk, the RSS can be changed sim ply by the per son’s inhaling and e x haling. In fact, when we measure the actual breathing rate a nd analyze the power spectral density of the RSS link data from the network as a whole, as shown in Figure 1, we see a peak ver y close to the a c tua l breathing rate. Our BreathT aking does not provide a d irect measure of breathing. In contrast to End- T idal CO 2 monitoring, for example, we do not measure the gasses exhale d from a person’s nose. W e simply make an observation about the ARXIV .ORG TECHNICAL REPOR T 2 presence (or ab se nce) of a stron g frequency component in the measured RSS in the human breathing range. Adults, at rest, breathe at about 14 breaths per minute (bpm) [ 6], while newborns breathe a t 37 bpm [ 7]. T o be inclusive, we consider a range of 1 0 to 40 bpm (0.1 67 to 0 .667 Hz ). Few other objects have cyclic motion with periodicity in this range, but if there were such an object in the deployment region, it might cause the same type of observation in the network RSS data . Context remains important to interpret results from the proposed system. In this paper , we make the follow ing important con- tributions in relation to system design, capa bilities, and limitations of BreathT aking. First, we develop methods to accur a tely estimate the breathing rate and reliably detect breathing of a person in the deployment area of a wireless network by considering the RSS mea- surements on many links simultaneously . W e approxi- mate the breathing signal to be sinusoidal and use the maximum likelihood estimation (MLE ) to e stimate the breathing rate. Second, we pe r form extensive exper imen- tal evaluation of BreathT aking in an indoor setting. W e demonstrate monitoring the breathing of a n otherwise motionless person, in an hospital room with no other person present. W ith thirty seconds of RSS data in a twenty-device network, we demonstrate (1) breathing rate estimates with RMSE betwee n 0.1-0.4 breaths per minute (bpm); (2 ) a breathing detector without false alarms or missed de tections during experiments per- formed with devices connected to directional antennas. W e a ddress the perf orma nce as a function of the number of devices in the network, relative position of the person with respect to the sensors, and actual breathing rate. Finally , we quantitatively a d dress the following key questions that relate to the c apability to use RSS mea - surements from static wir eless networks to monitor breathing for the above-descr ibe d applica tions: 1) What is the benefit of using da ta from multiple links simultaneously , as opposed to f rom one link? 2) How a ccurately c a n breathing rate be estimated? 3) How long of a measurement duration is required? 4) What is the effect of the directionality of the anten- nas? 5) How many devices are required for accurate mon- itoring? 6) Is there information in the phase of the breathing signal? Breathing monitoring in a wi reless network has ap- plications and implications besides health care. A search and rescue te a m may ar r ive at a collapsed building and throw transceivers into the rubble, hoping to detect the breathing of anyone still a live inside. Police or S W A T teams may de p loy a network around a building to determine if people a re inside. On the other hand, the ability to measure breathing f rom a wireless network has privacy implications. W e have shown previously that a network deployed around the external walls of a building ca n detect and track a p e rson who is moving or changing position [8], [9]. If this system can a lso detect a person’s breathin g, it can also de tect people who are sitting or laying motionless. The rest of the paper is organized as follows. In Section 2 we present the approach we ha v e used for Breath- T a king. Next, we describe the experimental testbed and methodology in Section 3. The results of the experiments are p resented and discussed in Section 4 . Finally , related work and conclusions are presented in Se c tions 5 and 6. 2 M E T H O D S In this section, we define the measurements, models, and goals of the BreathT aking system. 2.1 Network W e assume a network in which received power (a lso called RSS) measurements can be made on many links between pairs of wireless devices. W e assume these measurements can be made often, at regular intervals. Specifically , assuming a maximum breathing rate of 40 breaths per minute, BreathT aking requires RSS measure- ments to be made at a ra te higher than 4/3 Hz, the Nyquist sampling rate. W e denote y l ( i ) to b e the dBm received power on link l measured at time i . Note that link l is an ordered pa ir ( t l , r l ) of the particula r tra nsmitter t l and receiver r l for link l . W e do not generally require full connectivity of the network, a nd instead, a ssume that connected links a re numbered from 1 through L , where L is the total number of mea sured links. W e wish to maximize L and thus use a wireless sensor network with a mesh topology in our experiments, although we do not e xclude networks with other topologies. 