# Intelligent Transmission Control Scheme for 5G mmWave Networks Employing Hybrid Beamforming
## 4 Proposed Work
### Accurate Channel Estimation for mmWave Systems
#### 4.2.1 Sparse Signal Recovery Using LAMP Network
The following step involves obtaining the angular cascaded channel \(\widetilde{H_{c}}\) from the \(L_{G}\) row-sparse matrix \(H_{row}\), solving a different MMV problem:  
\[\left({H_{row}}^{e}\right)^{T}=A_{2}\widetilde{J}_{c}^{T}+X \tag{17}\]  
where \(X\) represents the leftover noise resulting from the estimation mistake in the initial LAMP network in every column of the matrix \(\widetilde{H_{c}}^{T}\). The outcome is a sparse matrix vector in the \(\left({H_{row}}^{e}\right)^{T}\) space from the shared measurement matrix \(A_{2}\); the rows of this matrix can be reconstructed by a different LAMP network. Just like in the initial phase, we build the second LAMP network using the corresponding measure matrix \(A_{2}\) to simultaneously retrieve the rows of \(\widetilde{H_{c}}\). In the end, the predictable cascaded network \(\widetilde{H_{c}}\) is obtained by converting the angular network to the time domain using the dictionary matrices \(A_{B}\) and \(A_{S}\), following Step 3 in Algorithm 1. The TS-LAMP network proposed eliminates the costly 3D measurement matrix from the joint CS method by breaking down the estimation process. In addition, deep learning can be used to optimize both LAMP networks for improved performance. Nevertheless, because the TS-LAMP network successfully restores all \(AK_{b},~{}BK_{s}\) components of the angular cascaded channel \(\widetilde{H_{c}}\) in the second phase, there is still a high computational complexity when using high grid resolutions \(AK_{b}\) and \(BK_{s}\). Luckily, because of the sparse structure of the angular cascaded channel \(\widetilde{H_{c}}\), the extra LAMP network provides redundancy in rows. In order to reduce computational complexity in the second phase, we can achieve a condensed version of the estimated row-sparse matrix by focusing on the rows of the evaluated row-sparse matrix with higher norms. Algorithm 2 outlines the structure of the RCTs-LAMP network and is an efficient channel estimation algorithm aimed at improving accuracy and lowering computational complexity in mmWave systems, especially in IRS-assisted networks. An adaptive thresholding approach and row compressing are used to improve TS-LAMP. Row norm filtering and soft-thresholding are used to remove noise/weak rows. We propose a method that takes weights from cascaded channel learning and uses them with transfer learning to improve direct channel estimation. This is critical because they are adaptive in the mmWave paths (direct and indirect, or IRS), greatly reduce training time, and improve spectral efficiency. Unlike traditional methods that estimate the whole channel matrix simultaneously, RCTs-LAMP adopts a two-stage process with row compression to achieve efficient computation. In the first stage, a LAMP network estimates the initial row-sparse matrix through soft thresholding to eliminate noise and extract meaningful channel components. A row compression (COMP) process is then used to eliminate low-power rows, keeping only useful data for subsequent processing. In the second phase, another LAMP network further refines the channel estimation, using only the compressed row support to reduce redundancy and enhance accuracy. This selective strategy minimizes the computational load while preserving high estimation accuracy. Through the utilization of deep learning-based parameter optimization, RCTs-LAMP adaptively adjusts thresholding and compression techniques, with a substantial enhancement in training efficiency, spectral purity, and processing speed. This makes it an excellent candidate for low-latency, high-accuracy mmWave communication systems where accurate channel state information (CSI) is essential to ensure network performance, which incorporates a row compression mechanism to generate the row support \(\hat{\Omega}\) for the estimated row-sparse matrix \(H_{row}^{e}\).