## 3 Simulation and Experimental Validation  
### Test Setting  
In this section, experiments are conducted using ANC headphones designed by Goertek (Qingdao, China) to validate the proposed method. The secondary path transfer function test is shown in Figure 3a, using Audio Precision 525 (AP525) (manufactured by Audio Precision Inc., Beaverton, OR, USA) as the measuring device. The ANC test experimental environment is shown in Figure 3b. The experiment is conducted in an anechoic room with a low-frequency cut-off frequency of 80 Hz and free field radius of 1 m. The noise source is generated by a Tannoy's Precision 6 speaker (Tannoy Brand is owned by Music Tribe. Manufactured in Coatbridge, UK), which has an effective frequency response range of 60 Hz to 50 kHz. A B&K's Type 4128C dummy Head and Torso Simulator (HATS) (manufactured in Teknikerbyen 28, Virum, Denmark) is used as the headphone wearing and sound recording device. The headphones are worn on the HATS facing the test speaker, and the distance between the test speaker and the HATS is 0.5 m. The real person ANC test is also conducted, and a microphone is placed at the ear canal to collect the residual noise, as shown in Figure 3c. A controller with the ADAU1777 (manufactured by Analog Devices, Inc., Norwood, MA, USA) as its core component is adopted to implement the feedback controller. The sampling frequency of ADAU1777 is configured to be 768 kHz, and the system latency from ADC to DSP and then to DAC is 4.7 us, which can be ignored. During the secondary path transfer function test, the AP525's left output is connected to the speaker of the headphone, and the right input is connected to the error microphone of the headphone. The left input is directly connected to the right output to offset the delay caused by the device's own ADC and DAC. The secondary path transfer function is tested using the steady-state noise signals. As current commercial ANC headphones use a proximity sensor to detect if the headphones are being worn, this experiment only focuses on the wearing state of headphones. However, the proximity sensor cannot distinguish between squeezed wearing and normal wearing states, so it is necessary to conduct the headphone squeeze scenario test. During the test, the headphones are worn in normal and simulated squeeze state alternatively. In the latter state, the headphones are tightened with a rubber band and the strength of the rubber band is adjusted until the headphone cushion has been squished. In order to increase the samples of secondary path, four real subjects  
Figure 3: (**a**) Test setting for secondary path; (**b**) ANC test environment; (**c**) microphone in the ear of subject for ANC test. and HATS substitute test are conducted under the same experimental conditions. The four subjects each have a head circumference of 52.8 to 59.1 cm. The subjects are two men and two women: one man and woman wear glasses, and the subjects with long hair have their hair pressed when wearing headphones. The parameters of the subjects are shown in Table 2.  
During the test, the headphones are adjusted to fit the wearing state of each subject's (both HATS and human subjects) headphones in the anechoic room for the first round of test, and then the strength of the rubber band is adjusted to make the headphones squished for the second round of test. In each round of test, the headphones are kept still for three times on each subject and the average value is recorded. The test results are shown in Figure 4a,b, displaying the amplitude and phase response of the secondary path transfer function, respectively, under the normal wearing state of the first round. In general, large differences are present in the low frequency range, and the results of male subjects have larger low-frequency amplitude than those of the females, since the male head circumference is larger and the headphones are more easily squeezed and sealed against the head. Air leakage may be created when the headphones press glasses legs or long hair, resulting in low-frequency attenuation.