2.2 Signal Model In the absence of any motion in the environment of the network, we denote y l ( i ) = ¯ y l + ǫ l ( i ) , (1) where ¯ y l is the mean RSS f or link l and ǫ l ( i ) is additive noise. W e assume that the noise on link l is i.i.d . z ero- mean Gaussian. W e also assume th at the noise ǫ l ( i ) is independent on different links l . In the presence of a breathing person, we assume that the link RSS has a n additional sinusoidal term, y l ( i ) = ¯ y l + A l cos(2 π f T s i + φ l ) + ǫ l ( i ) , (2) where A l , φ l , a nd f are the amplitude, phase, a nd frequency , respectively , of the periodic c omponent of the RSS signal on link l , and T s is the sampling period. W e assume that the periodic com ponent due to breathin g would have the same frequency on all links l , a nd that the sampling period is mad e to be identical on all links, thus we d o not use a subscript l for frequency f . Phase and amplitude are expected to differ b e tween links. ARXIV .ORG TECHNICAL REPOR T 3 2.3 Framew ork W e denote the measured signal on link l as a vector , y l = [ y l (1) , . . . , y l ( N )] ⊺ where N is the total number of samples, and () ⊺ indi- cates the vector tra nspose. Be c ause the sampling pe riod is T s , the measurement vector corresponds to what we call the observation period T , T = N T s . The observation period T is related to the la te ncy of breathing monitoring, since we measure RSS for a dura- tion T before obtaining estimates of breathing rate and detecting whether or not breathing occurred. Our objective from the measurements y l , for l = 1 , . . . L , is to dete ct whether or not a person is breathing within the network, and to estimate important parame- ters of the model, which we denote θ , θ = [ A T , φ T , f ] T where A = [ A 1 , . . . , A L ] T and φ = [ φ 1 , . . . , φ L ] T . Of most interest is the frequency f , as human breathing has a characte ristic frequency range, from f min to f max , as discussed in the Intr oduction. In th is pa p e r , we detect breathing only within f min = 0 . 167 Hz to f max = 0 . 667 Hz, and in general, we a ssume that the range is given. 2.4 DC Remov al Filtering When estimating the power spectral de nsity of noisy , finite-duration y l signals, the mean values ¯ y l (the DC component) can “hide” th e power of lower -amplitude sinusoidal components. Y e t the DC component does not hold information a bout the presence or a bsence of breathing. Since we assume that breathing is not present below a frequency of f min , we address this problem sim- ply by using a high pa ss filter which strongly attenuates the DC component. W e do not require a linear-phase filter , but we d o need a nearly flat amplitude gain above f min , since we do not want our system to bias towards some frequencies because they have b e en amplified by a filter ripple. In a ll results in this paper , we use a 7th order Chebychev high-pass filter with maximum passband ripple of 0.1 dB and pa ssband frequency f min = 0 . 16 7 Hz. A n order of 7 was found to be sufficient to have at least 40 d B attenuation at frequencies lower than 0 . 1 Hz. For all further discussion, we assume that each link’s y l ( i ) signal has been filtered using this high-pass filter , and thus ¯ y l = 0 . 2.5 Breathing Estimation Breathing frequency e stimation plays a primary role in breathing d e tection, and thus we discuss frequency estimation prior to breathing d e tection. In this section, we present the maximum likelihood estimate (MLE) of breathing para meters, including freq uency , link ampli- tudes, and link phases, given the model presented in Section 2.3. Maximum likelihood estimation of θ is an extension of the standard sinusoid para meter estimation problem [1 0, p. 193–1 95] in which there is a single signal composed of one sinusoid of unknown p ha se, amplitude, a nd frequency in a dditive white Gaussian noise. In our case, we add itionally have L different link signals, ea ch with its own amplitude and phase, and we have a frequency limited to the ra nge [ f min , f max ] . In our case, under the i.i.d. Gaussian noise model in the presence of breathing, the likelihood f unction is maximized when the following function J is minimized: J ( θ ) = L X l =1 N X i =1 [ y l ( i ) − A l cos(2 π f T s i + φ l )] 2 (3) One can mo dify the derivation of [10, p. 193–19 5] f or this ca se, that is, to minimize J ( θ ) in (3), and show that a good ap p roximation of the MLE of frequency ˆ f is given by ˆ f = argmax f min ≤ f ≤ f max L X l =1      N X i =1 y l ( i ) e − j 2 π f T s i      2 (4) The a pproximation is very good whenever the normal- ized frequency , f T s , is not very close to 0 or 1/2. In our case, we specifically exclud e frequencies c lose to zero, and sample a t a frequency significantly higher than the Nyquist rate. Note that if one wishes to estimate breathing fre- quency from one link alone, one may use (4) with L = 1 . The maximum likelihood link a mplitude estimates { ˆ A l } and phase estimates { ˆ φ l } a re then estimated using ˆ f , and are given by ˆ A l = 2 N      N X i =1 y l ( i ) e − j 2 π ˆ f T s i      (5) ˆ φ l = arcta n − P N i =1 y l ( i ) s in 2 π ˆ f T s i P N i =1 y l ( i ) co s 2 π ˆ f T s i . 