# An Accurate Direction Finding Scheme Using Virtual Antenna Array via Smartphones
## 5 Performance Evaluation
### Experiment Design  
The sketch of experiment design is shown in Figure 5a. The distance between the smartphone and the acoustic source is \(L\). \(\phi\) is the azimuth angle, \(\theta\) is the elevation angle of the phone and the loudspeaker and the orientation angle of the acoustic source is \(\beta\), which is shown in Figure 5b.  
After we deploy the common loudspeakers in the indoor environment, we hold the smartphone right in front of our body and start rotating our body clockwise for 360\({}^{\circ}\) with our system on the smartphone running. After the sampling process, we can read the azimuth angle and the elevation angle of the target speaker on the smartphone's screen.  
The main method of evaluating performance of our scheme is to vary \(L\), \(\phi\), \(\theta\) and \(\beta\) by deploying the loudspeakers and smartphones at different positions. The angular velocity of the body rotation has no particular restrictions. However, in most experiments, the experimenter rotates his body naturally and stable, during which the moving velocity of the smartphone can be treated as an approximately  
Figure 5: Experiment design. (**a**) the sketch of experiment design; and (**b**) the orientation angle \(\beta\) of the acoustic source.  
constant one. According to the gyroscope outputs in the experiments, the mean angular velocity of the smartphone is around 1.5 to 2.5 rad/s. We conduct the extensive comparison experiments to verify the influence of inconstant angular velocity to the accuracy of our system. We also conduct a lot of contrast experiments to the VULA direction finding and the VUCA direction finding in the same environment to verify the superiority of VUCA system. We measure \(\phi\) and \(\theta\) 50 times for each circumstance with both VULA system and VUCA system.  
Most of our experiments are conducted in an underground parking lot of a residential community. The devices that we use in the experiments are shown in Figure 6a. The real experiment scenario is shown in Figure 6b. There are several concrete pillars holding the ceiling with 0.8 m across. We conduct our experiments and vary the variables in the experiments as follows:  
1. **Distance \(L\):** We fix the speakers on the pillars and leverage a laser range finder to detect the relative distance between the experimenter and loudspeakers;
2. **Azimuth angle \(\phi\):** We leverage a marker rod, a laser range finder and a protractor to construct a right-angled triangle on the ground. The vertexes of the triangle are the loudspeaker, the experimenter and the marker rod. The hypotenuse is \(L\). Hence, we can vary different azimuth angles \(\phi\) by adjusting the sides of the triangle;
3. **Elevation angle \(\theta\):** As long as we know the distance \(L\), we can set the speakers on different heights of the pillars to vary different elevation angles \(\theta\);
4. **Orientation angle of the loudspeaker \(\beta\):** We put the loudspeakers on the chairs or the cars. We try to keep the loudspeakers upright or lay them down while \(\beta=0^{\circ}\) or \(90^{\circ}\). We also place the loudspeakers while \(\beta=45^{\circ}\) using a protractor and a support.  
In addition, we measure the noise maps of our experiment scenarios by the smartphone (underground parking lot and shopping mall, \(10\times 10\) m\({}^{2}\)) when there are no experimental loudspeakers in the environment. Figure 7a shows that the sound pressure of the underground parking lot is stably around 28 dB SPL (sound pressure level).  
Figure 6: (**a**) experiment devices; (**b**) the underground parking lot; (**c**) the shopping mall.  
Figure 7: (**a**) the noise map of the underground parking lot; and (**b**) the noise map of the shopping mall.