计算机科学与技术（参考文献）Understanding and Modeling of WiFi Signal Based Human Activity Recognition

Understanding and Modeling of WiFi Signal Based Human Activity Recognition Wei Wangt Alex X.Liutt Muhammad Shahzad:Kang Ling' Sanglu Lut tState Key Laboratory for Novel Software Technology,Nanjing University,China +Dept.of Computer Science and Engineering,Michigan State University,USA ww@nju.edu.cn,(alexliu,shahzadm)@cse.msu.edu,lingkang@smail.nju.edu.cn,sanglu@nju.edu.cn Abstract limited operation range of just tens of centimeters [2].Wearable Some pioneer WiFi signal based human activity recognition sys- sensors based approaches are inconvenient sometimes because of tems have been proposed.Their key limitation lies in the lack of the sensors that users have to wear.Recently.WiFi signal based hu- a model that can quantitatively correlate CSI dynamics and human man activity recognition systems,such as WiSee [17].E-eyes [27]. activities.In this paper.we propose CARM,a CSI based human and WiHear[26],have been proposed based on the observation that Activity Recognition and Monitoring system.CARM has two the- different human activities introduce different multi-path distortions oretical underpinnings:a CSI-speed model,which quantifies the in WiFi signals.WiSee uses USRP to capture the OFDM signals correlation between CSI value dynamics and human movement and measures the Doppler shift in signals reflected by human bod- speeds,and a CSI-activity model,which quantifies the correlation ies to recognize nine gestures.E-eyes uses Channel State Inform- between the movement speeds of different human body parts and ation(CSI)histograms as fingerprints for recognizing daily human a specific human activity.By these two models,we quantitatively activities such as brushing teeth.WiHear uses specialized direc- build the correlation between CSI value dynamics and a specific tional antennas to obtains CSI variations caused by lip movement human activity.CARM uses this correlation as the profiling mech- for recognizing spoken words.Their key advantages over camera anism and recognizes a given activity by matching it to the best-fit and sensor based approaches are that they do not require lighting, profile.We implemented CARM using commercial WiFi devices provide better coverage as they can operate through walls,preserve and evaluated it in several different environments.Our results show user privacy,and do not require users to carry any devices as they that CARM achieves an average accuracy of greater than 96%. rely on the WiFi signals reflected by humans Categories and Subject Descriptors 1.2 Limitations of Prior Art The key limitation of these pioneer WiFi based human activity C2.1 [Network Architecture and Design]:Wireless communica- recognition systems is the lack of a model that can quantitatively tion correlate CSI dynamics and human activities.As such,these sys- General Terms tems mostly rely on the statistical characteristics of WiFi signals such as Doppler movement directions and distributions of signal Experimentation,Measurement strength,to distinguish different human activities.The lack of such a model limits the further development of WiFi based human activ- Keywords ity recognition technologies.Without such a model,it is difficult Channel State Information(CSD);WiFi;Activity Recognition; to understand the correlation between WiFi signal dynamics and human activities.Furthermore,without such a model,it is diffi- 1.INTRODUCTION cult to optimize the performance of such systems due to the lack of adjustable parameters,and we have to resort to trial-and-error for 1.1 Motivation performance optimization. Human activity recognition is the core technology that enables a 1.3 Proposed Approach wide variety of applications such as health care,smart homes,fit- ness tracking.and building surveillance.Traditional approaches In this paper,we propose CARM,a CSI based human Activity use cameras [6],radars [2],or wearable sensors [7,33].How- Recognition and Monitoring system.CARM consists of two Com- ever,camera based approaches have the fundamental limitations mercial Off-The-Shelf(COTS)WiFi devices as shown in Figure 1,one for continuously sending signals,which can be a router. of requiring line of sight with enough lighting and breaching hu- and one for continuously receiving signals,which can be a laptop. man privacy potentially.Low cost 60 GHz radar solutions have When a human activity is performed in the range of these two devices,on the WiFi signal receiver end,CARM recognizes the Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed human activity based on how the CSI value changes.CARM has for profit or commercial advantage and that copies bear this notice and the full cita- two theoretical underpinnings that we propose in this paper:a tion on the first page.Copyrights for components of this work owned by others than CSI-speed model and a CSl-activity model.Our CSI-speed model ACM must be honored.Abstracting with credit is permitted.To copy otherwise,or re- quantifies the correlation between CSI value dynamics and human publish,to post on servers or to redistribute to lists,requires prior specific permission movement speeds.Our CSI-activity model quantifies the correla- and/or a fee.Request permissions from Permissions@acm.org. MobiCom'/5,September 7-11,2015,Paris.France. tion between the movement speeds of different human body parts ©2015ACM.ISBN978-1-4503-3619-2/1509.S15.00 and a specific human activity.By these two models,we quantitat- D0 http:ldx.doi.org/10.11452789168.2790093. ively build the correlation between CSI value dynamics and a spe-

Understanding and Modeling of WiFi Signal Based Human Activity Recognition Wei Wang† Alex X. Liu†‡ Muhammad Shahzad‡ Kang Ling† Sanglu Lu† †State Key Laboratory for Novel Software Technology, Nanjing University, China ‡Dept. of Computer Science and Engineering, Michigan State University, USA ww@nju.edu.cn, {alexliu,shahzadm}@cse.msu.edu, lingkang@smail.nju.edu.cn, sanglu@nju.edu.cn Abstract Some pioneer WiFi signal based human activity recognition sys￾tems have been proposed. Their key limitation lies in the lack of a model that can quantitatively correlate CSI dynamics and human activities. In this paper, we propose CARM, a CSI based human Activity Recognition and Monitoring system. CARM has two the￾oretical underpinnings: a CSI-speed model, which quantifies the correlation between CSI value dynamics and human movement speeds, and a CSI-activity model, which quantifies the correlation between the movement speeds of different human body parts and a specific human activity. By these two models, we quantitatively build the correlation between CSI value dynamics and a specific human activity. CARM uses this correlation as the profiling mech￾anism and recognizes a given activity by matching it to the best-fit profile. We implemented CARM using commercial WiFi devices and evaluated it in several different environments. Our results show that CARM achieves an average accuracy of greater than 96%. Categories and Subject Descriptors C2.1 [Network Architecture and Design]: Wireless communica￾tion General Terms Experimentation,Measurement Keywords Channel State Information (CSI);WiFi; Activity Recognition; 1. INTRODUCTION 1.1 Motivation Human activity recognition is the core technology that enables a wide variety of applications such as health care, smart homes, fit￾ness tracking, and building surveillance. Traditional approaches use cameras [6], radars [2], or wearable sensors [7, 33]. How￾ever, camera based approaches have the fundamental limitations of requiring line of sight with enough lighting and breaching hu￾man privacy potentially. Low cost 60 GHz radar solutions have Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full cita￾tion on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or re￾publish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org. MobiCom’15, September 7–11, 2015, Paris, France. c 2015 ACM. ISBN 978-1-4503-3619-2/15/09 ...$15.00. DOI: http://dx.doi.org/10.1145/2789168.2790093. limited operation range of just tens of centimeters [2]. Wearable sensors based approaches are inconvenient sometimes because of the sensors that users have to wear. Recently, WiFi signal based hu￾man activity recognition systems, such as WiSee [17], E-eyes [27], and WiHear [26], have been proposed based on the observation that different human activities introduce different multi-path distortions in WiFi signals. WiSee uses USRP to capture the OFDM signals and measures the Doppler shift in signals reflected by human bod￾ies to recognize nine gestures. E-eyes uses Channel State Inform￾ation (CSI) histograms as fingerprints for recognizing daily human activities such as brushing teeth. WiHear uses specialized direc￾tional antennas to obtains CSI variations caused by lip movement for recognizing spoken words. Their key advantages over camera and sensor based approaches are that they do not require lighting, provide better coverage as they can operate through walls, preserve user privacy, and do not require users to carry any devices as they rely on the WiFi signals reflected by humans. 1.2 Limitations of Prior Art The key limitation of these pioneer WiFi based human activity recognition systems is the lack of a model that can quantitatively correlate CSI dynamics and human activities. As such, these sys￾tems mostly rely on the statistical characteristics of WiFi signals, such as Doppler movement directions and distributions of signal strength, to distinguish different human activities. The lack of such a model limits the further development of WiFi based human activ￾ity recognition technologies. Without such a model, it is difficult to understand the correlation between WiFi signal dynamics and human activities. Furthermore, without such a model, it is diffi- cult to optimize the performance of such systems due to the lack of adjustable parameters, and we have to resort to trial-and-error for performance optimization. 1.3 Proposed Approach In this paper, we propose CARM, a CSI based human Activity Recognition and Monitoring system. CARM consists of two Com￾mercial Off-The-Shelf (COTS) WiFi devices as shown in Figure 1, one for continuously sending signals, which can be a router, and one for continuously receiving signals, which can be a laptop. When a human activity is performed in the range of these two devices, on the WiFi signal receiver end, CARM recognizes the human activity based on how the CSI value changes. CARM has two theoretical underpinnings that we propose in this paper: a CSI-speed model and a CSI-activity model. Our CSI-speed model quantifies the correlation between CSI value dynamics and human movement speeds. Our CSI-activity model quantifies the correla￾tion between the movement speeds of different human body parts and a specific human activity. By these two models, we quantitat￾ively build the correlation between CSI value dynamics and a spe-

cific human activity.CARM uses this quantitative correlation as the The third challenge is that CSI values are too noisy to be dir- profiling mechanism and recognizes a given activity by matching it ectly used for human activity recognition.Even in a static en- to the best-fit profile. vironment without any human activity,CSI values fluctuate be- cause WiFi devices are susceptible to surrounding electromagnetic noises.Moreover,the internal state changes in WiFi devices,e.g.. transmission rate adaptation and transmission power adaptation of- Wireless route ten introduce impulse and burst noises in CSI values.General pur- pose denoising methods,such as low-pass filters or median filters, do not perform well in removing these impulse and bursty noises for two reasons:First,the sampling rates that these methods require are much higher than the frequency of the WiFi signal.Second,the noise density in CSI values is too high for traditional filters,which Figure 1:CARM System only work well for low density noise.In this paper,we propose a Our CSI-speed model and CSI-activity model advance the state- principal component analysis(PCA)based CSI denoising scheme. of-the-art on WiFi signal based human activity recognition from This scheme is based on our observation that the signal fluctuations two fronts.First,they provide us the theoretical basis to under- caused by body movements in all subcarriers of the CSI values are stand,even quantitatively.the relationship between CSI value dy correlated. namics and human movement speeds,and the relationship between The fourth challenge is to capture body movements in the pres- the movement speeds of different human body parts and human ence of carrier frequency offset(CFO).CFO is the dynamically activities.Regarding the relationship between CSI value dynamics changing difference in carrier frequencies between a pair of WiFi and human movement speeds,for example,our model shows that devices,which occurs due to the minor physical differences in high-speed body part movement generates high-frequency changes hardware and other factors such as temperature changes [8].CFO in CSI values.Regarding the relationship between the movement causes the phase values of the received signal to change,making it speeds of different human body parts and human activities,tak- hard to distinguish whether the phase value changed is due to CFO ing the activity of falling down as an example,our model shows or due to human movement.To address this challenge.we use the that it can be characterized as a sudden increase in body movement CSI signal power to infer the body movement.We show that CSI speed in less than one second.Second,these two models provide us signal power is not affected by CFO,but retains information about the tunable parameters to optimize the performance of WiFi signal the movement speeds of the body. based human activity recognition.For example,according to our The fifth challenge is to automatically detect the start and end models,the CSI sampling rate should be chosen as 800 samples per of a human activity.To address this challenge,we use the eigen- second because the typical human movement speed corresponds to vectors obtained from PCA.The key idea is that in the absence of CSI components of lower than 300 Hz. any activity,the time-series of CSI values contain random noise and consequently,the signal eigenvector varies randomly.During a hu- 1.4 Technical Challenges and Our Solutions man activity,the signals in subcarriers become correlated and the The first technical challenge is to estimate human movement signal eigenvector becomes smooth.We capture the smoothness of speeds from CSI values based on our CSI-speed model.This the eigenvector by calculating its high-frequency energy and com is challenging because the CSI measurements at the receiver are pare it to a dynamically adapting threshold to detect start and end. mixed WiFi signals arrived from multiple paths,which changes as 1.5 Key Technical Novelty and Results human moves.Furthermore,different human body parts move at different speeds for a given activity and the WiFi signals reflected The key technical novelty of this paper is two fold.First,we pro- by different body parts are also mixed at the receiver.Our key ob- pose the CSI-speed model and the CSI-activity model to quantify servation is that these signals are linearly combined so that their the correlation between CSI value dynamics and a specific human frequencies are preserved when they are mixed together.There- activity.Second,we propose a set of signal processing techniques. fore,we use Discrete Wavelet Transform (DWT)to separate the such as PCA based denoising and DWT based feature extraction, for human activity recognition based on the CSI-speed model and frequency components that represent different movement speeds. The advantage of DWT is that it provides a proper tradeoff between the CSI-activity model.The key technical depth of this paper lies time and frequency resolution and enables the measurement of both in the signal processing aspect such as the theoretical analysis of the correlation between CSI values of subcarriers and the relation- fast and slow activities. The second challenge is to build the CSI-activity model that is ro- ship between multi-path speeds and CFR power.We implemented bust for different humans.For the same activity,to a certain degree, CARM on commercial WiFi devices and evaluated it in multiple environments.Our results show that CARM achieves an average different people perform it differently and even the same person performs it differently at different times.To address this challenge, activity recognition accuracy of 96%.For a new environment and we propose a Hidden Markov Model(HMM)based human activity a new person that the system has never been trained on,CARM can recognition approach.We use the patterns of movement speeds for still achieve a recognition accuracy for more than 80% different activities to build their corresponding HMM based mod- els.The features that we extract to infer the speed patterns are 2.RELATED WORK only affected by movement speeds of the body and are relatively Existing work on device-free human activity recognition and agonistic to environmental changes.This enables us to recognize localization can be divided into four categories:Received Signal activities even when the environment changes.We choose HMM Strength Indicator(RSSI)based,specialized hardware based.radar because of its inherent capability to recognize the same activities based,and CSI based. that are done at different speeds.To recognize a sample of an un- RSSI Based:RSSI based human activity recognition systems known activity,we evaluate the unknown samples against HMMs leverage the signal strength changes caused by human activities of all activities and find the model that gives the highest likelihood. [3,22,23].This approach can only do coarse grained human activity

