## 4 Experiment Results
With the parameters described above, the feedback controller is designed with both Method 1 and Method 2. For each method, the controller is designed respectively with two different noise enhancement limitations \(\delta\) = 5 dB and \(\delta\) = 3 dB. DE algorithm is used to solve the optimization problems defined in (13) and (14), where the crossover rate Cr, the stepsize F and the popular members NP are set to 1, 0.85 and 100, respectively. The iteration number is set to 10,000. For each case the optimization process with DE algorithm is repeated for 100 times in order for the global minimum. The design results with different \(\delta\) and different methods are shown in Table 1. The corresponding FRs of the controllers are shown in Figure 4. With these results, the expected NR performances could be calculated and are shown in Figure 5. Finally, the filter coefficients are download into ADAU1772 through SigmaStudio and the actual NR performances are tested by experiments, which is shown in Figure 6. All the NR performances shown in Figures 5 and 6 are represented by the magnitude responses of the corresponding sensitivity functions defined in (1) and (3). When the feedback controller is designed with Method 1, the performance is only evaluated at the feedback microphone position just as previous works. It could be observed from Figure 5a,b that the noise enhancements are nearly flat at high frequencies without exceeding its limitations, which generally indicates that almost the optimal NR performances could be expected. Meanwhile, a better NR performance could be obtained with a loose limitation on the noise enhancement. At the dummy head ear position, the NR performances below 1 kHz are in accordance with the ones at the feedback microphone position, which is a natural result since the FRs of the primary and secondary paths are almost the same. However, large noise enhancements appear within the frequency band [2 kHz, 6 kHz], which result from large FR mismatches shown in Figure 3. This indicates that the FR mismatches of both the primary path and the secondary path should be addressed in the controller design stage. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  
Figure 4: The FRs of designed controllers with different methods: the (**a**) magnitude and (**b**) phase responses with a 5 dB noise enhancement limitation, the (**c**) magnitude and (**d**) phase responses with a 3 dB noise enhancement limitation. Figure 3:0 Simulation results of the NR performances: (**a**) \(\delta\) = 5 dB and (**b**) \(\delta\) = 3 dB with Method 1, (**c**) \(\delta\) = 5 dB and (**d**) \(\delta\) = 3 dB with Method 2. With Method 2, such large noise enhancements could be avoided, as shown in Figure 5c,d, since the FR mismatches are considered and the NR performance at the dummy ear position is directly under evaluation. This results from the reduced magnitude and the shifted phase of the controller at frequencies where the FR mismatch is relatively large, as shown in Figure 3:1 Although the NR performances below 1 kHz are reduced compared with the ones of Method 1, which are also indicated by the reduced magnitude responses of the controllers, the designed results of Method 2 could still be seen as the ones with almost the best comprehensive performances. A reduced NR performance seems to be a necessary compromise for the limitation of noise enhancement at the dummy head ear if large FR mismatches exist. The above results have been confirmed by experiments, which are in high accordance with the simulations, as shown in Figure 3:2