## 3 Numerical Results and Discussion
### Channel Estimation Errors  
In order to detect symbols, all detectors require knowledge of the channel information. In the proposed dual-driven MIMO detection algorithm presented in Algorithm 1, the channel matrix \(\overline{\mathbf{H}}\) is crucial prior information. While some MIMO symbol detection methods assume perfect channel estimation with known channel state information (CSI), it is important to acknowledge that channel estimation errors are inevitable in practical \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(N_{\text{t}}\) & 16 \\ \(N_{\text{r}}\) & 64 \\ GS Height & 25 m \\ UAV Height & 1–100 m \\ Carrier Center Frequency & 73 GHz \\ Bandwidth & 100 MHz \\ Subcarrier spacing & 60 kHz \\ FFT/IFFT size & 1024 \\ Modulation & 4 QAM \\ UAV Mobility & 30 km/h \\ Batch Size & 100 \\ Learning Rate & \(1\times 10^{-3}/5\times 10^{-4}/1\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation settings. scenarios. To evaluate the robustness of the proposed dual-driven MIMO detector against channel estimation errors, we include channel estimation errors by adding complex Gaussian noise to the accurate channel matrix. Specifically, we modify the accurate channel matrix \(\mathbf{H}_{k}\) by introducing the estimated channel matrix \(\mathbf{H}_{k}\) as follows:  
\[\mathbf{\hat{H}}_{k}=\mathbf{H}_{k}+\mathbf{n}_{k}^{\mathrm{c}}, \tag{17}\]  
where \(\mathbf{n}_{k}^{\mathrm{c}}\in\mathbb{C}^{N_{t}\times N_{t}}\sim\mathcal{N}_{ \mathbb{C}}(0,\sigma_{\mathrm{c}}^{2}\mathbf{I}_{N_{t}\times N_{t}})\) represents the complex Gaussian noise vector with \(\sigma_{\mathrm{c}}^{2}\) as the noise variance. In our numerical simulations, \(\mathbf{\hat{H}}_{k}\) in (17) will replace \(\mathbf{H}_{k}\) in (1). To quantify the channel estimation error, we utilize the mean squared error (MSE) between \(\mathbf{\hat{H}}_{k}\) and \(\mathbf{H}_{k}\). In our implementation, all data sample combinations in the training dataset are generated under the condition of a signal-to-noise ratio (SNR) of 20 dB and an MSE of \(-30\) dB. ```
0: The received \(\overline{\mathbf{y}}\), the channel matrix \(\overline{\mathbf{H}}\), the noise variance \(\sigma_{\mathbf{n}}^{2}\), the number of iterations T, the number of UAVs \(N_{t}\), and the number of Rx antennas \(N_{t}\). 1:Initialize: Initialize the parameters \(\mathbf{\Theta}_{\mathbf{ON}}\) and \(\mathbf{\Theta}_{\mathbf{NN}}\). According to the distributions \(w_{p,q}^{[l]}\in\mathbb{R}\sim\mathcal{N}_{\mathbb{R}}\left(0,\frac{1}{ \gamma\times 2N_{t}}\right)\) and \(b_{j}^{[l]}\in\mathbb{R}\sim\mathcal{N}_{\mathbb{R}}\left(0,\frac{1}{4\times 1 0^{-8}}\right)\), \(w_{p,q}^{[l]}\) and \(b_{j}^{[l]}\)are generated randomly. \(\gamma_{1}=1\), \(\theta_{1}=1\), \(\phi=1\), and \(\xi_{1}=0\). \(\mathbf{\hat{s}}_{1}=0\) and \(\
u_{0}^{2}=1\). \(\epsilon=1\times 10^{-10}\). 2:for\(t=1,\dots,T\)do
3:\(v_{t}^{2}=\frac{\|\overline{\mathbf{y}}-\mathbf{H}_{k}\|_{2}^{2}-N_{t}\sigma_ {\mathrm{c}}^{2}}{\mathbf{r}(\overline{\mathbf{H}}^{\mathrm{T}})}\);
4:\(v_{t}^{2}=\frac{1}{2}\left(v_{t}^{2}+v_{t-1}^{2}\right)\);
5:\(v_{t}^{2}=\max(v_{t}^{2},\epsilon)\);
6:\(\mathbf{\hat{W}}_{t}=\frac{\overline{\mathbf{H}}^{\mathrm{T}}}{\left( \overline{\mathbf{H}}^{\mathrm{T}}+\frac{\xi_{1}^{2}}{2\tau_{t}^{2}}\right)}\);
7:\(\zeta_{t}=\frac{2N_{t}}{\overline{\mathbf{W}}}\);
8:\(\mathbf{r}_{t}=\widehat{\mathbf{s}}_{t}+\gamma_{t}\zeta_{t}\mathbf{\hat{W}}_{t }(\overline{\mathbf{r}}-\overline{\mathbf{H}}\mathbf{\hat{s}}_{t})\);
9:\(\mathbf{\hat{r}}_{t}=\mathbf{r}_{t}-\mathcal{F}_{\mathbf{NN}}(\mathbf{r}_{t} ;\mathbf{\Theta}_{\mathbf{NN}})\); //data-driven
10:\(\tau_{t}^{2}=v_{t}^{2}\left(\theta_{t}^{2}\zeta_{t}-2\theta_{t}+1\right)\);
11:\(\mathbf{\hat{s}}_{t+1}=\eta_{t}\left(\mathbf{\hat{r}}_{t},\tau_{t}^{2};\phi _{t},\xi_{t}\right)=\phi_{t}(\mathbf{E}[\mathbf{s}\mid\mathbf{\hat{r}}_{t}, \tau_{t}]-\zeta_{t}\mathbf{\hat{r}}_{t})\);
12:endfor
13:Output:\(\mathbf{\hat{s}}_{\mathbf{T}+1}\).