cific human activity. CARM uses this quantitative correlation as the profiling mechanism and recognizes a given activity by matching it to the best-fit profile. Wireless router Laptop Wireless signal reflection Figure 1: CARM System Our CSI-speed model and CSI-activity model advance the state￾of-the-art on WiFi signal based human activity recognition from two fronts. First, they provide us the theoretical basis to under￾stand, even quantitatively, the relationship between CSI value dy￾namics and human movement speeds, and the relationship between the movement speeds of different human body parts and human activities. Regarding the relationship between CSI value dynamics and human movement speeds, for example, our model shows that high-speed body part movement generates high-frequency changes in CSI values. Regarding the relationship between the movement speeds of different human body parts and human activities, tak￾ing the activity of falling down as an example, our model shows that it can be characterized as a sudden increase in body movement speed in less than one second. Second, these two models provide us the tunable parameters to optimize the performance of WiFi signal based human activity recognition. For example, according to our models, the CSI sampling rate should be chosen as 800 samples per second because the typical human movement speed corresponds to CSI components of lower than 300 Hz. 1.4 Technical Challenges and Our Solutions The first technical challenge is to estimate human movement speeds from CSI values based on our CSI-speed model. This is challenging because the CSI measurements at the receiver are mixed WiFi signals arrived from multiple paths, which changes as human moves. Furthermore, different human body parts move at different speeds for a given activity and the WiFi signals reflected by different body parts are also mixed at the receiver. Our key ob￾servation is that these signals are linearly combined so that their frequencies are preserved when they are mixed together. There￾fore, we use Discrete Wavelet Transform (DWT) to separate the frequency components that represent different movement speeds. The advantage of DWT is that it provides a proper tradeoff between time and frequency resolution and enables the measurement of both fast and slow activities. The second challenge is to build the CSI-activity model that is ro￾bust for different humans. For the same activity, to a certain degree, different people perform it differently and even the same person performs it differently at different times. To address this challenge, we propose a Hidden Markov Model (HMM) based human activity recognition approach. We use the patterns of movement speeds for different activities to build their corresponding HMM based mod￾els. The features that we extract to infer the speed patterns are only affected by movement speeds of the body and are relatively agonistic to environmental changes. This enables us to recognize activities even when the environment changes. We choose HMM because of its inherent capability to recognize the same activities that are done at different speeds. To recognize a sample of an un￾known activity, we evaluate the unknown samples against HMMs of all activities and find the model that gives the highest likelihood. The third challenge is that CSI values are too noisy to be dir￾ectly used for human activity recognition. Even in a static en￾vironment without any human activity, CSI values fluctuate be￾cause WiFi devices are susceptible to surrounding electromagnetic noises. Moreover, the internal state changes in WiFi devices, e.g., transmission rate adaptation and transmission power adaptation of￾ten introduce impulse and burst noises in CSI values. General pur￾pose denoising methods, such as low-pass filters or median filters, do not perform well in removing these impulse and bursty noises for two reasons: First, the sampling rates that these methods require are much higher than the frequency of the WiFi signal. Second, the noise density in CSI values is too high for traditional filters, which only work well for low density noise. In this paper, we propose a principal component analysis (PCA) based CSI denoising scheme. This scheme is based on our observation that the signal fluctuations caused by body movements in all subcarriers of the CSI values are correlated. The fourth challenge is to capture body movements in the pres￾ence of carrier frequency offset (CFO). CFO is the dynamically changing difference in carrier frequencies between a pair of WiFi devices, which occurs due to the minor physical differences in hardware and other factors such as temperature changes [8]. CFO causes the phase values of the received signal to change, making it hard to distinguish whether the phase value changed is due to CFO or due to human movement. To address this challenge, we use the CSI signal power to infer the body movement. We show that CSI signal power is not affected by CFO, but retains information about the movement speeds of the body. The fifth challenge is to automatically detect the start and end of a human activity. To address this challenge, we use the eigen￾vectors obtained from PCA. The key idea is that in the absence of any activity, the time-series of CSI values contain random noise and consequently, the signal eigenvector varies randomly. During a hu￾man activity, the signals in subcarriers become correlated and the signal eigenvector becomes smooth. We capture the smoothness of the eigenvector by calculating its high-frequency energy and com￾pare it to a dynamically adapting threshold to detect start and end. 1.5 Key Technical Novelty and Results The key technical novelty of this paper is two fold. First, we pro￾pose the CSI-speed model and the CSI-activity model to quantify the correlation between CSI value dynamics and a specific human activity. Second, we propose a set of signal processing techniques, such as PCA based denoising and DWT based feature extraction, for human activity recognition based on the CSI-speed model and the CSI-activity model. The key technical depth of this paper lies in the signal processing aspect such as the theoretical analysis of the correlation between CSI values of subcarriers and the relation￾ship between multi-path speeds and CFR power. We implemented CARM on commercial WiFi devices and evaluated it in multiple environments. Our results show that CARM achieves an average activity recognition accuracy of 96%. For a new environment and a new person that the system has never been trained on, CARM can still achieve a recognition accuracy for more than 80%. 2. RELATED WORK Existing work on device-free human activity recognition and localization can be divided into four categories: Received Signal Strength Indicator (RSSI) based, specialized hardware based, radar based, and CSI based. RSSI Based: RSSI based human activity recognition systems leverage the signal strength changes caused by human activities [3,22,23]. This approach can only do coarse grained human activity

recognition with low accuracy because the RSSI values provided quency f measured at time t.CSI measurements basically con- by the commercial devices have very low resolution [23].For RSSI tains these CFR values.Let Nr=and NR=represent the num- based gesture recognition,the accuracy is 56%over 7 different ges- ber of transmitting and receiving antennas,respectively.As CSI is tures [21].Sigg et al.use software radio to improve the granularity measured on 30 selected OFDM subcarriers for a received 802.11 of RSSI values and consequently improve the accuracy of activity frame.each CSI measurement contains 30 matrices with dimen- recognition to 72%for 4 activities [22].In comparison,CARM sions NTx NRz.Each entry in any matrix is a CFR value between uses CSI values and achieves an accuracy of 96%. an antenna pair at a certain OFDM subcarrier frequency at a par- Specialized Hardware Based:Fine-grained radio signal meas- ticular time.Onwards,we call the time-series of CFR values for urements can be collected by software defined radio or specially a given antenna pair and OFDM subcarrier as CS/stream.Thus, designed hardware [11,12.14,17].WiSee uses USRP to capture there are 30 x NTz x NRz CSI streams in a time-series of CSI the WiFi OFDM signals and measures the Doppler shift in signals values. reflected by human bodies to recognize a set of nine different ges tures with an accuracy of 95%[17].AllSee uses a specially de de signed analog circuit to extract the amplitude of the received sig- nals and uses their envelopes to recognize gestures within a short Q distance of 2.5 feet [14].Wision uses multi-path reflections to build Combined CFR an image for nearby objects [11].In comparison,CARM requires (t LoS path H(ft) no specialized hardware and at the same time achieves high activity recognition accuracy at longer distances. Reflected by Static component Radar Based:Device-free human activity recognition has also wall H,(fo) been studied using radar technology [4,5.16,25].Using the mi- Reflected by cro Doppler information,radars can measure the movement speeds body of different parts of human body [25].WiTrack uses specially Dynamic Component designed Frequency Modulated Carrier Wave(FMCW)signals to Receiver Hdf.t) track human movements behind the wall with a resolution of ap- proximately 20cm [4.5].Compared to the specially designed radar (a)Visual representation (b)Phasor representation signals such as FMCW or Ultra-wideband (UWB)signals,WiFi Figure 2:Multi-paths caused by human movements signals have much narrower bandwidth.For example,802.11a/b/g usually use a bandwidth of 20 MHz,while FMCW uses bandwidth of up to 1.79 GHz [4].Compared to prior work in radar techno- logy,CARM designed a new set of signal processing methods that 3.2 Phase Changes for Paths are suitable for the OFDM signal used in WiFi. Surrounding objects reflect wireless signals due to which a trans- CSI Based:CSI values are available in many commercial mitted signal arrives at the receiver through multiple paths.If a devices such as Intel 5300 [9]and Atheros 9390 network interface radio signal arrives at the receiver through N different paths,then cards(NICs)[19].Recently CSI has been used for human activity H(f,t)is given by the following equation [24]: recognition [10,26,27,30.35]as well as indoor localization [19,32]. Han et al.proposed to use CSI to detect a single human activity of HU,t)=e-2m△t∑akU,t)e-2xfr0 (1) falling [10].Zhou et al.proposed to use CSI to detect the presence where a(f,t)is the complex valued representation of attenuation of a person in an environment [35].Xi et al.proposed to use CSI to count the number of people in a crowd [30].WiHear uses spe- and initial phase offset of thepath,e()is the phase cialized directional antennas to obtain CSI variations caused by lip shift on thepath that has a propagation delay of().and eis phase shift caused by the carrier frequency difference movement for recognizing spoken words [26].E-eyes recognizes a Af between the sender and the receiver. set of nine daily human activities using CSI.Note that WiHear and The changes in the length of a path lead to the changes in the E-eyes use CSI in quite different ways than CARM.WiHear does phase of the WiFi signal on the corresponding path.Consider the not effectively denoise CSI values;thus,it has to use directional scenario in Figure 2(a),where the WiFi signal is reflected by the antennas to reduce the noise in CSI values to achieve acceptable ac- curacy.In comparison,we denoise CSI values and use commercial human body through thekh path.When the human body moves by a small distance between time 0 and time t,the length of theth WiFi devices with built-in omnidirectional antennas.E-eyes uses path changes from d(0)to d(t).Since wireless signals travel at CSI histograms as fingerprints for recognizing human daily activ the speed of light,denoted as c.the delay of theh path,denoted ities,such as brushing teeth,taking showers,and washing dishes, as TA (t)can be written as T(t)=di (t)/c.Let f and A repres- which are relatively location dependent.In comparison,CARM ents the carrier frequency and the wavelength,where A =c/f uses CSI values based on our CSI-speed and CSI-activity models. Thus,the phase shift e()on this path can be written as 3.UNDERSTANDING WIFI MULTI-PATH e(),which means that when the path length changes by one wavelength,the receiver experiences a phase shift of 2 in the received subcarrier. 3.1 Overview of CSI WiFi NICs continuously monitor variations in the wireless chan- 3.3 Practical Limitations nel using CSI,which characterizes the frequency response of the Theoretically,it is possible to precisely measure the phase of the wireless channel [1].Let X(f,t)and Y(f,t)be the frequency do- path in systems where sender and receiver are perfectly synchron- main representations of transmitted and received signals,respect- ized,e.g.,as in RFID systems [31].But,unfortunately,commercial ively,with carrier frequency f.The two signals are related by WiFi devices have non-negligible carrier frequency offsets(CFO) the expression Y(f,t)=H(f,t)xX(f,t),where H(f,t)is the due to hardware imperfections and environmental variations [8]. complex valued channel frequency response(CFR)for carrier fre- IEEE 802.11n standard allows the carrier frequency of a device to

