## 2 Materials and Methods
### System Components
#### 2.2.3 Speech Denoising Model  
As an alternative to the RES model, an off-the-shelf, pre-trained speech-denoising deep-learning model [17], which accepts a single input \(e(n)\) and outputs \(\tilde{d}(n)\), was utilized. A speech-denoising model might be considered an alternative to an RES in cases where the residual echo resembles noise more closely than speech. In these cases, the residual echo might be suppressed while preserving the near-end speech. The utilized speech-denoising model was based on the DEMUCS architecture [23]. The model operated in the time domain, and similarly to DCCRN, it employed a convolutional encoder-decoder structure  
Figure 3: Structure of a complex convolution block. The input features map, consisting of real and imaginary parts, was fed to a complex 2-D convolution layer, the outputs of which were fed to a complex 2-D batch normalization layer. A PReLU activation function provided the block’s output.  
and an LSTM between the encoder and the decoder. A single encoder block consisted of two 1-D convolution layers. The activation function of the first convolution layer was the rectified linear unit (ReLU) [24] and the activation function of the second convolution layer was the gated linear unit (GLU) [25]. The output of the encoder block was passed to the next encoder block (or to the LSTM when it was the final encoder block) and to its matching decoder block via a skip connection. A decoder block received both the output of the matching encoder block and the output of the previous decoder block (or the output of the LSTM when it was the first decoder block). The inputs were summed element-wise. The structure of the decoder block mirrored that of the encoder block, except after the first convolution layer, a 1-D transpose convolution layer was employed to upsample the signal. The structure of the encoder and decoder blocks is depicted in Figure 4. The general structure of the speech-denoising model is depicted in Figure 5. Further details regarding the model's architecture can be found in [17].  
As mentioned in Section 1, the speech enhancement field is well-studied, with an abundance of excellent works and a variety of readily-available, pre-trained models trained on large and diverse datasets. With careful fine-tuning, the features learned by such pre-trained models might be effectively utilized for the residual echo suppression task. This might be especially effective when there is only a small amount of data to train a residual echo suppression model. Therefore, a pre-trained model, provided by the authors [17], was employed. The model was pre-trained on the [PERSON] dataset [26] and the INTERSPEECH 2020 deep noise suppression (DNS) challenge dataset [27]. The model was subsequently fine-tuned with the same training data used for training the RES models,  
Figure 4: Structure of the speech-denoising model’s encoder and decoder blocks. Conv. stands for convolution, and Trans. stands for transpose.  
Figure 5: High-level structure of the speech denoising model.  
once with the NSLMS outputs and once with the NLMS outputs. The loss function that was minimized is given in (6).