2.6 Breathing Detection W e consider d eciding between two hypotheses: H 0 : A breathing person is not present (6) H 1 : A breathing person is present (7) For detection, we study two methods: 1) Single-link breathing detect ion : Use solely the RSS measured on one link in order to dete c t breathing. 2) Network-wide br eathing detection : U se the RSS mea- sured on a ll L > 1 links in the wireless network to detect breathing. By comparing the two methods, we quantify the im- provement in breathing detection possible when data from many links in a network a re used. ARXIV .ORG TECHNICAL REPOR T 4 2.6.1 Single-link breathing detection Consider one link’s RSS data. W ithout loss of genera lity , assume the link number is l = 1 . Then the MLE of ˆ f and ˆ A l are calcula ted from ( 4) and (5) using L = 1 . Our simple assumption is that ˆ A l will have higher amplitude when a breathing person is present. T hus we de tect breathing via the hypothesis test, N ˆ A 2 l H 1 > < H 0 γ link (8) where γ link is a user-defined threshold and N is the total number of samples. 2.6.2 Network-wide breathing detection From all L measured links, we must decide between H 0 and H 1 . W e d o not have a statistical model for A l for the case of H 1 , but we have assumed that the va lues of A l are higher during breathing. As a first proof of concept, we study breathing de tection based on a normalized sum of the squared amplitudes ˆ A 2 l over all links, ˆ S , N L L X l =1 ˆ A 2 l H 1 > < H 0 γ net (9) where γ net is a user-defined threshold and we call ˆ S the network-wide breathing statistic . Note that ˆ S is just a scaled version of the maximum of the sum in (4). Multiplication of the ave rage squared link magnitude by N helps ensure a constant threshold as a function of N , since the average squared link magnitude is approximately inversely proportional to N under H 0 . 2.7 P erformance Analysis W e study the experimental performance of ea ch de - tector via the probability of false alarm, P F A , and the probability of missed detec tion, P M . The value P F A is the fra ction of experiments that do not have b reathing occurring for which H 1 is decided ; and P M is the f raction of expe r iments that do have a person b reathing in the network for which H 0 is dec id ed. Obviously , we’d like P M = P F A = 0 , but there is a tradeoff between the two. Clearly , each application will have different require- ments for P M and P F A . For example, in post-surgical breathing monitoring, we will want to have a very low P M , a s we do not wa nt to miss the f a ct that a patient has stopped breathing. In contrast, in a search & rescue operation, we might be ver y sensitive to P F A , because saying that there is someon e alive in a pile of building rubble when there is not would cause us to begin a long a nd fruitless sea rch, when time should be used elsewhere to find true casualties. W e study the performance of breathing rate estimation via the RMSE of ˆ f , that is, RMSE = v u u t 1 K K X k =1 [ ˆ f ( k ) − f ( k )] 2 where ˆ f ( k ) and f ( k ) are the frequency estimate and actual breathing frequency , respectively , during exp e ri- ment realiza tion k , and there are K total experimental realizations. 3 E X P E R I M E N T S Our exper iments are designed to test BreathT aking for use in a medical enviro nment to monitor the breathing of a sleeping patient. This section describes the net- work hardware and software, e nviron ment, experimen- tal setup, and actua l b reathing r a te. 3.1 Network W e use a network of twenty MEMSIC T elosB wireless sensors opera ting the IEE E 802.1 5.4 protocol on channel 26 (a center frequency of 24 80 MHz). The sensors r un T inyOS and SPIN [ 11], a token passing p rotocol in which each node tra nsmits in sequence. When not transmitting, nodes are in receive mode, and record the RSS and node id f or any received packet. Each tra nsmitted packet in- cludes the most recent RSS value recorded for ea ch other node. A base station sensor , pla ced in the hallway about 3 meters from the clinical room door , overhears all of the transmitted pa cket d a ta, which is then time-stamped and recor ded on a laptop. A packet is transmitted by some node approximately once e very 12 ms, and thus an individual node transmits once every 2 40 ms. Thus each link has its RSS measured at a sampling rate of 4.1 6 Hz. W e note this is more than sufficient to mea sure our maximum breathing rate of f max = 0 . 