recognition with low accuracy because the RSSI values provided by the commercial devices have very low resolution [23]. For RSSI based gesture recognition, the accuracy is 56% over 7 different ges￾tures [21]. Sigg et al. use software radio to improve the granularity of RSSI values and consequently improve the accuracy of activity recognition to 72% for 4 activities [22]. In comparison, CARM uses CSI values and achieves an accuracy of 96%. Specialized Hardware Based: Fine-grained radio signal meas￾urements can be collected by software defined radio or specially designed hardware [11, 12, 14, 17]. WiSee uses USRP to capture the WiFi OFDM signals and measures the Doppler shift in signals reflected by human bodies to recognize a set of nine different ges￾tures with an accuracy of 95% [17]. AllSee uses a specially de￾signed analog circuit to extract the amplitude of the received sig￾nals and uses their envelopes to recognize gestures within a short distance of 2.5 feet [14]. Wision uses multi-path reflections to build an image for nearby objects [11]. In comparison, CARM requires no specialized hardware and at the same time achieves high activity recognition accuracy at longer distances. Radar Based: Device-free human activity recognition has also been studied using radar technology [4, 5, 16, 25]. Using the mi￾cro Doppler information, radars can measure the movement speeds of different parts of human body [25]. WiTrack uses specially designed Frequency Modulated Carrier Wave (FMCW) signals to track human movements behind the wall with a resolution of ap￾proximately 20cm [4, 5]. Compared to the specially designed radar signals such as FMCW or Ultra-wideband (UWB) signals, WiFi signals have much narrower bandwidth. For example, 802.11a/b/g usually use a bandwidth of 20 MHz, while FMCW uses bandwidth of up to 1.79 GHz [4]. Compared to prior work in radar techno￾logy, CARM designed a new set of signal processing methods that are suitable for the OFDM signal used in WiFi. CSI Based: CSI values are available in many commercial devices such as Intel 5300 [9] and Atheros 9390 network interface cards (NICs) [19]. Recently CSI has been used for human activity recognition [10,26,27,30,35] as well as indoor localization [19,32]. Han et al. proposed to use CSI to detect a single human activity of falling [10]. Zhou et al. proposed to use CSI to detect the presence of a person in an environment [35]. Xi et al. proposed to use CSI to count the number of people in a crowd [30]. WiHear uses spe￾cialized directional antennas to obtain CSI variations caused by lip movement for recognizing spoken words [26]. E-eyes recognizes a set of nine daily human activities using CSI. Note that WiHear and E-eyes use CSI in quite different ways than CARM. WiHear does not effectively denoise CSI values; thus, it has to use directional antennas to reduce the noise in CSI values to achieve acceptable ac￾curacy. In comparison, we denoise CSI values and use commercial WiFi devices with built-in omnidirectional antennas. E-eyes uses CSI histograms as fingerprints for recognizing human daily activ￾ities, such as brushing teeth, taking showers, and washing dishes, which are relatively location dependent. In comparison, CARM uses CSI values based on our CSI-speed and CSI-activity models. 3. UNDERSTANDING WIFI MULTI-PATH 3.1 Overview of CSI WiFi NICs continuously monitor variations in the wireless chan￾nel using CSI, which characterizes the frequency response of the wireless channel [1]. Let X(f, t) and Y (f, t) be the frequency do￾main representations of transmitted and received signals, respect￾ively, with carrier frequency f. The two signals are related by the expression Y (f, t) = H(f, t) × X(f, t), where H(f, t) is the complex valued channel frequency response (CFR) for carrier fre￾quency f measured at time t. CSI measurements basically con￾tains these CFR values. Let NT x and NRx represent the num￾ber of transmitting and receiving antennas, respectively. As CSI is measured on 30 selected OFDM subcarriers for a received 802.11 frame, each CSI measurement contains 30 matrices with dimen￾sions NT x×NRx. Each entry in any matrix is a CFR value between an antenna pair at a certain OFDM subcarrier frequency at a par￾ticular time. Onwards, we call the time-series of CFR values for a given antenna pair and OFDM subcarrier as CSI stream. Thus, there are 30 × NT x × NRx CSI streams in a time-series of CSI values. Sender Receiver dk(t) Wall Reflected by body Reflected by wall LoS path dk(0) (a) Visual representation I Q Combined CFR H(f,t) Static component Hs(f,t) Dynamic Component Hd(f,t) (b) Phasor representation Figure 2: Multi-paths caused by human movements 3.2 Phase Changes for Paths Surrounding objects reflect wireless signals due to which a trans￾mitted signal arrives at the receiver through multiple paths. If a radio signal arrives at the receiver through N different paths, then H(f, t) is given by the following equation [24]: H(f, t) = e −j2π∆ftXN k=1 ak(f, t)e −j2πfτk(t) (1) where ak(f, t) is the complex valued representation of attenuation and initial phase offset of the k th path , e −j2πfτk(t) is the phase shift on the k th path that has a propagation delay of τk(t), and e −j2π∆ft is phase shift caused by the carrier frequency difference ∆f between the sender and the receiver. The changes in the length of a path lead to the changes in the phase of the WiFi signal on the corresponding path. Consider the scenario in Figure 2(a), where the WiFi signal is reflected by the human body through the k th path. When the human body moves by a small distance between time 0 and time t, the length of the k th path changes from dk(0) to dk(t). Since wireless signals travel at the speed of light, denoted as c, the delay of the k th path, denoted as τk(t) can be written as τk(t) = dk(t)/c. Let f and λ repres￾ents the carrier frequency and the wavelength, where λ = c/f. Thus, the phase shift e −j2πfτk(t) on this path can be written as e −j2πdk(t)/λ, which means that when the path length changes by one wavelength, the receiver experiences a phase shift of 2π in the received subcarrier. 3.3 Practical Limitations Theoretically, it is possible to precisely measure the phase of the path in systems where sender and receiver are perfectly synchron￾ized, e.g., as in RFID systems [31]. But, unfortunately, commercial WiFi devices have non-negligible carrier frequency offsets (CFO) due to hardware imperfections and environmental variations [8]. IEEE 802.11n standard allows the carrier frequency of a device to

drift by up to 100 kHz from the central frequency of the channel for H.(f).is the sum of CFRs for static paths.Thus,the total CFR is 5 GHz band [1].Such frequency drift leads to rapid phase changes given by the following equation. in CSI values.Commercial WiFi NICs take one set of CSI meas- urements per frame.With a transmission rate of 4,000 frames per H(f,t)=e(H()+>ax(f,t)e (2) second,which is around the maximum number of frames that the kEPd commercial device can continuously transmit due to the frame ag- The total CFR has time-varying power because in complex gregation mechanism in 802.11n [1].the phase shift caused by the plane,the static component H(f)is a constant vector while the term e in Equation(1)cloud be as large as 50 between dynamic component Ha(f,t)is superposition of vectors with time consecutive CSI values. varying phases and amplitudes,as shown in Figure 2(b).When Our measurements on commercial devices show that phases of the phase of the dynamic component changes,the magnitude of the CFR are too noisy to be used for activity recognition due to CFO. combined CFR changes accordingly. Figure 3 shows the CSI phase differences for consecutive frames Now,consider how CFR power changes with an object mov- sent through a WiFi link between two commercial devices.Due ing around.Let an object move at a constant speed such that the to the randomness of the packet sending process,the interval At length of the kth path changes at a constant speed v for a short between two consecutive frames is randomly distributed in the time period,e.g.,100 milliseconds.Let d(t)be the length of the range of 300~550 microseconds (us).This gives us a chance to kth path at time t.Thus,d(t)=dk(0)+vxt.The instantaneous measure the fine grained phase differences for different At.Each CFR power at time t can be derived as follows (detailed derivations dot in Figure 3 gives the phase difference for a pair of frame separ- are omitted due to space constraints). ated by the given At,thus we can obtain the relationship between At and the phase shift.As shown by Figure 3,the phase differ- 1Hf,trP=∑2A.a,圳os(2+2d0+） 入 ence2r△f△t changes by8π(four vertical strips)when△tin- kEPd crease from 350 us to 400 us.Thus,the CFO can be calculated as 2lak(f,t)ai(f,t)l cos /2aos-m+2红(d0）-do+a Af==80 kHz.There are two causes that lead to k,lEPd the imprecision of CFR phase.First,from the width of the vertical k strips in Figure 3,we observe that CFR phase has measurement er- +Iak(f,t2+1H()2 (3) ror as large as 0.5.In most cases,the phase changes caused by kEPd human reflection are much smaller than 0.5m.Thus,phase changes where24@+中kand2红o-4o》+are constant caused by movements are often buried in phase nosies.Second, values representing initial phase offsets. our measurements on commercial devices show that the central fre- Equation (3)provides a key insight:the total CFR power is quency often drifts by tens of Hz per second,making it hard to the sum of a constant offset and a set of sinusoids,where the fre- predict CFR phase and separate the phase change caused by clock quencies of the sinusoids are functions of the speeds of path length drifts from the small phase shifts caused by body movements.Fur- changes.By measuring the frequencies of these sinusoids and mul- thermore,the phase sanitization method introduced in [20]could tiplying them with the carrier wavelength,we can obtain the speeds not work for our case because the phase sanitization process also of path length change.In this way,we can build a CSI-speed model removes the phase shifts caused by body movements. which relates the variations in CSI power to the movement speeds. 3.5 Model Verification We use a simple moving object to verify our CSI-speed model in Equation (3).We move a steel plate with diameter of 30 cm along the perpendicular bisector of the sender/receiver,similar to the scenario shown in Figure 2(a).Flat steel objects can serve as mirrors for radio waves [34].Thus,there is only one path dominat- ing the signal reflected by the steel plate and Equation(3)reduces to one sinusoid wave plus a constant offset.The frequency of the si- 350 400 4t(us)450 500 nusoid changes according to the instantaneous moving speed.This Figure 3:Phase differences for consecutive frames can be verified by Figure 4(a),which shows the CSI waveform caused by steel plate movements.When there is only one domin- ating sinusoid wave,the movement distance can be calculated by measuring the phase change of the signal,which is the integral of the signal frequency over time. 3.4 CSI-Speed Model We use Hilbert Transform to calculate the phase change of the While it is hard to directly measure the phase of a path,it is waveform as follows.We first remove the DC component that ac- possible to infer the phase of a path using the CFR power i.e.. counts for the static paths.We then use Hilbert Transform to derive H(f,t)2.The principle behind our method is that when the the analytic signal from the waveform.The unwrapped instantan- lengths of multi-paths change,the CFR power varies according to eous phase of the analytic signal keeps track of the phase change the path length change. of the waveform.We can then multiply the phase change with the To understand the relationship between CFR power and the wavelength to get the path length change.Since the reflected sig- length change of a path,we first express CFR as a sum of dy- nal goes through a round-trip from the reflector,the path length namic CFR and static CFR and then calculate the power.Dy- change is approximately two times of the movement distance of namic CFR,represented by Ha(f,t),is the sum of CFRs for paths the reflector in this case [29]. whose lengths change with the human movement,and is given by The Hilbert Transform based distance measurement has average Ha(f)=t)ed()where Pa is the set of accuracy of 2.86 cm,as showing in Figure 4(b)and 4(c).In the dynamic paths whose lengths change.Static CFR,represented by experiments,we move the steel plate for a random distance in the

