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 torecognition 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