## 5 Simulation Results and Analysis  
For comparison purposes, the CSI matrices dataset generated by COST 2100 [38] used in most DL-based CSI feedback studies is also used in this paper. The dataset contains channel matrices from indoor and outdoor scenarios, working at 5.3 GHz and 300 MHz, respectively. The number of transmitting antennas is set as \(N_{\rm t}=32\) and the number of subcarriers is \(N_{\rm c}=1024\). In the angular-delay domain, \(N_{\rm c}\) reduces to \(N_{\rm a}=32\) after truncation. As mentioned before, we adjust the dimension of TransNet+ \(d_{\rm model}\) to 64 and optimize the number of attention heads \(n_{\rm head}\) to 4. The training, validation, and testing datasets include 100,000, 30,000, and 20,000 matrices, respectively. We perform the accuracy evaluation by normalization mean square error (NMSE) following  
\[\rm{NMSE}=E\Bigg{\{}\frac{\left\|{\bf{H}}_{a}-\hat{{\bf{H}}}_{a}\right\|_{2}^{ 2}}{\left\|{\bf{H}}_{a}\right\|_{2}^{2}}\Bigg{\}} \tag{9}\]  
The model is built on PyTorch 1.12.0 (CUDA 10.2) and trained on a NVIDIA TITAN V GPU. The batch size is set as 200 and the training epoch is set as 1000. The warm-up aided cosine annealing training scheme is used to enable the model to learn higher resolution features. The maximum learning rate during training is \(2\times 10^{-4}\). Table 1 shows the performance of CSI feedback schemes that have used the attention mechanism so far mentioned in [39] compared to the scheme proposed in our work. This makes sense because most networks based on attention mechanisms have achieved good results, especially TransNet achieved SOTA in most scenarios and at most compression rates. The epoch and batch size of these attention-based methods are the same as that of our model. \(\eta\) represents the compression rate. The size of TransNet+ is in the middle compared to the other models, and this is acceptable because the FLOPs are not a hindrance compared to the exceptional CSI recovery accuracy attained by our model. The data marked in bold is the data with the smallest NMSE at each compression rate. As shown in Table 1, TransNet+ obtains the best results at almost every compression ratio. TransNet+ performs better indoors than the model does outdoors. To be specific, NMSE of TransNet+ decreases by 0.74 dB, 0.56 dB, 0.70 dB, 1.49 dB, and 1.91 dB or 15.67%, 12.10%, 14.89%, 29.04%, and 35.58% with \(\eta\) changing from 1/4 to 1/64 compared to TransNet. We observe that TransNet+ improves the performance of TransNet in particular at high compression ratios which is one of TransNet's major limitations. In outdoor scenarios, TransNet+ also makes some progress in NMSE performance at \(\eta=1/4,1/16,1/32\). In the primary experiments of our work, we set the \(n_{\rm head}\) as 4. Table 2 justifies this choice by listing the performance of the model under different \(n_{\rm head}\). The simulation is carried out in indoor scenarios. The epoch is set as 400 since the model tends to stabilize and the NMSE decreases at a noticeably slower rate after 400 epochs. With the result after 400 epochs, we can exclude some undesirable \(n_{\rm head}\). For instance, the convergence property when \(\eta=1/4\) is poor when \(n_{\rm head}\) is 8. When \(\eta\) equals 1/4 or 1/64, the NMSE performance reduces by more than 1 dB when \(n_{\rm head}\) changes from 2 to 4.