drift by up to 100 kHz from the central frequency of the channel for 5 GHz band [1]. Such frequency drift leads to rapid phase changes in CSI values. Commercial WiFi NICs take one set of CSI meas￾urements per frame. With a transmission rate of 4,000 frames per second, which is around the maximum number of frames that the commercial device can continuously transmit due to the frame ag￾gregation mechanism in 802.11n [1], the phase shift caused by the term e −j2π∆ft in Equation (1) cloud be as large as 50π between consecutive CSI values. Our measurements on commercial devices show that phases of CFR are too noisy to be used for activity recognition due to CFO. Figure 3 shows the CSI phase differences for consecutive frames sent through a WiFi link between two commercial devices. Due to the randomness of the packet sending process, the interval ∆t between two consecutive frames is randomly distributed in the range of 300∼550 microseconds (µs). This gives us a chance to measure the fine grained phase differences for different ∆t. Each dot in Figure 3 gives the phase difference for a pair of frame separ￾ated by the given ∆t, thus we can obtain the relationship between ∆t and the phase shift. As shown by Figure 3, the phase differ￾ence 2π∆f∆t changes by 8π (four vertical strips) when ∆t in￾crease from 350 µs to 400 µs. Thus, the CFO can be calculated as ∆f = 8π 2π(400−350)µs = 80 kHz. There are two causes that lead to the imprecision of CFR phase. First, from the width of the vertical strips in Figure 3, we observe that CFR phase has measurement er￾ror as large as 0.5π. In most cases, the phase changes caused by human reflection are much smaller than 0.5π. Thus, phase changes caused by movements are often buried in phase nosies. Second, our measurements on commercial devices show that the central fre￾quency often drifts by tens of Hz per second, making it hard to predict CFR phase and separate the phase change caused by clock drifts from the small phase shifts caused by body movements. Fur￾thermore, the phase sanitization method introduced in [20] could not work for our case because the phase sanitization process also removes the phase shifts caused by body movements. 300 350 400 450 500 550 −3 −2 −1 0 1 2 3 ∆t (µs) Phase difference (rad) Figure 3: Phase differences for consecutive frames 3.4 CSI-Speed Model While it is hard to directly measure the phase of a path, it is possible to infer the phase of a path using the CFR power i.e., |H(f, t)| 2 . The principle behind our method is that when the lengths of multi-paths change, the CFR power varies according to the path length change. To understand the relationship between CFR power and the length change of a path, we first express CFR as a sum of dy￾namic CFR and static CFR and then calculate the power. Dy￾namic CFR, represented by Hd(f, t), is the sum of CFRs for paths whose lengths change with the human movement, and is given by Hd(f, t) = P k∈Pd ak(f, t)e −j2πdk(t)/λ, where Pd is the set of dynamic paths whose lengths change. Static CFR, represented by Hs(f), is the sum of CFRs for static paths. Thus, the total CFR is given by the following equation. H(f, t) = e −j2π∆ft Hs(f) + X k∈Pd ak(f, t)e −j 2πdk(t) λ  (2) The total CFR has time-varying power because in complex plane, the static component Hs(f) is a constant vector while the dynamic component Hd(f, t) is superposition of vectors with time varying phases and amplitudes, as shown in Figure 2(b). When the phase of the dynamic component changes, the magnitude of the combined CFR changes accordingly. Now, consider how CFR power changes with an object mov￾ing around. Let an object move at a constant speed such that the length of the k th path changes at a constant speed vk for a short time period, e.g., 100 milliseconds. Let dk(t) be the length of the k th path at time t. Thus, dk(t) = dk(0) + vkt. The instantaneous CFR power at time t can be derived as follows (detailed derivations are omitted due to space constraints). |H(f, t)| 2 = X k∈Pd 2|Hs(f)ak(f, t)| cos  2πvkt λ + 2πdk(0) λ + φsk + X k,l∈Pd k6=l 2|ak(f, t)al(f, t)| cos  2π(vk − vl)t λ + 2π (dk(0) − dl(0)) λ + φkl + X k∈Pd |ak(f, t)| 2 + |Hs(f)| 2 (3) where 2πdk(0) λ + φsk and 2π(dk(0)−dl(0)) λ + φkl are constant values representing initial phase offsets. Equation (3) provides a key insight: the total CFR power is the sum of a constant offset and a set of sinusoids, where the fre￾quencies of the sinusoids are functions of the speeds of path length changes. By measuring the frequencies of these sinusoids and mul￾tiplying them with the carrier wavelength, we can obtain the speeds of path length change. In this way, we can build a CSI-speed model which relates the variations in CSI power to the movement speeds. 3.5 Model Verification We use a simple moving object to verify our CSI-speed model in Equation (3). We move a steel plate with diameter of 30 cm along the perpendicular bisector of the sender/receiver, similar to the scenario shown in Figure 2(a). Flat steel objects can serve as mirrors for radio waves [34]. Thus, there is only one path dominat￾ing the signal reflected by the steel plate and Equation (3) reduces to one sinusoid wave plus a constant offset. The frequency of the si￾nusoid changes according to the instantaneous moving speed. This can be verified by Figure 4(a), which shows the CSI waveform caused by steel plate movements. When there is only one domin￾ating sinusoid wave, the movement distance can be calculated by measuring the phase change of the signal, which is the integral of the signal frequency over time. We use Hilbert Transform to calculate the phase change of the waveform as follows. We first remove the DC component that ac￾counts for the static paths. We then use Hilbert Transform to derive the analytic signal from the waveform. The unwrapped instantan￾eous phase of the analytic signal keeps track of the phase change of the waveform. We can then multiply the phase change with the wavelength to get the path length change. Since the reflected sig￾nal goes through a round-trip from the reflector, the path length change is approximately two times of the movement distance of the reflector in this case [29]. The Hilbert Transform based distance measurement has average accuracy of 2.86 cm, as showing in Figure 4(b) and 4(c) . In the experiments, we move the steel plate for a random distance in the

35 Time (seconds) 65 Moving is(meter) 0.6 14 easmen2产 (a)CSI waveform for a movement with 0.8m (b)Measurements of path length change (c)CDF of measurement error pathlength change Figure 4:Experiments with steel plates moving along a straight line. range of 0~1.6 m which incurs 0~3.2 m path length change.The with the same speed may introduce different path length change ground truth path length change is measured by a laser rangefinder. speeds when movement directions are different.Furthermore,dif- which provides distance measurement accuracy of 0.1 cm.Under ferent people may perform the same activity with different speeds carrier frequency of 5.825 GHz,which has wavelength of 5.15cm. and the multi-path conditions may change under different environ- our path length measurement has maximal error of 5.87 cm and ments. mean error of 2.86 cm.The major error sources are errors in de- Our experiments show that different human activities actually in- ciding the phase of the starting and ending cycle.Therefore,the cur path length change speed with significant difference,so that the measurement error does not increase with the movement distance minor measurement differences caused by movement direction and and is uniformly distributed in the range of 0~6 cm,see Figure the different ways to perform the same activity can be safely ig- 4(c). nored.To study the robustness of the movement speeds,we collect more than 780 activity samples for three activities,walking,run- 4. MODELING OF HUMAN ACTIVITIES ning and sitting down,performed by 25 volunteers with different ages and genders.The activities are performed at different loca- 4.1 Human Activity Characteristics tions with different directions,e.g.,we ask the volunteer to walk Modeling CFR power change caused by human activity is chal- around a large table so that four different walking directions are lenging.Unlike the simple object used in section 3.5,human bod captured.Figure 6 shows the estimated torso speed distribution for ies have complex shapes and different body parts can move at dif- the three different activities.Note that we estimate the torso speed ferent speeds.Moreover,the reflections from body parts may go by dividing the speed of path length change by two.This usually through different paths in complex indoor environments.From gives a smaller estimation than the actual speed because depend Equation (3),we see that the CFR power is a linear combination ing on the movement direction,moving by 1 cm usually cause less of all the reflected paths and the speeds of path length change than 2 cm path length change [29].Even with different movement are preserved in the combination process.Therefore,we can use directions,we observe that the three activities have different speeds Time-Frequency analysis tools,such as Short-Time Fourier Trans- in Figure 6.Such speed difference can be used for activity classi- form (STFT)or Discrete Wavelet Transform (DWT)to separate fication.As an example,we can achieve a classification accuracy these components in the frequency domain.Human activity can of 88%for all three activities,when we divide the samples to three be modeled by profiling the energy of each frequency component types with estimated speed of 0~0.61 m/s,0.61~1.0 m/s and above 1.0 m/s.By looking at various different activities,we found that derived from Time-Frequency analysis tools.As an example,Fig- ure 5 illustrates the waveform and the corresponding spectrogram most human activities contains speed components ranging from for three human activities:walking.falling and sitting down.The 0~2.5 m/s and the frequency components for a given activity are spectrogram shows how the energy of each frequency component stable across different scenarios,including apartments,offices,and evolves with time,where high-energy components are colored in large open area,see our evaluations in Section 8.Therefore,the red.In the spectrogram for the walking activity,there is a high- strength of the frequency components can serve as a robust feature energy band around 35~40Hz frequency,as shown in Figure 5(d). for human activities. With a wavelength of 5.15 cm,these frequency components repres- 025 ent 0.91.0 m/s movement speed after considering the round-trip path length change.This coincides the normal movement speed of human torso while walking [25].Figure 5(e)shows the spec- 0.15 sitting dow trogram of falling,which has an energy increase in the frequency range of 40~80 Hz between 1~1.5 seconds.This indicates a fast speed-up from below 0.5 m/s speed to 2 m/s,during a short time period of 0.5 seconds,which is a clear sign of falling.The activ- 0.4 08 ity of sitting down shown in Figure 5(f)is different from falling. Estimated speed(m/s) as the speed for sitting down is much slower.Using the energy Figure 6:Histogram of speeds for different activities profile of different frequencies,we can build CSI-activity model. which quantifies the correlation between the movement speeds of 4.3 different human body parts and a specific human activity. CSI-Activity Model We propose to use Hidden Markov Model (HMM)to build CSI- 4.2 Robustness of Activity Speeds activity models that consist of mutiple movement states.As an ex- We next study whether the speed based CSI-activity model ample,we observe that the action of falling comprises several states are robust across different scenarios.It is well known that the from Figure 5(e).The person first moves slowly,with most CSI en- path length change is determined by both the position of the ergy on the low frequency (slow movement)components.Then. sender/receiver and the movement directions [29].Movements there is a fast transition to very high speed movement where sub-

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 50 100 150 200 Time (seconds) CSI power (a) CSI waveform for a movement with 0.8m pathlength change 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.5 1 1.5 2 2.5 3 Moving distance (meters) Path length change (meters) Ground truth Measurement results (b) Measurements of path length change 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.2 0.4 0.6 0.8 1 Measurement error (meters) CDF (c) CDF of measurement error Figure 4: Experiments with steel plates moving along a straight line. range of 0∼1.6 m which incurs 0∼3.2 m path length change. The ground truth path length change is measured by a laser rangefinder, which provides distance measurement accuracy of 0.1 cm. Under carrier frequency of 5.825 GHz, which has wavelength of 5.15cm, our path length measurement has maximal error of 5.87 cm and mean error of 2.86 cm. The major error sources are errors in de￾ciding the phase of the starting and ending cycle. Therefore, the measurement error does not increase with the movement distance and is uniformly distributed in the range of 0∼6 cm, see Figure 4(c). 4. MODELING OF HUMAN ACTIVITIES 4.1 Human Activity Characteristics Modeling CFR power change caused by human activity is chal￾lenging. Unlike the simple object used in section 3.5, human bod￾ies have complex shapes and different body parts can move at dif￾ferent speeds. Moreover, the reflections from body parts may go through different paths in complex indoor environments. From Equation (3), we see that the CFR power is a linear combination of all the reflected paths and the speeds of path length change are preserved in the combination process. Therefore, we can use Time-Frequency analysis tools, such as Short-Time Fourier Trans￾form (STFT) or Discrete Wavelet Transform (DWT) to separate these components in the frequency domain. Human activity can be modeled by profiling the energy of each frequency component derived from Time-Frequency analysis tools. As an example, Fig￾ure 5 illustrates the waveform and the corresponding spectrogram for three human activities: walking, falling and sitting down. The spectrogram shows how the energy of each frequency component evolves with time, where high-energy components are colored in red. In the spectrogram for the walking activity, there is a high￾energy band around 35∼40Hz frequency, as shown in Figure 5(d). With a wavelength of 5.15 cm, these frequency components repres￾ent 0.9∼1.0 m/s movement speed after considering the round-trip path length change. This coincides the normal movement speed of human torso while walking [25]. Figure 5(e) shows the spec￾trogram of falling, which has an energy increase in the frequency range of 40∼80 Hz between 1∼1.5 seconds. This indicates a fast speed-up from below 0.5 m/s speed to 2 m/s, during a short time period of 0.5 seconds, which is a clear sign of falling. The activ￾ity of sitting down shown in Figure 5(f) is different from falling, as the speed for sitting down is much slower. Using the energy profile of different frequencies, we can build CSI-activity model, which quantifies the correlation between the movement speeds of different human body parts and a specific human activity. 4.2 Robustness of Activity Speeds We next study whether the speed based CSI-activity model are robust across different scenarios. It is well known that the path length change is determined by both the position of the sender/receiver and the movement directions [29]. Movements with the same speed may introduce different path length change speeds when movement directions are different. Furthermore, dif￾ferent people may perform the same activity with different speeds and the multi-path conditions may change under different environ￾ments. Our experiments show that different human activities actually in￾cur path length change speed with significant difference, so that the minor measurement differences caused by movement direction and the different ways to perform the same activity can be safely ig￾nored. To study the robustness of the movement speeds, we collect more than 780 activity samples for three activities, walking, run￾ning and sitting down, performed by 25 volunteers with different ages and genders. The activities are performed at different loca￾tions with different directions, e.g., we ask the volunteer to walk around a large table so that four different walking directions are captured. Figure 6 shows the estimated torso speed distribution for the three different activities. Note that we estimate the torso speed by dividing the speed of path length change by two. This usually gives a smaller estimation than the actual speed because depend￾ing on the movement direction, moving by 1 cm usually cause less than 2 cm path length change [29]. Even with different movement directions, we observe that the three activities have different speeds in Figure 6. Such speed difference can be used for activity classi- fication. As an example, we can achieve a classification accuracy of 88% for all three activities, when we divide the samples to three types with estimated speed of 0∼0.61 m/s, 0.61∼1.0 m/s and above 1.0 m/s. By looking at various different activities, we found that most human activities contains speed components ranging from 0∼2.5 m/s and the frequency components for a given activity are stable across different scenarios, including apartments, offices, and large open area, see our evaluations in Section 8. Therefore, the strength of the frequency components can serve as a robust feature for human activities. 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.05 0.1 0.15 0.2 0.25 Estimated speed (m/s) Probability running walking sitting down Figure 6: Histogram of speeds for different activities 4.3 CSI-Activity Model We propose to use Hidden Markov Model (HMM) to build CSI￾activity models that consist of mutiple movement states. As an ex￾ample, we observe that the action of falling comprises several states from Figure 5(e). The person first moves slowly, with most CSI en￾ergy on the low frequency (slow movement) components. Then, there is a fast transition to very high speed movement where sub-

