Signal cross-correlation between the received and the transmitted sig- Separation Speaker nal to derive the CIR.We detect each path in random sampled ZC Modulation frames and calculate the respiration SNR in the frequency domain to select paths that are candidates of respiration related ZC reflections that will be used in the second stage. Demodulation The second stage is path combination.To expand the Microphone Array sensing range,we first perform cross-correlation between the Path Two-Round Breath detected paths and their surrounding samples to calculate delay Selection Combinations Estimation and conduct delay-and-sum in the local paths.We then use a Principal Component Analysis(PCA)algorithm to optimally Path Path Clustering Combination combine the time-domain waveform of the detected paths. Figure 3.System Overview of RESPTRACKER Based on the combined respiration signal,we perform the room-scale tracking by calculating the waveform of each ob- servation slot independently.Finally,we use the reconstructed each peak corresponds to one signal path.From Figure 2(a), we have two observations.First,due to the high resolution of breath signal to perform breath rate estimation for each user. the sound signal,the width of each peak is less than 10 cm so III.SIGNAL SEPARATION that theoretically we can separate two users even if they are We use ZC sequences that have ideal auto-correlation just 10 cm apart.Second,the sound signal attenuates quickly property to separate paths of different users and at different and it is hard to reliably detect peaks at a distance of 4 meters. distances Figure 2(b)further illustrates the time variations of the paths,where we removed the static components by subtracting A.ZC Modulation the paths that are not changing within a period of half a The transmitting signal used in RESPTRACKER is the ZC minute,e.g.,the LOS path and reflections of walls.We observe sequence modulated by a sinusoid carrier [15].The ZC se- from Figure 2(b)that the respiration of a user causes regular quence with a length of Nzc is given by: fluctuations in the corresponding path.More interestingly,a single user may incur correlated changes in multiple paths, scln]=eju ,n=0,,Nzc-1, (1) as the signal may be reflected by the wall before reaching the chest of the user and may reflect from different parts where the u and g are the parameters of the sequence.We set of the chest.While these reflections are weak,they provide q to 0,u to 1,and Nse to 199 representing a 2 kHz bandwidth important respiration information of the same user.This is in the modulated signal.Once we get the baseband signal,we because it is well known that the signal quality of a single path use frequency domain interpolation to expand the sequence largely depends on the posture and angle of the user [11].The to a length of L,which is the frame length of our OFDM fluctuations of a single path may be undetectable for certain symbol and is set to 4800 samples in our scheme.We then user orientations,which lead to interruptions in continuous modulate the signal with a carrier sinusoid at a frequency of monitoring.Therefore,it is vital to combine the information fe by moving the baseband sequence to the higher frequency of different paths to perform reliable continuous monitoring. part.Before performing Inverse Fast Fourier transform(IFFT) Figure 2(c)shows the waveform of the respiration signal of for OFDM modulation,we set the negative frequency part the same user at reflection paths at different distances.While to the conjugate counterpart of the signal on the positive the patterns of these signals are similar,they have different frequency.Algorithm 1 shows the detailed process,where fs phases and signal details.Therefore,directly adding these is the sampling frequency.After we generate one frame of the paths may not be an effective way to enhance the signal. time-domain real signal zcrn],we transmit it repeatedly so Based on the above observations,we find that that the transmitted signals are cyclical OFDM symbols. RESPTRACKER needs to address two important challenges. First,how to efficiently separate and identify the multipaths Algorithm 1:Transmitting signal generation of different users?Second,how to reliably combine and Result:The modulated sequence zcrn]with a length reconstruct the breath signals from different paths belonging of L and a carrier frequency of fe. to a single user? 1 Generate zcn]from Eq.1 with a length of Nze. 2 Perform FFT on zc[n]to get ZC[n]. B.System Design 3 Perform FFT shift on ZC[n]to get ZCa[n] To address the above challenges,RESPTRACKER proposes 4 Generate a all zero sequence ZC[n]with a length of L. a two-stage design as shown in Figure 3. 