6 67 Hz. T o study the effect of a ntenna directionality , exper- iments are conducted with the wireless sensors using one of two different antennas: ( 1) a d ipole antenna with omni-directional horizontal patte rn with gain of 2.25 dBi; and ( 2 ) a directional pa tc h antenna with a gain of 8.0 dBi. 3.2 En vir onment and Setup W e deploy the network in a clinical room in the Univer- sity of U tah School of Med icine. The clinical room is used for studies in the Department of Anesthesiology , and is designed to appe ar like a standard hospital patient room, with cabinets for blankets and medical supplies, mon- itoring equipment, computer monitors, and a hospital bed in the center of the room. The hospital bed is a Hill- Rom P1 900 bed which automatically changes pressure in different parts of the bed ev e ry 3-4 minutes (and thus prevents bed so res in immobile pa tients). W e mentio n this bed movement “feature” be cause it means that the person lying in the bed is not perfectly stationary , e ven when he does not move himself. A diagram of the experimental setup is shown in Figure 4. Sensors a re plac ed on the sides of the beds, but not connected in any way to the bed. In this wa y , we ensure tha t the patient’s breathing in no way moves the sensors. This is required bec a use we want to show that the pe riodicity in the RSS is caused by the breathing ARXIV .ORG TECHNICAL REPOR T 5 of the person, not the movement of the sensors. S everal of the sensors are placed at height of 0.9 meters on adjustable-height tab le s positioned at the long sides of the hospital bed. S ensors are also placed a t a height of 0.8 meters on two wheeled carts, one metal and one plastic, placed at the f oot a nd hea d of the bed, respectively . Finally , four sensors are attached to PVC- pipe sta nds which ho ld the sensors at a height o f 0.9 meters, and placed on the sides of the bed. 3.3 Breathing Rate During ea ch experiment in which a pe rson is present in the bed, we must have gro und truth knowledge of the person’s breathing rate. I n each expe riment, the pe rson listens to a metronome set to a desired breathing rate, and ensures that they breath at the same rate as the metronom e. The person is also connected to a end-tida l CO 2 monitor , which involves tubes, two to f e ed oxygen into the person’s nostrils, and a nother two to connect the first tubes to a gas sensor which mea sures CO 2 and displays it on a screen. The per son breathes through their nose in all exper iments to ensure proper functioning of the end- tidal CO 2 monitor . The monitor estimates frequency from the CO 2 sensor ’s signal, and displays its estimated breathing ra te. W e video record this screen, and in post-processing, e nsure that the person’s breath- ing was in fa ct at the desired rate. 4 R E S U LT S 4.1 Single Link Breathing Monitoring In this section, we quantify the observation made in the introduction that detection of breathing on a ny sin gle link is unreliable. W e compare an experiment run with the p a tch a ntennas on the nodes, with a person lying in the bed with their chest at a height of 1. 01 meters ( H 1 ) a nd without a person in the room ( H 0 ). During the H 1 condition (person lying on the bed ) the pe r son is using a metronome to breath at a known ra te of 15 bpm. In single-link breathing monitoring , we first use (4) with L = 1 to estimate f requency ˆ f which represents the breathing rate estimated for a n individual link. T hen, we use ( 5) to ca lculate ˆ A l , which represents the RSS signal amplitude a t that breathing ra te. Each link is considered separately , a nd we estimate ˆ A l for each T = 30 s observa tion period for the c ourse of the experiments. W e use all the links measured during the experiment to obtain an ensemble of results that characterize the ˆ A l during single-link measurements. W e display the histograms of ˆ A l in Figure 2. Occur- rences are normalized by the total number of realiza tions of ˆ A l in each experiment, and shown on a log scale to emphasize the tail behavior . From the histograms, it is possible to see that ˆ A l has a heavier tail during H 1 compared to H 0 . However , the maximum ˆ A l recorded during H 0 is 0.7 2, a nd only a ver y small percentage ( 63 out of 912 0) of realizations during H 1 fall a bove 0 .72. That is, a fe w links, during a few 30 -second periods, measure higher amplitude sinusoidal components when a p erson is present in the bed than when no one is present. If we set a thr eshold γ link = 0 . 72 in (8) so that we have zero f a lse alar ms, we would de tect breathing only on 0.7% of links. 0 0.5 1 1.5 10 −4 10 −3 10 −2 10 −1 10 0 Fraction of Occurrances Amplitude Estimate No Person Breathing Fig. 2. Nor maliz ed histogram, on log-s cale, of ˆ A l fo r single link breathing monitoring given H 0 and H 1 . Single- link amp litudes ha ve a some what hea vier tail than the no- person case. Despite the low detection rate , do these links’ data accurately estimate the breathing frequency? Of the 63 realizations with ˆ A l > 0 . 72 , 17 provide ˆ f estimates within 1 bpm of the a ctual breathing ra te (1 5 bpm) . However , the other 46 estimates are nearly uniformly distributed on [ f min , f max ] . In sum, one cannot expect to d etect breathing or estimate breathing ra te on any single deployed link. Further , even if one has many links in a network, it would be unreliable, as a mo nitoring method, to look at single-link amplitude and frequency e stimates. 