Path Speed Distance Delay Amplitude Structure(MicI)】 >2,000m/s 4.5 cm 家0.13ms Large 2 Structure (Mic 2) >2.000m/s 12 cm x013 ms Medium LOS (Mic 1) 343m/s 4.5cm 0.13ms Large 4 LOS (Mic 2) 343m/s 12 cm 0.341ms Medium -0 Reflection (Mic 1) 343m/s >4.5cm 0.131ms Small 512 840 96 Reflection(Mic 2) Small Samples 6 343m/s >12cm >0.34ms (a)Baseband signal in the time domain Table 2:Different propagation paths due to multipath propagation.Suppose that the transmitted (01.0 baseband signal is ZCr(t)and the system is a Linear Time- Invariant(LTI)system,then the received baseband signal 611,0211) can be represented as: 19 -258 256 512 Samples ZCR(t)= >Aje-iiZCT(t-Ti)=h(t)*ZCT(t). (2) (b)Autocorrelation of baseband signal i=l Figure 5:Baseband signal of the ZC sequence where L is the number of propagation paths,ti is the de- lay of the ith propagation path and Aie represents the inserting zeros after the positive frequency components and complex path coefficient(i.e.,amplitude and phase)of the before the negative frequency components,where B is tar- ith propagation path,respectively.The received signal can geting signal bandwidth (e.g,6 kHz)and fs is the sampling be viewed as a circular convolution,h(t)*ZCr(t),of the rate of the sound (e.g,48 kHz).In this way,the interpo- Impulse Response h(t)and the periodical transmitted signal lated ZC sequence only occupies a small bandwidth of B in ZCr(t).The Impulse Response (IR)function of the multipath the frequency domain.Finally,we use IFFT to convert the propagation model is given by interpolated signal back into the time domain. < In VSkin,we choose a ZC sequence length of 127 points h(t)=Aje-i68(t-i). (3) with a parameter of u=63.We pad the 127-point ZC se- quence into 1024 points.Therefore,we have B=5.953 kHz at the sampling rate of fs =48 kHz.The interpo- where 6(t)is Dirac's delta function. lated ZC sequence is a periodical complex valued signal We use the cross-correlation,h(t)=ZCR(-t)*ZCr(t). with a period of 1024 sample points(21.3ms)as shown in of the received baseband signal ZCR(t),with the transmit- Figure 5(a). ted ZC sequence ZCr(t)as the estimation of the impulse The second step of the modulation process is to up-convert response.Due to the ideal periodic auto-correlation property the signal into the passband.In the up-convert step,the inter- of ZC code,where the auto-correlation of ZC sequence is polated ZC sequence is multiplied with a carrier frequency non-zero only at the point with a delay r of zero,the estima- of fe as shown in Figure 4.The transmitted passband sig- tion h(t)provides a good approximation for the IR function. nal is T(t)=cos(2πfet)ZC(t)-sin(2πfet)ZC号(t),where In our system,h(t)is sampled with an interval of Ts ZCI(t)and ZC(t)are the real part and imaginary part of 1/fs =0.021 ms,which corresponds to 0.7 cm (343 m/s x the time domain ZC sequence,respectively.We set fe as 20.25 0.021 ms)of the propagation distance.The sampled version kHz so that the transmitted signal occupies the bandwidth of IR estimation,h[n],has 1024 taps with n=0 ~1023. from 17.297 kHz to 23.25 kHz.This is because of frequencies Therefore,the maximum unambiguous range of our system is higher than 17 kHz are inaudible to most people [20]. 1024x0.7/2=358 cm,which is enough to avoid interferences from nearby objects.Using the cross-correlation,we obtain The signal is transmitted through the speaker on the mo- bile device and recorded by the microphones using the same one frame of IR estimation h[n]for each period of 1,024 sampling frequency of 48 kHz.After receiving the sound sig- sound samples(21.33 ms),as shown in Figure 3.Each peak nal,VSkin first demodulates the signal by down-converting in the IR estimation indicates one propagation path at the the passband signal back into the complex valued baseband corresponding delay,i.e.,a path with a delay of ri will lead signal. to a peak at the ni=ri/Ts sample point. SOUND PATH SEPARATION AND 5.2 Sound Propagation Model In our system,there are three different kinds of propa- MEASUREMENT gation paths:the structure path,the LOS air path and the 5.1 Multipath Propagation Model reflection air path,see Figure 2. The received baseband signal is a superposition of mul- Theoretically,we can estimate the delay and amplitude tiple copies of the transmitted signals with different delays of different paths based on the speed and attenuation of0 128 256 384 512 640 768 896 1024 Samples -0.5 0 0.5 I\Q (normalized) I Q (a) Baseband signal in the time domain -512 -256 0 256 512 