# Deep Learning-Based Acoustic Echo Cancellation for Surround Sound Systems
## 5 Experimental Results and Discussions
### Experiment Settings
Besides, the height of the microphones, loudspeakers and sound sources were all set to 1.2 m.  
The far-end speech was convolved with four RIRs, which are from the same Ambisonic RIRs group as mentioned above, resulting in the four-channel Ambisonic B-format signals. The B-format signals were then decoded to the D-format signals by using the decoding rules as described in [21,24]. The echo signals were generated by convolving the D-format signals with randomly selected RIRs. Finally, the near-end speech was mixed with the echo signals under a signal-to-echo ratio (SER) value randomly selected from \(\{0,5,10,15\}\) dB to get the near-end microphone signals. The SER is evaluated on double-talk scenarios, which is defined as:  
\[\mathrm{SER}=10\mathrm{log}_{10}\Bigg{(}\frac{\sum_{n}s^{2}(n)}{\sum_{l}\sum_ {n}d_{l}^{2}(n)}\Bigg{)}. \tag{7}\]  
As described in [13], white Gaussian noise was also taken into consideration as the microphone internal noise and the signal-to-noise ratio (SNR) was set as 30 dB, which is defined as:  
\[\mathrm{SNR}=10\mathrm{log}_{10}\bigg{(}\frac{\sum_{n}s^{2}(n)}{\sum_{n}v^{2} (n)}\bigg{)}, \tag{8}\]The mean squared error (MSE) between the estimated and true compressed complex spectra of the near-end signal was used as a loss function, and optimized by the Adam algorithm [35]. The learning rate was set to \(3\times 10^{-4}\). The mini-batch size was set to 16 at the utterance level and each batch took about 1.20 s in the training stage. The GCRN network was trained for 50 epochs. All training samples were padded with zeros to have the same number of time frames as the longest sample within a mini-batch and cross-validation was used to select the best model and prevent overfitting. In single-talk scenarios, the AEC performance is evaluated in terms of ERLE and it is defined as:  
\[\text{ERLE}=10\text{log}_{10}\bigg{(}\frac{\sum_{n}y^{2}(n)}{\sum_{n}\delta^{2 }(n)}\bigg{)}. \tag{9}\]  
In double-talk scenarios, PESQ is used to evaluate the AEC performances of different algorithms. PESQ is a widely used speech quality metric which ranges from\(-0.5\) to \(4.5\), and highly correlates with subjective scores [20]. For both the ERLE and PESQ metrics, a higher score indicates better performance. The least mean square (LMS) algorithm is one of the most widely used adaptation methods in the echo path identification. Among LMS algorithms, the partitioned block frequency domain LMS (PBFDLMS) algorithm is popular for its lower computational complexity than the time-domain LMS algorithms and its lower latency than frequency-domain LMS algorithms, especially when the acoustic echo path is relatively long [14]. To validate the proposed algorithm, the PBFDLMS algorithm with Wiener post-filtering was chosen as the baseline. The PBFDLMS algorithm should be combined with the double-tale detector (DTD) algorithm [36; 37]. In order to reduce the performance degradation caused by the DTD method, an ideal DTD was assumed for the PBFDLMS algorithm. The test mixtures were generated in the same way, which were not used in the training procedure.