## 4 Performance Evaluation
### Simulations
#### 4.2.3 Analysis on Quality of Service Improved by Using _HealLow_ in WSNs  
In this section, we conducted an acoustic-related simulation. We argued that higher resolution brings finer grained results. That is, if a device using _HealLow_ can process the same acoustic signal with larger FFT indices, the result will be more accurate. First, we assume a smartphone device where the speaker and the microphone is separated 15 cm. After that, we implemented a chirp signal, and detect the chirp peak after cross correlation. Such implementation details are a naive implementation of an acoustic ranging application in [PERSON]'s work [22]. In other words, the sending sensor device offloads the data with 8000 Hz sampling rate. Instead of running FFT with 8000 Hz, the receiving device runs \(N\) times larger FFT, the coefficient of which is denoted as \(\times N\). There are two common methods of acoustic localization, one being a dead reckoning by tracking the velocity of the device using Doppler effect, the other being an exact location estimation using chirp detection. In this section, the target application we use is the latter, because we wanted to show the result that is independent of filtering algorithms that must accompany the former. In a chirp method, the distance between two devices is estimated using the time of arrival of the signals. This means that the accuracy and precision of the time of arrival will decide how accurate the distance is, and hence decides the accuracy of the location estimation. The exact method of localization after distance was obtained was MDS (Multi Dimensional Scaling). Figure 7 shows that the result improves even with the same data input. The result of chirp detection relies heavily on the accuracy and granularity of the peak detection. The peak detection uses cross correlation, which is composed of three FFT operations. The precision of the peak detection improves with higher resolution input, so the result improves as well. This result means that the use of _HealLow_ can improve the quality of applications or services operated in WSNs. _TMote Sky_ (_TMote Sky_ was released in 2005) is the wireless sensor module, and the _Raspberry Pi_ (_Raspberry Pi 1_, _Pi 2_, and _Pi 3_ were released in 2012, 2015, and 2016 respectively) is a series of small single-board computers. According to [PERSON] [44], performances of _TMote Sky_ and _Raspberry Pi 2_ were compared. Similarly, benchmarks available online in [45,46] run code for single precision FFT of size 1024K on _Raspberry Pi 2_, _Raspberry Pi 3_, and _Nexus 7_. In addition, Sysbench compared performances of _Raspberry Pi 1_, _Raspberry Pi 2_, and _Raspberry Pi 3_, which is available online in [47]. Geekbench also compared performances of _Nexus 7_ (_Nexus 7_ was released in 2012) and _Galaxy Nexus_ (_Galaxy Nexus_ was  
Figure 6: Smartphone processing simulation. released in 2011), which is available online in [48]. Based on the above benchmark results, we roughly surmises that _TMote Sky_, _Raspberry Pi 1_, _Raspberry Pi 2_, and _Raspberry Pi 3_ have 0.30%, 35%, 67%, and 88% of computational power compared to _Galaxy Nexus_, respectively. In other words, they can process about \(\times\)0.015, \(\times\)1.75, \(\times\)3.35, and \(\times\)4.40 workloads, respectively, as shown in Figure 7. This means _Raspberry Pi 1_ can only have highly erroneous results while a _TMote Sky_ node cannot provide acoustic capability at all. However, _TMote Sky_ nodes have 250 kbps communication capability. This translates to 125,000 samples per second, allowing _TMote Sky_ nodes to have \(\times\)3 workload capability when using _HeaLow_. Of course, the maximum network throughput is not achieved in practice, but we can still safely expect \(\times\)1 workload processing by using _TMote Sky_ nodes with _HeaLow_. Note that these specifications are only a rough estimation of the computing power of the devices, and not exact.