25 35 Time(seconds) Time (seconds) Time(seconds) (a)CSI waveform for walking (b)CSI waveform for falling (c)CSI waveform for sitting down 25 0.5 Time(seconds) Time (seconds) Time(seconds) (d)Sepctrogram for walking (e)Sepctrogram for falling (f)Sepctrogram for sitting down Figure 5:Waveforms and spectrograms for different activities. stantial energy are on high frequency components.After that,there the wavelength is 5.15 cm.Note that 7.7 m/s is already too fast is a quick transition to the silent state,where the movement energy a speed for a human to move with.Commercial WiFi NICs can reduces to nearly zero.By looking at these transitions between easily sample CSI values at a rate of up to 2500 samples/second, different states.we can infer that the person is possibly falling. which is far greater than the sampling rate required by the Nyquist Similarly,other human activities also contain states with can be criteria for a 300Hz signal.Thus,we can apply signal processing characterized by their movement speeds. techniques on the denoised CSI values and get the frequency com- Hidden Markov Model (HMM)is a suitable tool to build state ponents in CFR power and infer the speed.For slow movements transition models using time-dependent features.It has been ex- that only move a few centimeters per second,CARM utilizes wave- tensively used in several recognition applications such as speech let transforms to extract low frequency components below 1 Hz to recognition [18],handwriting recognition,and gesture recognition capture slow movements such as brushing teeth,see Section 6. in videos [6].Use of HMMs for activity recognition is based on Movement of different body parts:Time-frequency analysis the assumption that the sequence of observed feature vectors cor- tools can separate the movement of different body parts when they responding to an activity is generated by a Markov model,which is move at different speeds.For example,the weak energy bands in a finite state machine that changes state once every time unit.Each frequency components between 50~70 Hz in Figure 5(d)are actu- time a state is entered,a feature vector is generated from a prob- ally caused by swing of legs when walking [25].In general,CFR ability density called output probability density.Furthermore,the power changes caused by the movements of arms/legs have smaller transition from one state to another or back to itself is also prob- in energy compared to torso movements as the reflection areas for abilistic and is governed by a discrete probability called transition arms/legs are smaller.Our feature extraction process captures both probability.Hidden Markov Models are called hidden because in the body movement and arms/legs movements.Therefore,CARM practice,the sequence of feature vectors is known but the underly- can distinguish whether the activity involves the whole body or just ing sequence of states that generated those feature vectors is hid- arms/legs.For example,CARM can recognize falling,running and den. boxing,which are all high speed movements but involve different HMM can capture information from all training samples and body parts. thus works very well even when there is high within-class vari- Scenarios with multiple persons:When there are multiple per- ance.Provided that a sufficient number of representative training sons within the same room,CARM can recognize the activity when samples of an activity are available,an HMM can be constructed only one person is moving.see details in Section 8.When both that implicitly models all of the many sources of variability inherent persons are actively moving,we need multiple sender/receivers in the activity.Compared to existing works which uses statistical to capture the actions.Activities that are closer to the given features along a long period [10,27].HMM based models utilizes sender/receiver introduce higher distortions in CFR power.There- the transitions within the activity that provide more details about fore,we can use blind signal separation methods [15]to extract the activity.For details related to HMM model training and classi- CFR power distortions caused by different person.However,this fication,please refer to Section 7. is out of the scope of this paper and will be studied in our future works. 4.4 Discussion Detection of high-speed and low-speed movements:CARM 5.PCA BASED CSI DENOISING SCHEME can reliably detect both high-speed movement and low-speed CARM builds the HMM model in following three steps as de movements.Commercial WiFi devices provide CSI values with scribed in Sections 5.6,and 7,respectively.First,CARM collects sampling rates high enough to accurately obtain the values of these CSI values and removes the noises in the measurements.Second, frequencies.From our extensive activity dataset.we have observed CARM extracts human movement features from the denoised CSI that indoor human movements introduce frequency components of values using DWT.Third,CARM trains an HMM model for each no more than 300Hz in the CFR power,which corresponds to a top activity and uses the CSI-activity models to recognize activities in human movement speed of about 300 x 0.0515/2=7.7m/s,when real time

2 2.5 3 3.5 4 −15 −10 −5 0 5 10 15 Time (seconds) CSI (a) CSI waveform for walking 0.5 1 1.5 2 −40 −20 0 20 40 Time (seconds) CSI (b) CSI waveform for falling 0 0.5 1 1.5 2 −40 −20 0 20 Time (seconds) CSI (c) CSI waveform for sitting down (d) Sepctrogram for walking (e) Sepctrogram for falling (f) Sepctrogram for sitting down Figure 5: Waveforms and spectrograms for different activities. stantial energy are on high frequency components. After that, there is a quick transition to the silent state, where the movement energy reduces to nearly zero. By looking at these transitions between different states, we can infer that the person is possibly falling. Similarly, other human activities also contain states with can be characterized by their movement speeds. Hidden Markov Model (HMM) is a suitable tool to build state transition models using time-dependent features. It has been ex￾tensively used in several recognition applications such as speech recognition [18], handwriting recognition, and gesture recognition in videos [6]. Use of HMMs for activity recognition is based on the assumption that the sequence of observed feature vectors cor￾responding to an activity is generated by a Markov model, which is a finite state machine that changes state once every time unit. Each time a state is entered, a feature vector is generated from a prob￾ability density called output probability density. Furthermore, the transition from one state to another or back to itself is also prob￾abilistic and is governed by a discrete probability called transition probability. Hidden Markov Models are called hidden because in practice, the sequence of feature vectors is known but the underly￾ing sequence of states that generated those feature vectors is hid￾den. HMM can capture information from all training samples and thus works very well even when there is high within-class vari￾ance. Provided that a sufficient number of representative training samples of an activity are available, an HMM can be constructed that implicitly models all of the many sources of variability inherent in the activity. Compared to existing works which uses statistical features along a long period [10, 27], HMM based models utilizes the transitions within the activity that provide more details about the activity. For details related to HMM model training and classi- fication, please refer to Section 7. 4.4 Discussion Detection of high-speed and low-speed movements: CARM can reliably detect both high-speed movement and low-speed movements. Commercial WiFi devices provide CSI values with sampling rates high enough to accurately obtain the values of these frequencies. From our extensive activity dataset, we have observed that indoor human movements introduce frequency components of no more than 300Hz in the CFR power, which corresponds to a top human movement speed of about 300 × 0.0515/2 = 7.7m/s, when the wavelength is 5.15 cm. Note that 7.7 m/s is already too fast a speed for a human to move with. Commercial WiFi NICs can easily sample CSI values at a rate of up to 2500 samples/second, which is far greater than the sampling rate required by the Nyquist criteria for a 300Hz signal. Thus, we can apply signal processing techniques on the denoised CSI values and get the frequency com￾ponents in CFR power and infer the speed. For slow movements that only move a few centimeters per second, CARM utilizes wave￾let transforms to extract low frequency components below 1 Hz to capture slow movements such as brushing teeth, see Section 6. Movement of different body parts: Time-frequency analysis tools can separate the movement of different body parts when they move at different speeds. For example, the weak energy bands in frequency components between 50∼70 Hz in Figure 5(d) are actu￾ally caused by swing of legs when walking [25]. In general, CFR power changes caused by the movements of arms/legs have smaller in energy compared to torso movements as the reflection areas for arms/legs are smaller. Our feature extraction process captures both the body movement and arms/legs movements. Therefore, CARM can distinguish whether the activity involves the whole body or just arms/legs. For example, CARM can recognize falling, running and boxing, which are all high speed movements but involve different body parts. Scenarios with multiple persons: When there are multiple per￾sons within the same room, CARM can recognize the activity when only one person is moving, see details in Section 8. When both persons are actively moving, we need multiple sender/receivers to capture the actions. Activities that are closer to the given sender/receiver introduce higher distortions in CFR power. There￾fore, we can use blind signal separation methods [15] to extract CFR power distortions caused by different person. However, this is out of the scope of this paper and will be studied in our future works. 5. PCA BASED CSI DENOISING SCHEME CARM builds the HMM model in following three steps as de￾scribed in Sections 5, 6, and 7, respectively. First, CARM collects CSI values and removes the noises in the measurements. Second, CARM extracts human movement features from the denoised CSI values using DWT. Third, CARM trains an HMM model for each activity and uses the CSI-activity models to recognize activities in real time

5.1 Sources of Noise in CSI tipaths across subcarriers.We make two observations from Equa- The CSI streams provided by commercial WiFi devices are ex- tion (4).First,the time-varying terms in the equation above are tremely noisy.Figure 7 plots a noisy CSI stream that we collected approximately equal,i.e.,cos 2A@）≈cos(2s但）and A1 入2 from an Intel 5300 NIC at a sampling rate of 2.5 kHz for a period of 1.75 seconds.One major sources of noise in CSI streams are the sin(②mA@）≈sin(2m@）because△k(d)is small and1 入1 入 internal state transitions in sender and receiver WiFi NICs such as and A2 differ only slightly.Second,the constant terms in Equa- transmission power changes,transmission rate adaptation,and in- tion (4)are unequal for the two subcarriers because initial path ternal CSI reference level changes.These internal state transitions length d&(0)is much greater than Ak(t)and thus,results in a non- result in high amplitude impulse and burst noises in CSI streams. negligible initial phase difference between the two subcarriers even An interesting feature of these impulse and burst noises is that their though the wavelengths differ only slightly.For example,for a path effect is highly correlated across all CSI streams,i.e.,they affect length of 10 meters.a radio signal with wavelength of 5.150 cm tra- samples in all streams at the same time.For example,if sender verses distance equal to 194.1 full wavelengths on this path,where WiFi NIC increases the transmission power by 0.5dB,all streams as a radio signal with wavelength of 5.168 cm (5.15 x 1.0034) see a power increase of 0.5dB. traverses distance equal to 193.5 wavelengths.Thus,there is an initial phase difference of(194.1-193.5)x 2=1.2m between 5.2 Traditional Filter based Denoising these two signals at the receiver. Traditional filters such as low-pass filters or median filters do These two observations show that CFR for different subcar- not perform well in removing the impulse and burst noises.The- riers is a linear combination of the same set of time-varying oretically,a low-pass filter,such as a Butterworth filter,should be waveforms with different initial phases,i.e.,cos and 入 able to remove such noise.However,due to the high energy and high bandwidth of impulse noises in CSI,the pass band for the sin (Therefore,the CSI streams are correlated.Similar A low-pass filters usually need to be less than one-twentieth of the results can be obtained for CSI streams between different antenna sampling rate so that the energy of residual noise in the pass band pairs because the difference in positions of antennas only causes becomes negligible compared to the signal energy [26].When the initial phases and attenuations for each multipath to be different sampling rate is not high enough,the residual noises can still distort Our measurements confirm the observation that CSI streams are the filtered stream.Figure 7(b)shows the output of a low-pass filter correlated.Figure 8 plots the 180 CSI streams for a link with with a cutoff frequency of 100 Hz when applied to the CSI stream in Nr=2 and Nr=3 when a human is walking around.We Figure 7(a),which has sampling rate of 2,500 samples per second. group the CSI streams in their transmission/receiving antenna pairs, We observe that the filtered stream is still severely distorted and e.g.,streams 1~30 are the 30 subcarriers for transmitting antenna the low-pass filter could not effectively denoise it.Another type of 1 and receiving antenna 1.Each CSI stream is a curve that is sim- filters,called median filters,is specifically designed to remove im- ilar to the one in Figure 5(a),where the amplitudes for CSI values pulse noise,but they do not work well on CSI streams because the are represented by the color,i.e.,red colors are "peaks"and blue density of the noises is very high.Figure 7(c)shows the output of a colors are "valleys"in the curve.We have following observation in 5-point median filter when applied to the CSI stream in Figure 7(a) the CSI streams.First.CSI streams are correlated.The"peaks"and We again observe that the filtered stream is still severely distorted. "valleys"have similar shapes in all CSI streams across different an- tenna pairs and different subcarriers.Moreover,the phases of CSI 5.3 Correlation in CSI Streams streams changes smoothly across different subcarriers in the same Our denoising method leverages the fact that the changes intro- antenna pair,e.g.,streams 1~30 and 151~180.because the sub- duced in all CSI streams by body movement are correlated.CSI carriers on the same antenna pair only differs slightly in their fre- streams of different subcarriers are linear combinations of the same quencies.Second,there is no single "good"CSI stream.Although set of time-varying signals and thus they are highly correlated. we can see clear"peaks"and "valleys"in stream 151~180 at time To show this,consider an object that moves by a small distance between 2.5~2.6 and 2.8~2.9 seconds,the changes in measure between time 0 and time t.Let the length of the path changes by ments are vague during the time 2.9~3 seconds for the same set of A(t)between time 0 and time t when the object moves.Thus. streams.However,we observe streams 1~30 give clear CSI fluc- dk(t)=Ak(t)+dk(0),where d(0)is the initial length of the tuations during time 2.9~3 seconds.This implies that we need to path.When the initial phase offset of the subcarrier is,the phase combine different streams to get optimal observations in the move- of the subcarrier s in Equation (3)seen by the receiver at time t is ments.Third,simply using weighted average over CSI streams [13] given by the following equation. cannot provide good results.We see that the phase of different CSl streams are different so that if we simply add them up.they can s(24但+)=os(2mA但+2d0+)） cancel each other as the time point for the "peak"of a stream may 入。 入。 be the "valleys"of other streams.Therefore.it is important to find a good way to combine CSI streams. cos (2d0+）os(2mA@ 、入 Phase changes by 2 Noises present in all streams -sim(240+）in(2@ (4) 入。 Consider two subcarriers with wavelengths A1 and A2 that tra- verse the k multipath.The difference between wavelengths of subcarriers in a WiFi channel is small.For example,in a 20MHz WiFi channel.the lowest and highest frequency subcarriers are separated by about 17MHz.Thus,in 5GHz band,wavelengths Time (seconds) A of subcarriers differ by at most 0.34%.This slight differ- ence in wavelengths usually does not change the number of mul- Figure 8:Correlation in CSI streams

