VECTOR:Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices.144:5 20 -12 2C同 1000 500 cy (Hz) 500 1000 20000 10000 020 150017形o20d (a)Baseband signal for odd subcarriers in (b)Modulated odd subcarriers in frequency (c)CIR of odd subcarriers with rich environ- frequency domain. domain mental multipaths. Fig.2.Key intermediate steps of signal processing. 3 SIGNAL DESIGN In the section,we first introduce the physical relationship between temperature and the speed of sound.We then design an OFDM sound signal to accurately measure the ToF along a sound path to derive the temperature. 3.1 Background The speed of sound in the air depends on environmental variables such as temperature,humidity,and air pressure.Within the normal room temperature range,the speed of sound can be approximated as c=331.3+0.606×T m/s, (1) where the temperature T is in degrees Celsius(C).While there are better approximations that relate the speed of sound to both temperature and air pressure [32],we use Eq.(1)as it is accurate enough for our system. We observe that the speed of sound increases by around 0.2%when the air temperature raises by one degree Celsius at room temperature.As an example,for two devices that are separated by a distance of 60 cm,the ToF measurement will decrease by a small amount of 3.02 us based on Eq.(1).Under the widely supported sampling rate of 48 kHz for sound playing/recording,the interval between consecutive samples is 20.8us,which is far greater than the small change in ToF.Therefore,traditional correlation-based ranging schemes cannot reliably detect such small changes in ToF,which is less than the sampling interval.To this end,we use an OFDM modulated signal to capture both the coarse-grained cross-correlation measure and the fine-grained phase measurement to detect microsecond-level changes in ToF. Phase-based ToF measurement provides high-resolution and reliable ToF results.The phase change for a specific path p,p,is related to the speed of sound by p=-2dpfe/c,where dp is the length of the path and fe is the carrier frequency of the signal.In the following discussion,we use the carrier frequency of fe=19 kHz if not specified.For two devices that are separated by a distance of 60 cm,the phase change will decrease by an amount of 0.360 in radian when the temperature raises by one degree at room temperature.Such phase increase can be reliably measured using OFDM signals [33].However,as phase changes are limited in the range of 0~2m, it cannot determine whether the phase changes by 0.5 or 2.5.We use coarse-grained cross-correlation results to resolve the ambiguity in phase measurements.As a phase change of 2m at 19 kHz carrier is equivalent to 52.6 us in ToF,we can use the cross-correlation result that has a resolution of 20.8 us to determine how many 2m the phase has been changed.Therefore,we design an OFDM signal that can measure both the phase and the cross-correlation offset at the same time. Proc.ACM Interact.Mob.Wearable Ubiquitous Technol.,Vol.6,No.3,Article 144.Publication date:September 2022.VECTOR: Velocity Based Temperature-field Monitoring with Distributed Acoustic Devices • 144:5 -1000 -500 0 500 1000 Frequency (Hz) 0.5 1.0 1.5 2.0 Magnitude ZCodd[n] Zero at central frequency bin. (a) Baseband signal for odd subcarriers in frequency domain. -20000 -10000 0 10000 20000 Frequency (Hz) 0.5 1.0 1.5 2.0 Magnitude ZC ZCodd[n] ∗ odd[n] (b) Modulated odd subcarriers in frequency domain. 0 250 500 750 1000 1250 1500 1750 2000 Sample Points 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Magnitude ϕpositive = 1.714 ϕnegative = −1.427 (c) CIR of odd subcarriers with rich environ￾mental multipaths. Fig. 2. Key intermediate steps of signal processing. 3 SIGNAL DESIGN In the section, we first introduce the physical relationship between temperature and the speed of sound. We then design an OFDM sound signal to accurately measure the ToF along a sound path to derive the temperature. 3.1 Background The speed of sound in the air depends on environmental variables such as temperature, humidity, and air pressure. Within the normal room temperature range, the speed of sound can be approximated as 𝑐 = 331.3 + 0.606 ×𝑇 𝑚/𝑠, (1) where the temperature 𝑇 is in degrees Celsius (◦C). While there are better approximations that relate the speed of sound to both temperature and air pressure [32], we use Eq. (1) as it is accurate enough for our system. We observe that the speed of sound increases by around 0.2% when the air temperature raises by one degree Celsius at room temperature. As an example, for two devices that are separated by a distance of 60 𝑐𝑚, the ToF measurement will decrease by a small amount of 3.02 𝜇𝑠 based on Eq. (1). Under the widely supported sampling rate of 48 𝑘𝐻𝑧 for sound playing/recording, the interval between consecutive samples is 20.8𝜇𝑠, which is far greater than the small change in ToF. Therefore, traditional correlation-based ranging schemes cannot reliably detect such small changes in ToF, which is less than the sampling interval. To this end, we use an OFDM modulated signal to capture both the coarse-grained cross-correlation measure and the fine-grained phase measurement to detect microsecond-level changes in ToF. Phase-based ToF measurement provides high-resolution and reliable ToF results. The phase change for a specific path 𝑝, 𝜙𝑝 , is related to the speed of sound by 𝜙𝑝 = −2𝜋𝑑𝑝 𝑓𝑐/𝑐, where 𝑑𝑝 is the length of the path and 𝑓𝑐 is the carrier frequency of the signal. In the following discussion, we use the carrier frequency of 𝑓𝑐 = 19 𝑘𝐻𝑧 if not specified. For two devices that are separated by a distance of 60 𝑐𝑚, the phase change will decrease by an amount of 0.360 in radian when the temperature raises by one degree at room temperature. Such phase increase can be reliably measured using OFDM signals [33]. However, as phase changes are limited in the range of 0 ∼ 2𝜋, it cannot determine whether the phase changes by 0.5𝜋 or 2.5𝜋. We use coarse-grained cross-correlation results to resolve the ambiguity in phase measurements. As a phase change of 2𝜋 at 19 𝑘𝐻𝑧 carrier is equivalent to 52.6 𝜇𝑠 in ToF, we can use the cross-correlation result that has a resolution of 20.8 𝜇𝑠 to determine how many 2𝜋 the phase has been changed. Therefore, we design an OFDM signal that can measure both the phase and the cross-correlation offset at the same time. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., Vol. 6, No. 3, Article 144. Publication date: September 2022