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 intensity11 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