5.1 Sources of Noise in CSI The CSI streams provided by commercial WiFi devices are ex￾tremely noisy. Figure 7 plots a noisy CSI stream that we collected from an Intel 5300 NIC at a sampling rate of 2.5 kHz for a period of 1.75 seconds. One major sources of noise in CSI streams are the internal state transitions in sender and receiver WiFi NICs such as transmission power changes, transmission rate adaptation, and in￾ternal CSI reference level changes. These internal state transitions result in high amplitude impulse and burst noises in CSI streams. An interesting feature of these impulse and burst noises is that their effect is highly correlated across all CSI streams, i.e., they affect samples in all streams at the same time. For example, if sender WiFi NIC increases the transmission power by 0.5dB, all streams see a power increase of 0.5dB. 5.2 Traditional Filter based Denoising Traditional filters such as low-pass filters or median filters do not perform well in removing the impulse and burst noises. The￾oretically, a low-pass filter, such as a Butterworth filter, should be able to remove such noise. However, due to the high energy and high bandwidth of impulse noises in CSI, the pass band for the low-pass filters usually need to be less than one-twentieth of the sampling rate so that the energy of residual noise in the pass band becomes negligible compared to the signal energy [26]. When the sampling rate is not high enough, the residual noises can still distort the filtered stream. Figure 7(b) shows the output of a low-pass filter with a cutoff frequency of 100 Hz when applied to the CSI stream in Figure 7(a), which has sampling rate of 2,500 samples per second. We observe that the filtered stream is still severely distorted and the low-pass filter could not effectively denoise it. Another type of filters, called median filters, is specifically designed to remove im￾pulse noise, but they do not work well on CSI streams because the density of the noises is very high. Figure 7(c) shows the output of a 5-point median filter when applied to the CSI stream in Figure 7(a). We again observe that the filtered stream is still severely distorted. 5.3 Correlation in CSI Streams Our denoising method leverages the fact that the changes intro￾duced in all CSI streams by body movement are correlated. CSI streams of different subcarriers are linear combinations of the same set of time-varying signals and thus they are highly correlated. To show this, consider an object that moves by a small distance between time 0 and time t. Let the length of the path changes by ∆k(t) between time 0 and time t when the object moves. Thus, dk(t) = ∆k(t) + dk(0), where dk(0) is the initial length of the path. When the initial phase offset of the subcarrier is φk, the phase of the subcarrier s in Equation (3) seen by the receiver at time t is given by the following equation. cos  2πdk(t) λs + φk  = cos  2π∆k(t) λs + 2πdk(0) λs + φk  = cos  2πdk(0) λs + φk  cos  2π∆k(t) λs  − sin  2πdk(0) λs + φk  sin  2π∆k(t) λs  (4) Consider two subcarriers with wavelengths λ1 and λ2 that tra￾verse the k th multipath. The difference between wavelengths of subcarriers in a WiFi channel is small. For example, in a 20MHz WiFi channel, the lowest and highest frequency subcarriers are separated by about 17MHz. Thus, in 5GHz band, wavelengths λ of subcarriers differ by at most 0.34%. This slight differ￾ence in wavelengths usually does not change the number of mul￾tipaths across subcarriers. We make two observations from Equa￾tion (4). First, the time-varying terms in the equation above are approximately equal, i.e., cos  2π∆k(t) λ1  ≈ cos  2π∆k(t) λ2  and sin  2π∆k(t) λ1  ≈ sin  2π∆k(t) λ2  because ∆k(t) is small and λ1 and λ2 differ only slightly. Second, the constant terms in Equa￾tion (4) are unequal for the two subcarriers because initial path length dk(0) is much greater than ∆k(t) and thus, results in a non￾negligible initial phase difference between the two subcarriers even though the wavelengths differ only slightly. For example, for a path length of 10 meters, a radio signal with wavelength of 5.150 cm tra￾verses distance equal to 194.1 full wavelengths on this path, where as a radio signal with wavelength of 5.168 cm (= 5.15 × 1.0034) traverses distance equal to 193.5 wavelengths. Thus, there is an initial phase difference of (194.1 − 193.5) × 2π = 1.2π between these two signals at the receiver. These two observations show that CFR for different subcar￾riers is a linear combination of the same set of time-varying waveforms with different initial phases, i.e., cos  2π∆k(t) λs  and sin  2π∆k(t) λs  . Therefore, the CSI streams are correlated. Similar results can be obtained for CSI streams between different antenna pairs because the difference in positions of antennas only causes initial phases and attenuations for each multipath to be different. Our measurements confirm the observation that CSI streams are correlated. Figure 8 plots the 180 CSI streams for a link with NT x = 2 and NRx = 3 when a human is walking around. We group the CSI streams in their transmission/receiving antenna pairs, e.g., streams 1∼30 are the 30 subcarriers for transmitting antenna 1 and receiving antenna 1. Each CSI stream is a curve that is sim￾ilar to the one in Figure 5(a), where the amplitudes for CSI values are represented by the color, i.e., red colors are “peaks” and blue colors are “valleys” in the curve. We have following observation in the CSI streams. First, CSI streams are correlated. The “peaks” and “valleys” have similar shapes in all CSI streams across different an￾tenna pairs and different subcarriers. Moreover, the phases of CSI streams changes smoothly across different subcarriers in the same antenna pair, e.g., streams 1∼30 and 151∼180, because the sub￾carriers on the same antenna pair only differs slightly in their fre￾quencies. Second, there is no single “good” CSI stream. Although we can see clear “peaks” and “valleys” in stream 151∼180 at time between 2.5∼2.6 and 2.8∼2.9 seconds, the changes in measure￾ments are vague during the time 2.9∼3 seconds for the same set of streams. However, we observe streams 1∼30 give clear CSI fluc￾tuations during time 2.9∼3 seconds. This implies that we need to combine different streams to get optimal observations in the move￾ments. Third, simply using weighted average over CSI streams [13] cannot provide good results. We see that the phase of different CSI streams are different so that if we simply add them up, they can cancel each other as the time point for the “peak” of a stream may be the “valleys” of other streams. Therefore, it is important to find a good way to combine CSI streams. Figure 8: Correlation in CSI streams

Time econds)12 12 Time (econds) 2 (a)Original CSI Stream (b)Butterworth low-pass filter (c)5-point median filter (d)PCA based denoising Figure 7:Denoising the time-series of CSI values 5.4 Principal Component Analysis 6.FEATURE EXTRACTION To address the challenges in combining CSI streams,we apply 6.1 Extracting Features from CSI PCA to discover the correlations between CSI streams.With PCA. we can track the time-varying correlations between CSI streams, To obtain activity features from CSI,CARM needs to extract and optimally combine them to extract principal components of frequency components from different activities at different time CSI streams.CARM applies PCA to CSI streams using the fol- scales.This is because human activities have two aspects asso- ciated with them,duration and frequency.Duration represents the lowing four steps. (1)Preprocessing:In this step,CARM first removes the static path time a person takes to perform an activity and frequency represents components from each CSI stream by subtracting the correspond- the speed of multi-paths due to body movements during the activ- ing constant offsets from the streams.It calculates the constant off- ity.Different activities may have similar durations but different frequencies.For example,sitting down and falling both have short set for each stream through long-term averaging over that stream, i.e.,average CSI amplitude for 4 seconds.After that,it cut CSI durations but the speeds of paths are significantly higher in falling streams into chunks that contain samples obtained in 1-second in than in sitting down.Consequently,the frequencies in CFR power terval and arrange chunks of different CSI streams in columns to for falling are greater than the frequencies for sitting down.Simil- form a matrix of H.We choose interval size to be 1 second so that arly,different activities may have similar frequencies but different the distance moved by the object is short and at the same time the durations.For example,running and falling both have similar fre number of samples is large enough to ensure accurate correlation quencies but the duration of falling is shorter than running.Thus, estimation,which is the next step. to analyze CFR power for human activities,we need to extract fre- (2)Correlation estimation:CARM calculates the correlation mat quencies from it at multiple resolutions on multiple time scales. rix as H x H.The correlation matrix has dimension of N x N. The most relevant signal processing tool that can enable us to ex- where N is the number of CSI streams.For the example in Figure tract frequencies at multiple resolutions on multiple time scales is discrete wavelet transform (DWT).DWT provides high time res 8.we have N=180. (3)Eigendecomposition:CARM performs Eigendecomposition of olution for activities with high frequencies in CFR signals and the correlation matrix to calculate the eigenvectors high frequency resolution for activities with slow speeds.DWT (4)Movement Signal Reconstruction:In this step,CARM con- calculates the energies in different levels at any given time in the CFR signals,where each level corresponds to a frequency range. structs the principal components using the equation hi=H x qi. where q:and h;are the ith eigenvector and the ith principal com- The frequency ranges of adjacent DWT levels decrease exponen- ponents,respectively. tially.For example,if level 1 DWT represents a frequency range of CARM discards the first principal component hi and retains the 150~300Hz,which corresponds to 3.85~7.7 m/s movement speed next five principal components to be used for feature extraction in 5GHz band,then level 2 DWT represents a frequency range that is half of the frequency range for level 1.i.e..75~150Hz.which As discussed in 5.1,noises caused by internal state changes present in all CSI streams,which are the vertical lines appear in Figure corresponds to 1.925~3.85 m/s.The higher the energy in a DWT 8.Due to the high correlation,these noises are captured in hi level is,the more likely it is that the speed of the path is in a range along with the human movement signal.However,an interest- associated with the frequency range of that level.Figure 9(a)shows ing result is that all the information about the human movement the wavelet transform for a falling action,where higher brightness signal captured in h is also captured in other principal compon represents higher energy level.Although DWT has lower resolu- tion compared to spectrogram in Figure 5(e),we can see the high ents,because by Equation (4),the phase of a subcarrier is a lin- energy region moves from level 6 to level 2 from 1 to 1.5 seconds. ear combination of two orthogonal components:cos The advantage of DWT compared to STFT is as follows:First. and sin Since the PCA components are uncorrelated. DWT has nice tradeoffs in time and frequency resolutions.DWT the first principal component only contains one of these ortho- naturally groups frequencies that differ by several orders of mag- nitude into a few levels so that both high speed movements and low gonal components and the other component is retained in the rest PCA components.Therefore,we can safely discard the first prin- speed movements can be captured.Second,DWT reduces the size of data so that the classification algorithm can run in real time cipal component without losing any information.The number of To extract features for classification from a sample of an activity. PCA components used for feature extraction is empirically selec- CARM applies DWT to decompose the PCA components into 12 ted to achieve a good tradeoff between classification performance levels that span the frequency range from 0.15Hz to 300Hz.The and computational complexity.Figure 7(d)shows the second PCA DWT results of the five PCA components are averaged to capture component of our denoising scheme.We observe that our proposed the movement information present in different PCA components. method outperforms traditional filtering methods and does not con- From the output of DWT on each 200ms interval,CARM extracts tain the high frequency noise. a 27 dimensional feature vector that includes three types of fea- tures.1).The energy in each level,which represents the intensity

