# Intelligent Transmission Control Scheme for 5G mmWave Networks Employing Hybrid Beamforming
## 4 Proposed Work
### Accurate Channel Estimation for mmWave Systems
#### 4.2.2 Row-Compressed Two-Stage LAMP (RCTS-LAMP) for Channel Estimation
Therefore, we can utilize the LAMP-MMV for purposes of calculating both \(H_{row}\) and \(\widetilde{H_{c}}\). Yet, for clarity, we provide details on the training process in three stages for the network of RCTs-LAMP. During the initial phase of the training process, we address the issue of cascaded channel estimation when the direct channel is obstructed or accurately determined. To retrieve the cascaded channel \(H_{e}\) the RCTs-LAMP network takes the total received signal Y as input and generates the predicted cascaded channel \(H_{e}^{d}\) using two LAMP networks. Before fine-tuning the tuneable parameters of the two LAMP networks, \(W_{1}=\left\{Q_{2},X_{[2},\alpha_{[2})\right\}_{l=1}^{L}\) and \(W_{2}=\left\{Q_{2},X_{[2},\alpha_{[2})\right\}_{l=1}^{L}\), we initialize \(W_{1}\) and \(W_{2}\) as \(Q_{l,1}=X_{l,1}^{H}=A_{1},\;Q_{l,2}=X_{l,2}^{H}=A_{2}\) and \(\alpha_{i,1}=\alpha_{i,2}=constant\) as the original AMP procedure, which provides an efficient starting point guaranteed by performance. The normalized mean square error (NMSE)loss of \(H_{e}\), which is defined as follows, can then be minimized by optimizing the tuneable parameters \(W_{1}\) and \(W_{2}\) through end-to-end training:  
\[L_{CC}=\frac{1}{u_{CC}}{\sum_{u=1}^{u_{CC}}}\left\{\frac{\left\|H_{C}^{(u)}-H_{C} ^{e(u)}\right\|^{2}}{\left\|H_{C}^{(u)}\right\|^{2}}\right\} \tag{20}\]  
where \(H_{C}^{(u)}\) represents the predicted cascaded channel for every instance u. Following the initial training phase, the RCTS-LAMP network can be used to expect the cascaded channel in cases where the direct channel is obstructed or has already been accurately estimated. This situation is comparable to the overall system, excluding the estimation error of the direct channel, and we view it as a preliminary stage for the overall system with both direct and cascaded channels present. The two LAMP networks are only appropriate for cascaded channel estimation because, despite the first LAMP network's ability to reconstruct a row-sparse signal \(H_{row}^{e}\) from the measurement of \(A_{1}\), the loss function in the first stage is the NMSE loss of the \(H_{e}\). We use transfer learning for cascaded channel estimation to enable the first LAMP network to be capable of the direct estimation of the channels. Therefore, the sparse \(\widetilde{H_{e}}\) might be recovered using the knowledge obtained from the extraction from the row-sparse signal \(H_{row}^{e}\). The angular direct channel \(\widetilde{H_{e}}^{e}\) is displayed, which is converted to the estimated direct channel \(H_{e}^{d}\) in the time domain \(H_{e}^{d}=A_{B}\widetilde{H_{e}}^{e}\). The data used for training purposes \(D_{DC}=\left\{\left(Z_{e}^{(u)},H_{e}^{d}\right)\right\}_{u=1}{}^{u_{DC}}\) can be generated with \(u_{DC}\) realizations. We use transfer learning to fine-tune the parameter \(W_{1}\) based on the parameters learned from stage 1 to minimize the NMSE loss of \(H_{e}\), which is defined as follows:  
\[L_{DC}=\frac{1}{u_{DC}}{\sum_{u=1}^{u_{DC}}}{\left\{\frac{\left\|H_{d}^{(u)}- H_{d}^{e(u)}\right\|^{2}}{\left\|H_{d}^{(u)}\right\|^{2}}}\right\} \tag{21}\]  
where the predicted direct channel for each realization \(u\) is indicated by the symbol \(H_{d}^{e(u)}\). Following the subsequent training phase, the initial LAMP network may recover \(H_{e}\) high-definition data. We consider the entire system to include direct and indirect connections. The initial and subsequent LAMP networks can reconstruct the sparse signals obtained from matrices \(A_{1}\) and \(A_{2}\), respectively, because the RCTS-LAMP network has progressively acquired the ability to estimate the cascaded and direct channels in the first two training phases, shown as follows:  
\[L_{JO}=\frac{1}{u_{JO}}{\sum_{u=1}^{u_{JO}}}\left\{\frac{\left\|H_{d}^{(u)}- H_{d}^{e(u)}\right\|^{2}}{\left\|H_{d}^{(u)}\right\|^{2}}+\frac{\left\|H_{C}^{ (u)}-H_{C}^{e(u)}\right\|^{2}}{\left\|H_{C}^{(u)}\right\|^{2}}\right\} \tag{22}\]  
where two pairs of input and output for each of the two estimated tasks are included for each instance of u.