# Research on the Robustness of Active Headrest with Virtual Microphones to Human Head Rotation
## 3 Simulations
### System Performance  
The noise reduction performance of a single channel system, whose layout is shown in Figure 3 is discussed firstly. The range of the optimization angle is set as [\(-90^{\circ}\), \(90^{\circ}\)], including the maximum rotation angle in practical scenarios, such as a passenger sleeping in a couchette train. However, in practical applications the range should be set for specific requirements. If designed for all head rotation angles simultaneously, error microphones of the multiple virtual error microphone method need to be evenly distributed over half the \"ear circle\", which is too large in range and results in poor noise reduction performance at each virtual error point. Similarly, the optimal virtual plant model of the transfer response model optimization method is difficult to satisfy for all rotation angles. Then the system performance is optimized against the head rotation in the positive and negative directions separately. The multiple virtual microphone method optimizes two filters for the virtual microphone locations of a quarter of the \"ear circle\" in the positive and negative directions, while the transfer response model optimization designs two virtual plant models corresponding to the two directions. For the latter method, the transfer response model for the nominal position was chosen to be the one with the larger noise reduction of the optimization results in the two directions. For the multiple virtual microphone method, 13 virtual error points are evenly distributed on the \"ear circle\" and the measurement microphone coincides with these virtual error points when the head rotates \(15^{\circ}\)\(\times\)\(i\) (\(i=0\dots\) 6) clockwise and counterclockwise. For transfer response model optimization, the virtual error microphone is placed near the ear as shown in Figure 3 and moves accordingly to the head rotation. It was concluded in the previous section that \(S_{\rm v}\) changes the most with the head rotation, so only the model of \(S_{\rm v}\) was optimized, while the models of \(S_{\rm p}\) and \(G\) were obtained with the head at the nominal position. Figure 7 presents the noise attenuation \(NR\) with respect to the head rotation angle before and after optimization  
changes is significantly reduced compared to the original system, which can lead to a better subjective listening experience. However, multiple virtual signals significantly increase the computational effort of the adaptive algorithm, and the performance robustness to changes in the acoustic transfer paths may be reduced due to the addition of several times more acoustic transfer paths. It has been shown that for the transfer response model optimization method, noise reduction is only 1.7-6.2 dB at rotation angles of \(\pm 30^{\circ}\) and \(\pm 45^{\circ}\) than with multiple virtual microphones, while the optimization performance at most rotation angles is very close to each other, with a difference of less than 1.5 dB. As noise reduction performance is already good at angles of \(\pm 30^{\circ}\) and \(\pm 45^{\circ}\), this difference does not affect the subjective listening experience when the human head is rotated. Therefore, the transfer response model optimization method can be used to improve the robustness against human head rotation. Figure 7 shows that the noise reduction of the optimized single channel system is still less than 10 dB as the head rotates over 60\({}^{\circ}\), and the minimum noise reduction is only 5.5 dB. Increasing the number of secondary sources can improve the noise reduction performance, so a dual-channel system can be adopted [16; 17; 18]. The control performances of the dual-channel system before and after optimization of the transfer response model with the two physical system arrangements in Figure 4 are compared in Figure 8, while the control performances of the single channel system are also given.