11 11.5 12 12.5 60 65 70 75 CSI Time (seconds) (a) Original CSI Stream 11 11.5 12 12.5 65 70 75 CSI Time (seconds) (b) Butterworth low-pass filter 11 11.5 12 12.5 65 70 75 CSI Time (seconds) (c) 5-point median filter 11 11.5 12 12.5 −10 −5 0 5 10 Time (seconds) CSI (d) PCA based denoising Figure 7: Denoising the time-series of CSI values 5.4 Principal Component Analysis To address the challenges in combining CSI streams, we apply PCA to discover the correlations between CSI streams. With PCA, we can track the time-varying correlations between CSI streams, and optimally combine them to extract principal components of CSI streams. CARM applies PCA to CSI streams using the fol￾lowing four steps. (1) Preprocessing: In this step, CARM first removes the static path components from each CSI stream by subtracting the correspond￾ing constant offsets from the streams. It calculates the constant off￾set for each stream through long-term averaging over that stream, i.e., average CSI amplitude for 4 seconds. After that, it cut CSI streams into chunks that contain samples obtained in 1-second in￾terval and arrange chunks of different CSI streams in columns to form a matrix of H. We choose interval size to be 1 second so that the distance moved by the object is short and at the same time the number of samples is large enough to ensure accurate correlation estimation, which is the next step. (2) Correlation estimation: CARM calculates the correlation mat￾rix as H T × H. The correlation matrix has dimension of N × N, where N is the number of CSI streams. For the example in Figure 8, we have N = 180. (3) Eigendecomposition: CARM performs Eigendecomposition of the correlation matrix to calculate the eigenvectors. (4) Movement Signal Reconstruction: In this step, CARM con￾structs the principal components using the equation hi = H × qi , where qi and hi are the i th eigenvector and the i th principal com￾ponents, respectively. CARM discards the first principal component h1 and retains the next five principal components to be used for feature extraction. As discussed in 5.1, noises caused by internal state changes present in all CSI streams, which are the vertical lines appear in Figure 8. Due to the high correlation, these noises are captured in h1 along with the human movement signal. However, an interest￾ing result is that all the information about the human movement signal captured in h1 is also captured in other principal compon￾ents, because by Equation (4), the phase of a subcarrier is a lin￾ear combination of two orthogonal components: cos  2π∆k(t) λ  and sin  2π∆k(t) λ  . Since the PCA components are uncorrelated, the first principal component only contains one of these ortho￾gonal components and the other component is retained in the rest PCA components. Therefore, we can safely discard the first prin￾cipal component without losing any information. The number of PCA components used for feature extraction is empirically selec￾ted to achieve a good tradeoff between classification performance and computational complexity. Figure 7(d) shows the second PCA component of our denoising scheme. We observe that our proposed method outperforms traditional filtering methods and does not con￾tain the high frequency noise. 6. FEATURE EXTRACTION 6.1 Extracting Features from CSI To obtain activity features from CSI, CARM needs to extract frequency components from different activities at different time scales. This is because human activities have two aspects asso￾ciated with them, duration and frequency. Duration represents the time a person takes to perform an activity and frequency represents the speed of multi-paths due to body movements during the activ￾ity. Different activities may have similar durations but different frequencies. For example, sitting down and falling both have short durations but the speeds of paths are significantly higher in falling than in sitting down. Consequently, the frequencies in CFR power for falling are greater than the frequencies for sitting down. Simil￾arly, different activities may have similar frequencies but different durations. For example, running and falling both have similar fre￾quencies but the duration of falling is shorter than running. Thus, to analyze CFR power for human activities, we need to extract fre￾quencies from it at multiple resolutions on multiple time scales. The most relevant signal processing tool that can enable us to ex￾tract frequencies at multiple resolutions on multiple time scales is discrete wavelet transform (DWT). DWT provides high time res￾olution for activities with high frequencies in CFR signals and high frequency resolution for activities with slow speeds. DWT calculates the energies in different levels at any given time in the CFR signals, where each level corresponds to a frequency range. The frequency ranges of adjacent DWT levels decrease exponen￾tially. For example, if level 1 DWT represents a frequency range of 150∼300Hz, which corresponds to 3.85∼7.7 m/s movement speed in 5GHz band, then level 2 DWT represents a frequency range that is half of the frequency range for level 1, i.e., 75∼150Hz, which corresponds to 1.925∼3.85 m/s. The higher the energy in a DWT level is, the more likely it is that the speed of the path is in a range associated with the frequency range of that level. Figure 9(a) shows the wavelet transform for a falling action, where higher brightness represents higher energy level. Although DWT has lower resolu￾tion compared to spectrogram in Figure 5(e), we can see the high energy region moves from level 6 to level 2 from 1 to 1.5 seconds. The advantage of DWT compared to STFT is as follows: First, DWT has nice tradeoffs in time and frequency resolutions. DWT naturally groups frequencies that differ by several orders of mag￾nitude into a few levels so that both high speed movements and low speed movements can be captured. Second, DWT reduces the size of data so that the classification algorithm can run in real time. To extract features for classification from a sample of an activity, CARM applies DWT to decompose the PCA components into 12 levels that span the frequency range from 0.15Hz to 300Hz. The DWT results of the five PCA components are averaged to capture the movement information present in different PCA components. From the output of DWT on each 200ms interval, CARM extracts a 27 dimensional feature vector that includes three types of fea￾tures. 1). The energy in each level, which represents the intensity

of movement in each speed range.2).Difference in the energy of also calculates the initial transition probabilities by first counting each level between consecutive 200ms intervals,which represents the number of transitions between every pair of states from the se- the rate of change of speed of a multi-path for the activity.3).Es- quence of feature vectors of all training samples divided equally timated torso and leg speeds using the percentile method introduced amongst states and then dividing the counts by total number of in Doppler radar [25]. transitions in all training samples.To decide the number of states. CARM iterates through various number of states and selects the 6.2 Resilience to Environmental Changes number that provides highest cross validation accuracy.To avoid Environmental changes such as adding an extra chair in a room overfitting of Baum-Welch algorithm to a particular person or mov- change the number of multi-paths arriving at the receiver.How- ing direction,in generating the model of an activity,we include ever,even when the number of multi-paths changes due to environ- samples of that activity from different people and different move- mental changes,the speed of change in lengths of multi-paths does ment directions.Furthermore,we evaluate the models using both not change because it depends on the movement of human body and 10-fold cross validation and separated testing samples collected in not on the number of multi-paths in an environment.Consequently, different environments to ensure that the models do not overfit on the frequency components in the CFR power stay the same as long samples from specific scenarios. as the person performs the same activity,and DWT gives higher energy in the same levels regardless of how many multi-paths have 7.2 Real Time Activity Recognition appeared or disappeared.Figures 10(a)and 10(b)plot the time- Once CARM generates HMMs for all activities,it can recognize series of denoised CSI values for the activity of falling.To emu activities in real-time.We will first explain how CARM detects the late the change in environment,our volunteer performed the action start and end of the activity and then explain how it recognizes the at two different locations.Figures 9(a)and 9(b)plot the DWTs unknown activity. of these two waveforms.We observe from these figures that even Activity Detection:To detect the start and end of an activity. though the time-series of denoised CSI values look very different CARM monitors the second eigenvector q2 and the corresponding for the same activity in different environments,the features that principal component h2.Our activity detection method is based CARM extracts look very similar.Compared to directly using the on two key observations.First,in the absence of an activity,the ei- CSI waveform.the features that CARM uses are resilient to envir- genvector q2 varies randomly over neighboring subcarriers because onmental changes,see detailed evaluations in Section 8. CSI streams contain uncorrelated values;whereas,in the presence of an activity,the CSI streams become correlated and q2 varies smoothly over neighboring subcarriers.Second,in the absence of an activity,the principal component h2 has smaller variance; whereas in the presence of an activity,it has higher variance. CARM empirically calculates the variance,Eh2).of the time series h2 and the mean of first difference of the eigenvector q2 06 1.6 05 1.5 given by2=s六∑L2l4z()-4el-1 where S is the Time (seconds) Time (seconds) number of CSI streams and q2(l)-q2(I-1)I is the difference in (a)Environment 1 (b)Environment 2 coefficients for neighboring subcarriers.In the presence of an activ- ity,Efh2 has a higher value because the time-series for human Figure 9:DWT of time-series for falling movement signal varies more frequently,whereas has a smaller value because the eigenvector becomes more smooth.Therefore. we define the activity indicator as E(h)/62.Figure 11 plots E(h.and the activity indicator over a period of about 10 seconds.We observe that activity indicator increase at 1.4 second and decreases at 9 seconds,which is the start and end times of the action,respectively.The activity indicator Efh2/has better 15 detection performance because it has sharper edges than the met- Time(seconds) Time(conds rics of E(h2}and 62 (a)Environment 1 (b)Environment 2 Figure 10:Denoised CSI time-series for falling 7.CLASSIFICATION RECOGNITION E(hM oh的 7.1 Building Activity Models CARM constructs an HMM for each activity using the training Time (seconds) samples of that activity.It also constructs an activity model for the situation when there is no activity in the room.To estimate Figure 11:Activity detection indicators mean vector and covariance matrix corresponding to each state and the transition probabilities for the HMM,CARM uses the well- To automatically detect the start or end of an activity.CARM known Baum-Welch algorithm[28].Baum-Welch algorithm needs compares the activity indicator with a threshold that it adjusts dy. a rough guess of these probabilities to start with.To guess the initial namically based on the background noise level.To dynamically ad- values,CARM first divides the sequence of feature vectors from just the threshold,we use an Exponential Moving Average (EMA) each training sample equally amongst the states and then calcu- algorithm to update the detection threshold.In case of a sudden lates the initial values for the mean vector and covariance matrix of increase in noise level,CARM can incorrectly detect the start of an each state using the feature vectors assigned to that state.CARM activity.To handle this,when CARM builds activity models,it also

