# Research on the Robustness of Active Headrest with Virtual Microphones to Human Head Rotation
## 4 Experiments
### Noise Control Performance  
The measured transfer responses in the previous section are used to optimize the models of the virtual plant responses and calculate the noise attenuation before and after optimization. Due to the complex sound field in the room, the calculated noise attenuation curves with the head rotation can vary considerably even for two frequencies with 1 Hz difference. For more general, the noise attenuation is evaluated in 1/3 octave bandwidth, where the sound energy for each 1/3 octave is counted from that of five uniformly distributed sampling frequencies within that bandwidth. Figure 16 presents the noise attenuation curves with head rotation for 1/3 octave with 125 Hz, 250 Hz and 500 Hz as the center frequency before and after optimization. It can be seen that, before optimization, the noise reduction achieves a maximum at the initial position and decreases as head rotates, with the larger the rotation angle, the less the noise reduction. After optimization, the noise reduction variation curve flattens out relatively, i.e., the noise reduction at larger rotation angles increases while that near the initial position decreases. In addition, the system performance with single virtual microphone is also presented as a comparison. It can be seen that the results before optimization perform the same as the simulation results, but for the results after optimization, the advantage is more pronounced when using two  
Figure 14: Measured results of the transfer responses for virtual plants and the transfer responses between the virtual microphone locations and the physical microphone locations in the primary field with human head rotation: (**a**) magnitude; (**b**) phase.  
Figure 15: Measured results of the transfer responses for physical plants with human head rotation: (**a**) magnitude; (**b**) phase.  
virtual microphones than when using single virtual microphone. This is because in the more complex primary sound field, the system with two virtual microphones provides four virtual secondary path models for optimization, more than the two path models for the system with a single virtual microphone, so the performance is better due to the increase in degrees of freedom.  
After optimization, the minimum noise reduction increases from \(-0.1\) dB to \(9.0\) dB at \(500\) Hz, which experiences a significant improvement and the performance curves for clockwise and counterclockwise rotation are largely symmetrical. For \(250\) Hz, the optimization results in a better performance improvement for the counterclockwise head rotation case than the clockwise one, mainly due to an unexpected trough in the amplitude response curve of the virtual plant. Thus, the minimum noise reduction increases from \(-1.2\) dB to \(6.0\) dB for clockwise head rotation, with an improvement of \(7.2\) dB; however, for counterclockwise head rotation the improvement is from \(-0.9\) dB to \(11.4\) dB with an increase of \(12.3\) dB. As at \(250\) Hz, the optimization results in better noise reduction at \(125\) Hz with the clockwise head rotation, increasing the minimum noise reduction from \(14.3\) dB to \(21.7\) dB, with an improvement of \(7.4\) dB; however, the minimum noise reduction increases by \(10.7\) dB when the head is turned counterclockwise. In summary, the robustness optimization method increases the minimum noise reduction by at least \(7.2\) dB, and the difference in noise reduction at different head rotation angles becomes smaller.  
Figure 16: Noise attenuation when head rotates at (**a**) \(125\) Hz, (**b**) \(250\) Hz and (**c**) \(500\) Hz.