# 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  
Before delving into the proposed RCTS-LAMP network, we provide a quick indication of the LAMP network for sparse signal recovery. AMP, an iterative thresholding approach, recovers the sparse angular channel directly using the soft-thresholding function, in contrast to the TRICE framework, which requires the calculation of the true three-dimensional occurrences. We are able to recreate each cascaded channel path when the grid points are close to the real spatial frequencies. The AMP method works well for general sparse recovery situations, but its channel estimation performance is limited because the shrinkage parameters and linear transform matrices stay fixed during the rounds. By deeply unfolding the AMP algorithm's iterations into trainable layers, we can improve AMP's performance and adapt it to the cascaded channel estimation problem. While the primary focus of the RCTs-LAMP network is arranged, the complex task of estimating cascaded channels with the direct channel blocked can be expanded to include the simultaneous estimation of both series of channels without changing the network structure. This approach tackles the joint estimation of direct and cascaded channels for IRS-assisted mmWave systems. It applies a two-stage LAMP network that incorporates row compression to save computational complexity with high estimation accuracy. An LAMP network estimates the row-sparse channel matrix in the first stage, discarding noise and choosing significant channel elements. The second stage deals with accurate channel estimation using compressed rows. This method balances estimation precision and computational complexity very well, particularly for mmWave communication systems. The equation for this situation is shown as follows:  
\[X_{c}\approx B_{1}\;\widetilde{H_{c}}+m_{0} \tag{19}\]  
where the angular direct channel \(\widetilde{H_{c}}\) is evaluated using the matrix \(B_{1}=W^{H}B_{d}\;\in\;C^{Q\times K_{B}}\), just like in the row-sparse matrix \(H_{row}\). As a result, using the equivalent measure matrix A1, we may build an LAMP network to accurately estimate the angle of the straight channel \(\widetilde{H_{c}}\). The transmitted channel estimate can be resolved using the RCTs-LAMP network once the direct channel has been estimated, considering the primary channel \(e_{d}\) estimation error. The added memory and training expense caused by the supplementary LAMP structure for straightforward channel estimation, however, might make the networks less feasible for use in real-world IRS-assisted systems of communication. The added memory and training expense caused by the supplementary LAMP networks for straightforward channel calculation, however, might make the networks less feasible for use in real-world IRS-assisted communication systems. The development process and storage requirements for an entirely novel LAMP network may be challenging and redundant, even though two separate LAMP networks for the estimate of \(H_{row}\) and \(\widetilde{H_{c}}\) may improve visualization strength and produce higher estimation performance. Given that the row-sparse matrix \(H_{row}\) and the direction of the straight channel \(\widetilde{H_{c}}\) are both determined by the same equivalent matrix \(B_{1}\), our suggestion is to estimate \(H_{row}\) and \(\widetilde{H_{c}}\) using the first LAMP network in the RCTs-LAMP network. Thus, the knowledge gained from estimating \(H_{row}\) can be used for estimating \(\widetilde{H_{c}}\). To enhance the functionality of the initial LAMP network and improve the RCTs-LAMP network with consideration to the estimation error \(e_{d}\), we suggest a three-step training approach for the RCTs-LAMP network. It is important to remember that the three-step training process applies to the RCTs-LAMP-MMV network as well, as the LAMP-MMV network will transform into the LAMP network if there is only one measurement vector.