# Screen-Based Sports Simulation Using Acoustic Source Localization +
## 5 Experimental Results
### Three-Dimensional Impulsive Acoustic Source Localization  
Our experiments were performed in a room with dimensions of width 5 m \(\times\) length 7 m \(\times\) height 3 m and did not consider the effects of reflection and noises that were not caused by users. Figure 7 shows all input signals from the MEMS microphones array, capturing an impulsive acoustic source (kicking and hitting a ball) for a short period of time (less than 2 ms). As shown in the figure, it is noticeable that the variations of the TDOA from the single impulsive source depends on the position of the microphone. Figure 8 shows the sound pressure level, that is, the decibel sound pressure level (dBSPL), of the selected microphone (microphone 1) in the array. The peak value is approximately 100 dB and the average peak value is approximately 85 dB. Background noises that are slightly less than and equal to the average dBSPL of the estimated impulsive acoustic source were used for the experiments, as shown in Figure 8.  
Figure 6: FPGA-based design of the DSBF processor. Figure 8: Acoustic source input (**top**) and background noise (**bottom**) of microphone 1. Figure 7: The 24-bit converted input signal voltages of 49 channels of MEMS microphones for an impulsive acoustic source generated by kicking a soccer ball. Figure 9 shows the accuracy of the beamforming results with background noises which are ambient white noises caused by users and impulsive acoustic sources such as clapping and footstep sounds. To evaluate the beamforming accuracy, \(BA\), Equation (5) is rewritten as follows:  
\[BA=255\times\left(\frac{DSBF(\theta)-\min[DSBF(\theta)]}{\max[DSBF(\theta)]} \right). \tag{16}\]  
It shows that even in a noisy environment, if the average level of the background sound is smaller than the average value of the ball impact sound, the noise sources do not affect the direction estimation results. Figure 10 shows the estimation results of the proposed 3D acoustic source localization engine for both direction- and position-based methods. The estimated position errors are evaluated by the differences between the position (\(P_{O}\) in Figure 11) of the true impulsive acoustic source generated by kicking a ball and the position (\(P_{D}\) and \(P_{P}\) in Figure 11) estimated by the proposed DSBF engine. For the direction-based DSBF method, the error values get smaller as the distance between the microphone array and the acoustic source becomes larger. This is because \(|\mathbf{r}_{\mathrm{s}}|\) becomes much larger than \(\frac{(d\times M)^{2}}{\lambda}\) when the distance is larger, making the wavefront more planar and resulting in a higher accuracy for our system. The spectrum of the impulsive sound by striking a ball is in the range of 100 Hz to 10 kHz. In our experiment, the right part of Inequality (1) does not exceed 0.9 m since \(d\) is 0.025 m, \(M\) is 7, and \(\lambda\) is 0.034 m, which is the shortest wavelength in the spectrum. Therefore, the accuracy of the estimated position is high when the impulsive sounds are generated 1 m away from the microphone  
Figure 9: The results of proposed beamforming engine with background ambient white noise (**top**) and impulsive sound (bottom): (**a**) Degree of beamforming results under 40 dB background noise, (**b**) degree of beamforming results about 70 dB background noise, and (**c**) degree of beamforming results over 80 dB background noise. Here, X-Z is \(\theta_{xx}\) between the x and z axis, and Y-Z is \(\theta_{yz}\) between the y and z axis as shown in Figure 1.  
array, as shown in Figure 10. However, if the acoustic source is generated too far away from the microphone array, the SNR significantly decreases, and the errors increases. For the position-based method, the errors are estimated using 49 microphones with a given predefined depth plane. Therefore, the errors remain constant until the SNR significantly decreases. Figure 11 shows the results of our system with the generated impulsive acoustic source.