Samples 0 0.5 1 Absolute value (0,1.0) (-11,0.211) (b) Autocorrelation of baseband signal Figure 5: Baseband signal of the ZC sequence inserting zeros after the positive frequency components and before the negative frequency components, where B is tar￾geting signal bandwidth (e.g., 6 kHz) and fs is the sampling rate of the sound (e.g., 48 kHz). In this way, the interpo￾lated ZC sequence only occupies a small bandwidth of B in the frequency domain. Finally, we use IFFT to convert the interpolated signal back into the time domain. In VSkin, we choose a ZC sequence length of 127 points with a parameter of u = 63. We pad the 127-point ZC se￾quence into 1024 points. Therefore, we have B = 5.953 kHz at the sampling rate of fs = 48 kHz. The interpo￾lated ZC sequence is a periodical complex valued signal with a period of 1024 sample points (21.3ms) as shown in Figure 5(a). The second step of the modulation process is to up-convert the signal into the passband. In the up-convert step, the inter￾polated ZC sequence is multiplied with a carrier frequency of fc as shown in Figure 4. The transmitted passband sig￾nal is T (t) = cos(2π fc t)ZCI T (t) − sin(2π fc t)ZCQ T (t), where ZCI T (t) and ZCQ T (t) are the real part and imaginary part of the time domain ZC sequence, respectively. We set fc as 20.25 kHz so that the transmitted signal occupies the bandwidth from 17.297 kHz to 23.25 kHz. This is because of frequencies higher than 17 kHz are inaudible to most people [20]. The signal is transmitted through the speaker on the mo￾bile device and recorded by the microphones using the same sampling frequency of 48 kHz. After receiving the sound sig￾nal, VSkin first demodulates the signal by down-converting the passband signal back into the complex valued baseband signal. 5 SOUND PATH SEPARATION AND MEASUREMENT 5.1 Multipath Propagation Model The received baseband signal is a superposition of mul￾tiple copies of the transmitted signals with different delays Path Speed Distance Delay Amplitude 1 Structure (Mic 1) >2,000 m/s 4.5 cm ≪0.13 ms Large 2 Structure (Mic 2) >2,000 m/s 12 cm ≪0.13 ms Medium 3 LOS (Mic 1) 343 m/s 4.5 cm 0.13 ms Large 4 LOS (Mic 2) 343 m/s 12 cm 0.34 ms Medium 5 Reflection (Mic 1) 343 m/s >4.5 cm >0.13 ms Small 6 Reflection (Mic 2) 343 m/s >12 cm >0.34 ms Small Table 2: Different propagation paths due to multipath propagation. Suppose that the transmitted baseband signal is ZCT (t) and the system is a Linear Time￾Invariant (LTI) system, then the received baseband signal can be represented as: ZCR (t) = X L i=1 Aie −jϕiZCT (t − τi ) = h(t) ∗ ZCT (t), (2) where L is the number of propagation paths, τi is the de￾lay of the i th propagation path and Aie −jϕi represents the complex path coefficient (i.e., amplitude and phase) of the i th propagation path, respectively. The received signal can be viewed as a circular convolution, h(t) ∗ ZCT (t), of the Impulse Response h(t) and the periodical transmitted signal ZCT (t). The Impulse Response (IR) function of the multipath propagation model is given by h(t) = X L i=1 Aie −jϕi δ (t − τi ), (3) where δ (t) is Dirac’s delta function. We use the cross-correlation, ˆh(t) = ZC∗ R (−t) ∗ ZCT (t), of the received baseband signal ZCR (t), with the transmit￾ted ZC sequence ZCT (t) as the estimation of the impulse response. Due to the ideal periodic auto-correlation property of ZC code, where the auto-correlation of ZC sequence is non-zero only at the point with a delay τ of zero, the estima￾tion ˆh(t) provides a good approximation for the IR function. In our system, ˆh(t) is sampled with an interval of Ts = 1/fs = 0.021 ms, which corresponds to 0.7 cm (343 m/s × 0.021 ms) of the propagation distance. The sampled version of IR estimation, ˆh[n], has 1024 taps with n = 0 ∼ 1023. Therefore, the maximum unambiguous range of our system is 1024×0.7/2 = 358 cm, which is enough to avoid interferences from nearby objects. Using the cross-correlation, we obtain one frame of IR estimation ˆh[n] for each period of 1,024 sound samples (21.33 ms), as shown in Figure 3. Each peak in the IR estimation indicates one propagation path at the corresponding delay, i.e., a path with a delay of τi will lead to a peak at the ni = τi /Ts sample point. 5.2 Sound Propagation Model In our system, there are three different kinds of propa￾gation paths: the structure path, the LOS air path and the reflection air path, see Figure 2. Theoretically, we can estimate the delay and amplitude of different paths based on the speed and attenuation of