# Adjustable Structure for Feedback Active Headest System Using the Virtual Microphone Method
## 5 Real-Time Experimental Results and Discussion
### Experiment 2: Varying Head Positions  
In the practical application of active headrest, it is necessary to satisfy the need for a sufficient movable space for the head. Moreover, it is inconvenient to re-estimate any transfer function in some circumstances. To validate the superiority of the proposed headrest structure while taking the above issues into consideration, appropriate comparison experiments were carried out with fixed structure and movable microphone structure. In these two comparative structures, as illustrated in Section 4, the secondary sources were fixed at a horizontal distance of 10 cm from the left and right ears. The dummy head was moved in steps of 3 cm within the \(-6\,\mathrm{cm}\leq x\leq 6\,\mathrm{cm}\) sideways range, as illustrated in Figure 5b. The configuration of the primary source was identical to that described in Section 5.1. All of the required transfer functions were derived from those measured at the initial position and no longer re-estimated. After each head movement, the secondary loudspeakers and monitoring microphones in the proposed structure were adjusted together, keeping their relative distances to the ears constant. For the movable microphone structure, the positions of the monitoring error microphones were adapted to be close to the ears of the dummy head and the fixed headrest structure was not adjusted in any way.  
Figure 7 shows the results of the total SPL attenuation at the ears when the dummy head was moved to different positions with various headrest structures. It could be observed that, when using the same VS method, the SPL reduction performance with the proposed headrest structure was optimal and stable at all positions compared to the other two structures. Moreover, when the proposed structure was utilized, the noise attenuation performances of the AFM and RMM were at the same level. When using the VMM, the performance was generally approximately 4 dB lower than that of the RMM. At the initial position, the performance with the movable microphone structure was slightly inferior to that with the proposed structure. This was because the secondary loudspeaker was farther away from the error microphone, which resulted in an increased delay in the acoustic path; thus, the performance of the feedback controller was degraded [2]. The fixed  
Figure 6: Three-dimensional histograms of the reduction results at the left ear when the secondary loudspeakers were moved at different distances with various VS methods and headrest structures. (**a**) AFM, fixed structure/proposed adjustable structure. (**b**) RMM, fixed structure/proposed adjustable structure. (**c**) Virtual microphone method (VMM), fixed structure/proposed adjustable structure. (**d**) AFM, movable microphone structure. (**e**) RMM, movable microphone structure. (**f**) VMM, movable microphone structure.  
structure performed the worst at the nominal position. The reason for this phenomenon was the long distance between the physical microphone and the target microphone resulting in decreased accuracy of the estimated transfer functions [17]. In particular, utilizing the VMM with the fixed structure corresponded to a significant drop in performance, due to the long distance between the monitoring microphone and target error microphone causing the assumption \(d_{m}(n)=d_{v}(n)\) to be unsatisfied. Considering the effect of head movement, both the fixed structure and movable microphone structure were affected by the transfer function perturbations and the performance of all of the VS methods was degraded. The movable microphone structure mitigated the effects of the perturbations to some extent and performed better than the fixed structure. Therefore, it could be verified that the proposed headrest structure is guaranteed to provide effective and stable performance for practical applications. With the proposed adjustable structure applied, the AFM and RMM performed at the same level and outperformed the VMM when the head moved slightly.