4.2 BreathT aking Rate Estimation Next, we consider at network-wide breathing monitor- ing. For the sa me H 1 experiment described in Se ction 4.1, we study network-wide breathing rate estimates, which are ca lculated using (4) with L set to the total number of links in the network. W e calculate ra te estimation performance for a variety of different periods T . The vast majority of breathing rate estimates fall within 5 bpm of the actual rate – a small frac tion do not. W e call these estimates that a re more than 5 bpm from the actual rate “invalid” rate estimates, a nd report the percentage of rate estimates that a re invalid. W e also calculate the RMSE and bias of the estimates that are valid, i.e. , within 5 bpm of the true rate. The exp e rimental results, shown in Figure 3, show that for T ≥ 30 s, less than 2% of ra te e stimates can be described as invalid. The RMS E for va lid estim ates is lower than 0.5 for all observation periods T ≥ 25 s. ARXIV .ORG TECHNICAL REPOR T 6 20 30 40 50 60 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Breathing Rate Error (bpm) Observation Period T (s) 20 30 40 50 60 0 2 4 6 8 10 12 14 16 Percent of Estimates Invalid RMSE Bias Fig. 3. RMSE and bias of valid BreathT aking frequency estimates for controlled breathing / patch antenna exper- iment (actual breathing rate of 15 bpm), and percent of rate estimates that are inv alid (r ight y- axis), vs. obser va- tion period T . For perspective, current medical d evices typically re- port breathing rate as a n integer number of breaths per minute, thus rate errors less than 0.5 bpm would be ins ignificant. The bia s is small, on the order of 0.1 bpm. For T ≥ 50 s, there are no invalid breathin g rate estimates. 4.3 BreathT aking Amplitude Estimation Once we obtain the MLE of frequency ˆ f using the network RSS data a s in Section 4.2, we ca n estimate the amplitudes ˆ A l . Note that there are no “actua l” values of ˆ A l ; some links will measure high amplitude, and others will not. W e are particularly interested in the links l with particularly high ˆ A l . For the same H 1 experiment described in Section 4.1, consider the ˆ A l for T = 30 s. Only 5% of links l have an amplitude ˆ A l > 0 . 33 1 , links we refer to as h igh amplitude links . In Figure 4, we plot the locations of the high amplitude links by drawing a d a shed line between their tr ansmitter and receiver coordinates. W e can see that the link s which cross through the chest area are the ones that a re particularly affected by breathing. Still, only a fraction of the links that cross through the chest measure high ˆ A l . What other characteristics do these high amplitude links have? W e find that high amplitude links have unusually low avera ge RSS. Over all links, the average measured RSS is -3 9.9. When considering only high amplitude links, the a verage mea - sured RSS is -48 .6, almost 9 dB lower , a very significant difference. This difference cannot be e xplained by longer path length – high amplitude links are only 13% longer , on average, than the average path length of all links. Since links that in a deep fade exper ience greater tem- poral variations due to changes in the environment [9], it makes sense that the amplitude of the breathing-induced 0 0.5 1 −0.5 0 0.5 1 1.5 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 X Coordinate (m) Y Coordinate (m) Be d Ou t l i n e P e r s o n 6 Sen so r Coo r d & No . Hi g h Am p l . Li n k Fig. 4. Exper imental la yout showing sensors, bed, and person’ s approximate pos ition. Dashed lines in dicate high amplitude links . change would be more noticeable for links with lower than aver a ge RSS. One lesson is that links in a deep f ade are more use- ful f or breathing monitoring. Future work may explore changing the center frequency on links, or measuring wideband frequency response, with the goal of ada p - tively using da ta from links’ frequency nulls. Although we do not explore this idea in this pape r , we would expect to be able to improve results by taking advantage of “deep fade s” wherever in the frequency spectrum they occur . 4.4 BreathT aking Detection P erf ormance In the network-wide ca se, breathing detection is per- formed using a normalized sum of the squared am- plitudes | ˆ A l | 2 over all links l , as given in (9). In this section, we study the performance of this detector . Using the same exp e riments as presented in Section 4 .1, we calculate ˆ S from (9) for each T second period, testing detector p e rformance for each T in the r ange 15 to 60 seconds, in 5 second increments. Figure 5 shows the probability density functions (pdf s) of ˆ S for H 0 and H 1 cases, f or T = 15 (top subplot) and T = 30 (bottom subplot). W e fin d first that ˆ S in the H 0 case a lways f alls in a narrow range, between 0.98 a nd 1.45. During H 1 , the ˆ S values ha s a minimum of 1 .57 (at T = 15 ). Further , as T increases, ˆ S values also increase. For T = 30 and T = 60 , the minimum ˆ S values recorded are 1.6 3 and 2.03, respectively . W e can conclude that for this e x periment, because of the lack of overla p in value of ˆ S in the two cases, one can build a reliable detector . For example, we can set γ net = 1 . 