5ZC'-Ng-山：'+N1←ZCm Ja The first stage is signal separation.We use COTS speakers to transmit ZC modulated sound signals.The reflected signals 6ZC-华-2：L-华+←ZCm 7 Perform IFFT on ZC to the time-domain zcr[n]. are received by a microphone array that collects multiple copies of the reflection signal.We perform frequency domainFigure 3. System Overview of RESPTRACKER each peak corresponds to one signal path. From Figure 2(a), we have two observations. First, due to the high resolution of the sound signal, the width of each peak is less than 10 cm so that theoretically we can separate two users even if they are just 10 cm apart. Second, the sound signal attenuates quickly and it is hard to reliably detect peaks at a distance of 4 meters. Figure 2(b) further illustrates the time variations of the paths, where we removed the static components by subtracting the paths that are not changing within a period of half a minute, e.g., the LOS path and reflections of walls. We observe from Figure 2(b) that the respiration of a user causes regular fluctuations in the corresponding path. More interestingly, a single user may incur correlated changes in multiple paths, as the signal may be reflected by the wall before reaching the chest of the user and may reflect from different parts of the chest. While these reflections are weak, they provide important respiration information of the same user. This is because it is well known that the signal quality of a single path largely depends on the posture and angle of the user [11]. The fluctuations of a single path may be undetectable for certain user orientations, which lead to interruptions in continuous monitoring. Therefore, it is vital to combine the information of different paths to perform reliable continuous monitoring. Figure 2(c) shows the waveform of the respiration signal of the same user at reflection paths at different distances. While the patterns of these signals are similar, they have different phases and signal details. Therefore, directly adding these paths may not be an effective way to enhance the signal. Based on the above observations, we find that RESPTRACKER needs to address two important challenges. First, how to efficiently separate and identify the multipaths of different users? Second, how to reliably combine and reconstruct the breath signals from different paths belonging to a single user? B. System Design To address the above challenges, RESPTRACKER proposes a two-stage design as shown in Figure 3. The first stage is signal separation. We use COTS speakers to transmit ZC modulated sound signals. The reflected signals are received by a microphone array that collects multiple copies of the reflection signal. We perform frequency domain cross-correlation between the received and the transmitted sig￾nal to derive the CIR. We detect each path in random sampled frames and calculate the respiration SNR in the frequency domain to select paths that are candidates of respiration related reflections that will be used in the second stage. The second stage is path combination. To expand the sensing range, we first perform cross-correlation between the detected paths and their surrounding samples to calculate delay and conduct delay-and-sum in the local paths. We then use a Principal Component Analysis (PCA) algorithm to optimally combine the time-domain waveform of the detected paths. Based on the combined respiration signal, we perform the room-scale tracking by calculating the waveform of each ob￾servation slot independently. Finally, we use the reconstructed breath signal to perform breath rate estimation for each user. III. SIGNAL SEPARATION We use ZC sequences that have ideal auto-correlation property to separate paths of different users and at different distances. A. ZC Modulation The transmitting signal used in RESPTRACKER is the ZC sequence modulated by a sinusoid carrier [15]. The ZC se￾quence with a length of Nzc is given by: zc[n] = e −j πu(n+1+2q) Nzc , n = 0, ..., Nzc − 1, (1) where the u and q are the parameters of the sequence. We set q to 0, u to 1, and Nzc to 199 representing a 2 kHz bandwidth in the modulated signal. Once we get the baseband signal, we use frequency domain interpolation to expand the sequence to a length of L, which is the frame length of our OFDM symbol and is set to 4800 samples in our scheme. We then modulate the signal with a carrier sinusoid at a frequency of fc by moving the baseband sequence to the higher frequency part. Before performing Inverse Fast Fourier transform (IFFT) for OFDM modulation, we set the negative frequency part to the conjugate counterpart of the signal on the positive frequency. Algorithm 1 shows the detailed process, where fs is the sampling frequency. After we generate one frame of the time-domain real signal zcT [n], we transmit it repeatedly so that the transmitted signals are cyclical OFDM symbols. Algorithm 1: Transmitting signal generation Result: The modulated sequence zcT [n] with a length of L and a carrier frequency of fc. 1 Generate zc[n] from Eq.1 with a length of Nzc. 2 Perform FFT on zc[n] to get ZC[n]. 3 Perform FFT shift on ZC[n] to get ZCs[n]. 4 Generate a all zero sequence ZCd[n] with a length of L. 5 ZCd[ fcL fs − (Nzc−1) 2 : fcL fs + (Nzc−1) 2 ] ⇐ ZCs[n]. 6 ZCd[L − fcL fs − Nzc−1 2 : L − fcL fs + Nzc−1 2 ] ⇐ ZC∗ [n]. 7 Perform IFFT on ZCd to the time-domain zcT [n]