# Closed-Loop Cognitive-Driven Gain Control of Competing Sounds Using Auditory Attention Decoding
## 2 Methods
### Correlation Coefficient Generation
This can mainly be explained by the fact that the large correlation window provides a larger amount of data from the reconstructed attended envelope and the envelopes of the speech signals compared to the small correlation window. A large discriminability and reliability of the correlation coefficients and the probabilistic attention measures are obviously essential to obtain a large decoding performance. Figure 5: Exemplary correlation coefficients of speaker 1 and speaker 2 and probability of attending to speaker 1 from the open-loop AAD phase when using AAD algorithms employing (**a**) a large correlation window (LW-GLM, LW–SSM) and (**b**) a small correlation window (SW–SSM). For the considered AAD algorithms, Figure 6 depicts the decoding performance for the open-loop and the closed-loop AAD phase. It can be observed that all AAD algorithms yield a median decoding performance that is larger than chance level (50%). For the open-loop AAD phase, the LW-GLM, LW-SSM, and SW-SSM algorithms yield a median decoding performance of 65.0%, 60.5%, and 56.5%, respectively. For the closed-loop AAD phase, the LW-GLM, LW-SSM, and SW-SSM algorithms yield a median decoding performance of 67.7%, 64.2%, and 60.4%, respectively. The larger median decoding performance obtained by the LW-GLM and LW-SSM algorithms is consistent with the probabilistic attention measures in Figure 5, where due to the large correlation window more reliable probabilistic attention measures are obtained compared to the SW-SSM algorithm. A statistical multiple comparison test (Kruskal-Wallis test followed by post-hoc Dunn and [PERSON] test [34]) revealed no significant difference (\(p>0.05\)) in decoding performance between the open-loop and the closed-loop AAD phase nor between the considered AAD algorithms. To further investigate the performance of the proposed AAD algorithms, Figure 7 depicts the delay to detect a cued attention switch for the open-loop and the closed-loop AAD phase. For the open-loop AAD phase, the LW-GLM, LW-SSM, and SW-SSM algorithms yield a median delay of 16.0 s, 7.7 s, and 13.9 s, respectively. For the closed-loop AAD phase, the LW-GLM, LW-SSM, and SW-SSM algorithms yield a median delay of 19.8 s, 11.5 s, and 17.4 s, respectively. A statistical multiple comparison test (Kruskal-Wallis test followed by post-hoc [PERSON] and [PERSON] test) revealed no significant difference (\(p>0.05\)) between the open-loop and the closed-loop AAD phase nor between the considered AAD algorithms. ### Signal-to-Interference Reduction of Adaptive Gain Controller

For the considered AAD algorithms, Figure 8 depicts the SIR improvement for the closed-loop AAD phase. It can be observed that the LW-GLM, LW-SSM, and SW-SSM algorithms yield a median SIR improvement of 1.1 dB, 1.7 dB, and 0.5 dB, respectively. The larger SIR improvement obtained by the LW-GLM and LW-SSM algorithms can be explained by the larger decoding performance compared to the SW-SSM algorithm. The larger decoding performance leads to a larger number of windows during which the attended speaker is correctly amplified and the unattended speaker is correctly attenuated. In addition, it can be observed that the SW-SSM algorithm yields an SIR improvement with a larger variability (\(-\)2.7-3.0 dB) than the LW-GLM algorithm (0.6-2.1 dB) and the LW-SSM algorithm (0.7-3.8 dB). This can be explained by the larger variability of the probabilistic attention measures obtained by the SW-SSM algorithm (see Figure 5). Due to the linear role of the probabilistic attention measure in the AGC for determining the desired

Figure 6: Decoding performance for (**a**) the open-loop AAD phase and (**b**) the closed-loop AAD phase when using the LW–GLM, LW-SSM, and SW–SSM algorithms. The boxplots display the median, the first quartile, the third quartile, the minimum, and the maximum of the decoding performance across participants. The dashed-line represents the upper boundary of the confidence interval corresponding to chance level based on a binomial test at the 5% significance level.