50 in ( 9) and perfectly d istinguish betwee n no person present and a breathing person present. ARXIV .ORG TECHNICAL REPOR T 7 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 7.5 P rob . D e n s it y T = 15s N e t w o r k -w ide B r e at h in g S ta t is t ic ˆ S 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 7.5 P rob . D e n s it y T = 30s N e t w o r k -w ide B r e at h in g S ta t is t ic ˆ S Empty Person Empty Person Fig. 5. Probability density functions fo r ˆ S giv en H 0 (Empty) v s. given H 1 (P erson) for the (top) T = 15 and (bottom) T = 30 s econd observation per iods, fo r e xper iments using patch antennas . 4.5 Antennas Experiments discussed above use pa tc h antennas with a 8 dBi a ntenna gain. In this section , we compare the results when using less directional antennas. W e run more experiments with all nodes connected to dipole antennas, which have a omnidirection al pattern in the horizontal plane. The first exper iment is a n H 0 experi- ment, with no person in the room, and little movement in the hallway outside of the room. The second experiment is an H 1 experiment, with the person lying in the bed and b reathing at a constant rate of 15 bpm (using a metronom e). The results, shown in Figure 6, are worse than with the directional antennas. The values of ˆ S given H 0 have increased regardless of T , to the ra nge from 1.15 to 1.8 5. The values of ˆ S given H 1 now overlap with those given H 0 for T = 15 s (and T up to 25 s), so regardless of the threshold chosen, we cannot have a p e rfect d etector . W e further b e lieve that movement in the hallway outside of the room will have a greater impact when using dipole antennas, a s compared to when using patch antennas. T o test this, we have an experimenter sta nd outside of the (closed) door waving his arms above his head and moving from side to side. While this motion is occurring, we r un two more H 0 experiments, one with dipole antennas, a nd one with patch antennas. Using this data, we recalculate the values of ˆ S given H 0 . The results are shown in Figure 7 . The change in H 0 values for ˆ S c ha nges slightly when using pa tch antennas, and changes significantly with dipole antennas. W ith pa tc h a ntennas, the max imum value of ˆ S given H 0 has increased to 1.52 (compared to 1. 45 without motion outside of the door). W ith dipole antennas, the max has increased to 2.08 (compared to 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 P rob . D e n s it y T = 15s Ne t w or k - w i de B r e at h in g St ati s t ic ˆ S 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 P rob . D e n s it y T = 30s Ne t w or k - w i de B r e at h in g St ati s t ic ˆ S Empty Person Empty Person Fig. 6. Probability density functions for the ˆ S gi ven H 0 (Empty) vs. given H 1 (P erson) f or the (top) T = 15 and (bottom) T = 30 s econd observation periods, fo r e xper iments using di pole antennas. 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 P rob . D e n s it y P at c h A n te nna N e t w ork -w i de B r e at hi ng St at is t ic ˆ S Empty Person 1 1.5 2 2.5 3 3.5 4 4.5 5 0 2.5 5 P rob . D e n s it y D ipole An te nna N e t w ork -w i de Br ea t hi ng St at i s t ic ˆ S Empty Person Fig. 7. Probabili ty density functions for the ˆ S whe n T = 30 s given H 0 (Empty) wit h motion outside of the door vs. given H 1 (P erson), for experiments using (top) patch antennas and (bottom) dipole antennas. 1.80 without motion outside of the d oor). In this latter case, even f or medium T ( T = 30 s is shown in Figure 7) , there is overlap in the pdfs of ˆ S given H 0 and H 1 , and thus it is impossible to select a threshold for z ero false alarms and zero missed detections. In conclusion, it remains possible to monitor breathing using dipole antennas. However , it is clearly better , in terms of robustness to motion occurring outside of the room, to use direction al a ntennas. Our experiments using patch antennas are only marginally affected by this motion “noise”. ARXIV .ORG TECHNICAL REPOR T 8 Actual Breathing Rate (bpm) 12.0 15.0 19.0 Percent Estimat e s Invalid 0% 1.6% 0% RMSE of V alid Ests. (bpm) 0.08 0.42 0.30 Bias of V alid Ests. (bpm) -0.03 -0.16 0.21 T ABLE 1 Rate estimation performance fo r three breathing rates Person chest h eight (m) 0.88 1.01 1.13 Percent Estimat e s Invalid 0% 1.6% 0% RMSE of V alid Est s. (bpm) 0.17 0.42 0.32 Bias of V alid Ests. (bpm) 0.008 -0.16 0.24 T ABLE 2 Rate estimation performance fo r three bed heights 4.6 Rate Changes In this section, we compare f requency estimation perfor- mance when the actual breathing rate changes. First, we perform three experiments with sensors using patch a n- tennas in which the per son’s breathing rate is either 12.0 , 15.0, or 1 9.0 bpm. Using the metronome set at d ifferent rates, the person