of movement in each speed range. 2). Difference in the energy of each level between consecutive 200ms intervals, which represents the rate of change of speed of a multi-path for the activity. 3). Es￾timated torso and leg speeds using the percentile method introduced in Doppler radar [25]. 6.2 Resilience to Environmental Changes Environmental changes such as adding an extra chair in a room change the number of multi-paths arriving at the receiver. How￾ever, even when the number of multi-paths changes due to environ￾mental changes, the speed of change in lengths of multi-paths does not change because it depends on the movement of human body and not on the number of multi-paths in an environment. Consequently, the frequency components in the CFR power stay the same as long as the person performs the same activity, and DWT gives higher energy in the same levels regardless of how many multi-paths have appeared or disappeared. Figures 10(a) and 10(b) plot the time￾series of denoised CSI values for the activity of falling. To emu￾late the change in environment, our volunteer performed the action at two different locations. Figures 9(a) and 9(b) plot the DWTs of these two waveforms. We observe from these figures that even though the time-series of denoised CSI values look very different for the same activity in different environments, the features that CARM extracts look very similar. Compared to directly using the CSI waveform, the features that CARM uses are resilient to envir￾onmental changes, see detailed evaluations in Section 8. (a) Environment 1 (b) Environment 2 Figure 9: DWT of time-series for falling 0 0.5 1 1.5 2 2.5 −20 −10 0 10 Time (seconds) CSI (a) Environment 1 0.5 1 1.5 −20 −10 0 10 20 Time (seconds) CSI (b) Environment 2 Figure 10: Denoised CSI time-series for falling 7. CLASSIFICATION & RECOGNITION 7.1 Building Activity Models CARM constructs an HMM for each activity using the training samples of that activity. It also constructs an activity model for the situation when there is no activity in the room. To estimate mean vector and covariance matrix corresponding to each state and the transition probabilities for the HMM, CARM uses the well￾known Baum-Welch algorithm [28]. Baum-Welch algorithm needs a rough guess of these probabilities to start with. To guess the initial values, CARM first divides the sequence of feature vectors from each training sample equally amongst the states and then calcu￾lates the initial values for the mean vector and covariance matrix of each state using the feature vectors assigned to that state. CARM also calculates the initial transition probabilities by first counting the number of transitions between every pair of states from the se￾quence of feature vectors of all training samples divided equally amongst states and then dividing the counts by total number of transitions in all training samples. To decide the number of states, CARM iterates through various number of states and selects the number that provides highest cross validation accuracy. To avoid overfitting of Baum-Welch algorithm to a particular person or mov￾ing direction, in generating the model of an activity, we include samples of that activity from different people and different move￾ment directions. Furthermore, we evaluate the models using both 10-fold cross validation and separated testing samples collected in different environments to ensure that the models do not overfit on samples from specific scenarios. 7.2 Real Time Activity Recognition Once CARM generates HMMs for all activities, it can recognize activities in real-time. We will first explain how CARM detects the start and end of the activity and then explain how it recognizes the unknown activity. Activity Detection: To detect the start and end of an activity, CARM monitors the second eigenvector q2 and the corresponding principal component h2. Our activity detection method is based on two key observations. First, in the absence of an activity, the ei￾genvector q2 varies randomly over neighboring subcarriers because CSI streams contain uncorrelated values; whereas, in the presence of an activity, the CSI streams become correlated and q2 varies smoothly over neighboring subcarriers. Second, in the absence of an activity, the principal component h2 has smaller variance; whereas in the presence of an activity, it has higher variance. CARM empirically calculates the variance, E{h 2 2}, of the time series h2 and the mean of first difference of the eigenvector q2 given by δq2 = 1 S−1 PS l=2 |q2 (l) − q2 (l − 1)|, where S is the number of CSI streams and |q2 (l) − q2 (l − 1)| is the difference in coefficients for neighboring subcarriers. In the presence of an activ￾ity, E{h 2 2} has a higher value because the time-series for human movement signal varies more frequently, whereas δq2 has a smaller value because the eigenvector becomes more smooth. Therefore, we define the activity indicator as E{h 2 2}/δq2 . Figure 11 plots E{h 2 2}, δq2 , and the activity indicator over a period of about 10 seconds. We observe that activity indicator increase at 1.4 second and decreases at 9 seconds, which is the start and end times of the action, respectively. The activity indicator E{h 2 2}/δq2 has better detection performance because it has sharper edges than the met￾rics of E{h 2 2} and δq2 . 1 2 3 4 5 6 7 8 9 10 10−1 100 101 102 Amplitude (log scale) E{h2 2 }/δ q 2 E{h2 2 } δ q 2 Time (seconds) Figure 11: Activity detection indicators To automatically detect the start or end of an activity, CARM compares the activity indicator with a threshold that it adjusts dy￾namically based on the background noise level. To dynamically ad￾just the threshold, we use an Exponential Moving Average (EMA) algorithm to update the detection threshold. In case of a sudden increase in noise level, CARM can incorrectly detect the start of an activity. To handle this, when CARM builds activity models, it also

collects some samples for the situation when there is no activity ☆Training location △Testing location and builds a model for"no activity"using these samples.CARM classifies a detected activity using all activity models and decides Fridge whether a detected activity indeed had an activity in it or not.If it finds that there was no activity.it adjusts the detection threshold accordingly Table Activity Recognition:CARM identifies the activity in follow- ing four steps.First,it takes all CSI values between the start and end times and denoises them using the PCA based denoising Walking/running route method described in Section 5.4.Second.from every 200ms in- 77m Tx/Fridge terval between the start and end times,it extracts a 27 dimensional (a)Lab feature vector as described in Section 6.1.Third,it uses dynamic (b)Apartment programming to calculate the likelihood of each HMM generating this sequence of feature vectors [18].Finally,the model with the Figure 12:Floor plans highest likelihood identifies the activity. the path marked with a dashed line around the table in the center of 6 IMPLEMENTATION EVALUATION the lab.Tx and Rx represent the locations of the transmitter AP and receiver laptop.While collecting the training data,we requested the 8.1 Implementation volunteers to change their orientation to ensure the generality of the collected data.Triangles in Figures 12(a)and 12(b)represent the CARM consists of two components:a laptop with a WiFi card locations where our volunteers performed activities when evaluat- and a commercially available WiFi access point(AP).We imple- ing accuracy of CARM.The total training time for our activity data mented CARM on a Think-pad X200 laptop equipped with Intel set with 1,400 samples was 100.55 seconds on a laptop with Intel 5300 WiFi card and tested it using two commercially available i5-4285 CPU.as shown in Table 1.Note that our activities have 802.11ac APs:NETGEAR JR6100 and TP-Link TL-WDR7500. no location dependency.Furthermore,once CARM is trained on To obtain CSI values from regular data frames transmitted by the the given training set,it can be directly applied to environments access point,we installed the CSI tool developed by Halperin et al. and persons that have not been included in the training set.Thus, on the laptop [9]. CARM does not need the on-site training data collection as for E- All the experiments that we report in this paper were performed eyes [27].Consequently,the one-time training can be done on a in the 5GHz frequency band with 20MHz bandwidth channels.We large training set using a data center choose 5GHz band for shorter wavelength,which lead to better movement speed resolution.We also tested CARM in 2.4GHz. Activity Samples Training Time Due to the longer wavelength,frequencies of the CSI waveforms (R)Running 205 16.383 in 2.4GHz are lower for the same activity compared to those in (W)Walking 315 26.84s 5GHz.CARM acquires CSI measurements from the CSI tool and (S)Sitting down 266 14.49s processes it in real-time using MATLAB.CARM is computation- (O)Opening refrigerator 213 13.49s ally efficient.For example,on a Think-pad laptop with Intel i5- (F)Falling 98 5.02s 3320 CPU and 4GB RAM,CARM takes 85.6ms to process 200ms (B)Boxing 75 4.883 (P)Pushing one hand 72 7.00s CSI values sampled at a rate of 2,500 samples/second.Note that (T)Brushing teeth 96 7.35s it is possible to further improve the computational efficiency of (E)Empty (i.e.,no activity) 60 5.10s CARM by implementing it in C or using DSP to accelerate the signal processing. Table 1:Summary of activity dataset 8.2 Evaluation Setup 8.3 Activity Detection We collected training samples for eight different activities in our lab.which is 7.7m in length and 6.5m in width,as shown in Figure Now we present the accuracy CARM achieves in detecting the 12(a).We collected a total of 1,400 samples for the testing activities presence of an activity.We evaluate the accuracy using two metrics: from 25 volunteers.The volunteers included 20 male and 5 female true positive rate(TPR)and false alarm rate(FAR).TPR is the ratio graduate/undergraduate students with ages in the range of 19-22. of the number of times CARM correctly detects the presence of an We evaluated the recognition accuracy of CAMR through two activity to the total number of times the activity is performed.FAR sets of experiments,one is in the trained environments and the is the ratio of the number of times that CARM incorrectly detects other is in the untrained environments.We use the lab where we the presence of an activity when actually there is no activity. collected the training dataset as the trained environments.For the untrained environments,we evaluate on three typical indoor scen- arios,including:1)a large open lobby area,which has a length, width,and height of 45m,5.3m,and 4m,respectively;2)a small apartment,which has area of 70m-as shown in Figure 12(b);3)a 垂-Walking(PCA) 60 ◆Pushing(PCA) small office,which has a length,width,and height of 5.6m,3.4m, DWalking(Filter and 2.7m,respectively. OPushinolFilter) The activities for which we collected training samples are listed in Table 1.along with their abbreviations and number of training Distance(meters) samples for each activity.We collected training samples for each activity except walking and running at the location marked with star Figure 13:Detection range of CARM in Figure 12(a).For walking and running,our volunteers followed

collects some samples for the situation when there is no activity and builds a model for “no activity” using these samples. CARM classifies a detected activity using all activity models and decides whether a detected activity indeed had an activity in it or not. If it finds that there was no activity, it adjusts the detection threshold accordingly. Activity Recognition: CARM identifies the activity in follow￾ing four steps. First, it takes all CSI values between the start and end times and denoises them using the PCA based denoising method described in Section 5.4. Second, from every 200ms in￾terval between the start and end times, it extracts a 27 dimensional feature vector as described in Section 6.1. Third, it uses dynamic programming to calculate the likelihood of each HMM generating this sequence of feature vectors [18]. Finally, the model with the highest likelihood identifies the activity. 8. IMPLEMENTATION & EVALUATION 8.1 Implementation CARM consists of two components: a laptop with a WiFi card and a commercially available WiFi access point (AP). We imple￾mented CARM on a Think-pad X200 laptop equipped with Intel 5300 WiFi card and tested it using two commercially available 802.11ac APs: NETGEAR JR6100 and TP-Link TL-WDR7500. To obtain CSI values from regular data frames transmitted by the access point, we installed the CSI tool developed by Halperin et al. on the laptop [9]. All the experiments that we report in this paper were performed in the 5GHz frequency band with 20MHz bandwidth channels. We choose 5GHz band for shorter wavelength, which lead to better movement speed resolution. We also tested CARM in 2.4GHz. Due to the longer wavelength, frequencies of the CSI waveforms in 2.4GHz are lower for the same activity compared to those in 5GHz. CARM acquires CSI measurements from the CSI tool and processes it in real-time using MATLAB. CARM is computation￾ally efficient. For example, on a Think-pad laptop with Intel i5- 3320 CPU and 4GB RAM, CARM takes 85.6ms to process 200ms CSI values sampled at a rate of 2,500 samples/second. Note that it is possible to further improve the computational efficiency of CARM by implementing it in C or using DSP to accelerate the signal processing. 8.2 Evaluation Setup We collected training samples for eight different activities in our lab, which is 7.7m in length and 6.5m in width, as shown in Figure 12(a). We collected a total of 1,400 samples for the testing activities from 25 volunteers. The volunteers included 20 male and 5 female graduate/undergraduate students with ages in the range of 19–22. We evaluated the recognition accuracy of CAMR through two sets of experiments, one is in the trained environments and the other is in the untrained environments. We use the lab where we collected the training dataset as the trained environments. For the untrained environments, we evaluate on three typical indoor scen￾arios, including: 1) a large open lobby area, which has a length, width, and height of 45m, 5.3m, and 4m, respectively; 2) a small apartment, which has area of 70m2 as shown in Figure 12(b); 3) a small office, which has a length, width, and height of 5.6m, 3.4m, and 2.7m, respectively. The activities for which we collected training samples are listed in Table 1, along with their abbreviations and number of training samples for each activity. We collected training samples for each activity except walking and running at the location marked with star in Figure 12(a). For walking and running, our volunteers followed Table Walking/running route Table 7.7 m 6.5 m 1.6 m Fridge Training location Tx Rx (a) Lab Table Fridge Kitchen Tx Bath room Rx Testing location (b) Apartment Figure 12: Floor plans the path marked with a dashed line around the table in the center of the lab. Tx and Rx represent the locations of the transmitter AP and receiver laptop. While collecting the training data, we requested the volunteers to change their orientation to ensure the generality of the collected data. Triangles in Figures 12(a) and 12(b) represent the locations where our volunteers performed activities when evaluat￾ing accuracy of CARM. The total training time for our activity data set with 1,400 samples was 100.55 seconds on a laptop with Intel i5-4285 CPU, as shown in Table 1. Note that our activities have no location dependency. Furthermore, once CARM is trained on the given training set, it can be directly applied to environments and persons that have not been included in the training set. Thus, CARM does not need the on-site training data collection as for E￾eyes [27]. Consequently, the one-time training can be done on a large training set using a data center. Activity Samples Training Time (R) Running 205 16.38s (W) Walking 315 26.84s (S) Sitting down 266 14.49s (O) Opening refrigerator 213 13.49s (F) Falling 98 5.02s (B) Boxing 75 4.88s (P) Pushing one hand 72 7.00s (T) Brushing teeth 96 7.35s (E) Empty (i.e., no activity) 60 5.10s Table 1: Summary of activity dataset 8.3 Activity Detection Now we present the accuracy CARM achieves in detecting the presence of an activity. We evaluate the accuracy using two metrics: true positive rate (TPR) and false alarm rate (FAR). TPR is the ratio of the number of times CARM correctly detects the presence of an activity to the total number of times the activity is performed. FAR is the ratio of the number of times that CARM incorrectly detects the presence of an activity when actually there is no activity. 2 4 6 8 10 12 14 16 0 0.2 0.4 0.6 0.8 1 Distance (meters) True postive rate Walking(PCA) Pushing(PCA) Walking(Filter) Pushing(Filter) Figure 13: Detection range of CARM