ensures that their breathing follows the desired breathing rate. W e set T = 30 s f or all results. T he results in T able 1 show best performance at the lowest breathing rate tested, 12 bpm, but performance d oes not strictly d e grade with increased a c tual breathing ra te. 4.7 Bed Height In this section, we analyze three e xperiments with the bed (and thus the p e rson) at different heights. In the experiments discussed to this point, the person’s chest is at a height of 1 .01 m above the ground. Here, we ra ise or lower the bed height so that the per son’s chest is at 0.88 m, 1.01 m, and 1.13m, in three different ex periments. At the lowest height, the sensors are nearly line-of- sight (LOS), that is the line connecting two sensors a re mostly unobstructed by the person’s body . At the highest height, the sensors are predominantly at the height of the mattress. In all exper iments, the actual breathing rate is 15 bpm, and we use T = 3 0 s. T able 2 shows the breathing ra te estimation performance. W e find that the best perf ormance is in the nea rly LOS ca se, a b out half the RMSE of the 2nd best height. Note that all bed heights show ac c eptable results, with a ve ry small chance of invalid estimate, and RMSE below 0 .5 bpm. 4.8 Fewer Sensor s In this section, we analyze what happe ns when we use a smaller number of sensors in the network. Since the number of links is proportional to the square of the number of nodes, we expect that ha ving more sensors will dramatica lly improve performance. In fact, the two sensor case is a limiting case which we have explored in Section 4 .1, which showed that one link is insufficient to reliably d e tect and monitor breathing. 7 10 13 16 19 0 0.3 0.6 0.9 1.2 Breathing Rate Error (bpm) Number of Network Nodes 7 10 13 16 19 0 6 12 18 24 Percent of Estimates Invalid RMSE Bias Fig. 8. RMSE and bias of vali d BreathT aking frequency estimates f or controlled breathi ng / patch antenna e xperi- ment (actual breathing rate of 15 bpm and person height of 0.88 m), and percent of rate estimates that are inva lid (right y -axis), vs. number of sensors in the network T . Results are an a ver age over 100 trials using randomly selected subsets of the giv en size. W e use the same da ta collected with the 20-node network a nd test what would have happened with a smaller network as f ollows. Let Y ⊂ { 0 , . . . , 19 } be the subset of nodes which we use in a particular trial. W e run tests with |Y | = 7 , 1 0 , 13 , 16 , 19 . For each subset size, we r un 100 tria ls and aver a ge the results. Subsets are randomly selected in each trial from the full set of nodes { 0 , . . . , 19 } . Figure 8 presen ts the results for the RMSE, bias, and percent valid of the breathing rate estimates. W e can see that estimates with just seve n sensors in the network are poor – a lmost one in four breathing rate estimates is invalid (greater than 5 bpm error). When the number of sensors is increased to thirteen, the pe rcentage of invalid estimates is 1 .3%, and the RMSE of valid estimates is below 0.3 bpm; and the results impro ve somewhat a s the network size incr eases to 16 and 1 9. Notably , there are ze ro invalid frequency estimates with 19 nodes. 4.9 Phase Estimation Beyond link amplitudes and network-wide frequency estimates, there is also information to be ga thered in the p ha se of the sinusoidal signal due to the person’s breathing, in particular , for links which have a high amplitude | ˆ A l | . Consider that if two links measure a sinusoid caused by one person’s breathing, both should be synchrono us, that is, rise or fall a t the same times. However , we d o not know whether inhaling will in- crease or de crease the RSS on any pa rticular link, so one link may reach a maximum while another link reaches its minimum. In ter ms of phase, the { ˆ φ l } l might be π radians apa rt from each other . T o show this effect in the da ta , we study the ˆ φ l estimates f or T = 60 s observation period. For example, ARXIV .ORG TECHNICAL REPOR T 9 1 2 3 4 5 0 o 90 o 270 o 180 o Fig. 9. Estimated phases, ˆ φ l fo r high-amplit ude links l , shown on polar plots for five diff erent experiments. Each e xper iment’ s ˆ φ l val ues, to sa ve s pace, are plotted on a diff erent concentric circle labeled b y experiment number ∈ { 1 , 2 , 3 , 4 , 5 } . Wi thin an experiment, phases are seen to be bimodal, with modes separated b y 180 o . consider what we label experiment 1, a pa tch antenna experiment with the person at heigh t 1.01m breathin g at 15 bpm. For this experiment, we plot φ l for links with the highest 5 % of amplitudes ˆ A l in Figure 9 in the circle with rad ius 1. One may observe from the figure that the phases a re bimodal with two modes at a bout 90 and 27 0 de grees. W e repeat this plotting for four other experiments, denoted exper iments 2 through 5, on different concentric circles on the same polar plot to save space. Aga in, for eac h experiment, phase e stimates for the highest 5 % amplitude links hav e two modes, in each case, separa ted by 18 0 o . These results are promising in the sense that when there a re multiple stationary people breathing in the network, we might be able to estimate the number of people, even when the breathing rates are nearly identi- cal, by the number of modes in the distribution of phase. Further , we may be able to improve breathing detection and monitoring using the fact that phase distribution is bimodal. Such methods must be explored in future work. 5 R E L AT E D W O R K Breathing monitoring via capnography is standard pra c- tice for anaesthetized patients in emergency de p artments and in intensive care uni ts [ 1 2]. The capnometer uses an infrared ab sorption gas analyzer to measure the carbon dioxide concentration in exhaled air (end-tida l C0 2 ). The breathing r ate in th is case is determined by finding the frequency content of the CO 2 concentration signal. The exhaled air is measured using tubes in the nostrils ( e.g. , nasal ca nnula), or from tubes connected to a face ma sk or tracheal tube , which are connected to the capnometer . These tubes may be c ome detached; if so, the capnometer will detect apnea and alar m. Generally , the mask or nasa l cannula may be uncomfortable and limit the p a tient’s movement. W e propose a new non-invasive sensor ( i.e. , sensor not physically attac hed to the patient) for repiratory monitoring, which would a llow a pa tient to sleep normally while be ing monitored. W e note that capnography directly measures exhala tion, while our method indirectly measures br eathing via the periodic changes in the pa tient’s body size. Breathing monitoring can also be performed us- ing plethysmography (respiratory inductive or thoracic impedance p le thysmography). These methods measure, using electrodes placed on the body , the change in inductance or impedance caused by inhalation and ex- halation. These electro des can be contained in a band worn around the chest. This is a method used in home monitors for infants at risk of SIDS [ 13]. In comparison, the proposed system does not need to be atta c hed to a person’s body or have wires connected to the p e rson. Note that a t physi cian’s offices where procedures requiring sedation are performed, capnography and plethysmography are not typically used due to equip- ment costs. Instead, patients are monitor ed by a p ulse oximeter , which measures oxygen saturation in blood. I f a pa tient stops breathing, oxygen satura tion decreases; however , the pulse oximeter will de tect this desa tur a tion only minutes after breathing ceases [14]. Most closely related to the proposed system a re other proposed non-invasive b reathing sensors. Microwave Doppler rad a r systems have bee n proposed for breathing rate e stimation [15] [16]. Ultra-wideba nd (UWB) radar has also been proposed f or unobtrusive mo nitoring of patient’s vital signs [17] [18]. In fact, UWB radars may even be sensitive enough to be able to de te ct a stationary person’s heart rate [19]. In comparison, our proposed system uses o ff-the-shelf wireless devices which are significantly lower in cost than ra dar devices. Rather than using a single high-capab ility rad a r transceiver , our system uses a network of many simple tra nsceivers. 6 C O N C L U S I O N S This paper presents a non-invasive respiration moni- toring te chnique called BreathT aking which uses signal strength measurements be tween many pairs of wireless devices to monitor breathing of an otherwise stationary person. W e present a maximum likelihood estimator to estimate breathing pa r ameters, including breathing rate , using a ll of the measured links’ RSS data simultane- ously . W e present detection algorithms based on those estimated pa rameters, a nd an experimental testbed and procedure to valida te BreathT a king. Using extensive ex p erimental data collected with a person lying in a hospital bed, we demonstrate the performance of BreathT a king. W e find breathing rate can be estimated within 0. 1 to 0. 4 bpm erro r using 30 seconds of mea surements. W e show that the links most ARXIV .ORG TECHNICAL REPOR T 10 affected by breathing a re the ones which receive low average RSS. B reathing detection is d emonstrated to re- liably distinguish between the breathing and its absence using 15 seconds of RSS data (in patch antenna experi- ments) and using 30 sec onds of da ta (in dipole a ntenna experiments), without f a lse alarm or missed d etection. Antenna directionality is useful to increase robustness to external motion. Interestingly , the estimated phases of links which are affected by breathing distribution have a bimodal distribution with the two modes separated by 180 de grees. If BreathT aking is to be used for medical purposes, extensive evaluation on many people, and in many settings, must be performed . In addition, this work explored RSS-based breathing monitoring using 2.4 GHz 802.15 .4 ra dios – the system may benefit from transceivers with other physical layer protocols and center frequencies. 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