# 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
Note that the recovery of \(H_{row}\) is an MMV problem, where each column of \(H_{row}\) results in a \"single measurement vector (SMV)\". Since all the vectors in \(Y\) result from the common measure matrix \(A_{1}\), we can address MMV concerning Equation (16) using only one LAMP network with concurrent processing. While the measurement matrix \(A\) is in use by using the collaborative CS approach, we can create the initial LAMP system to recover the columns from the equivalent measure matrix \(A_{1}\) of Originate by running all the SMV simultaneously through parallel computation. In \(Y\), the rows of \(H_{row}\) can be concurrently recreated within the original LAMP network. The result from the initial network is referred to as \(H_{row}\); it represents the approximate value of \(H_{row}\). In the next step, the angular cascaded channel \(\overset{\sim}{H_{c}}\) is extracted from the \(L_{G}\) row-sparse matrix \(H_{row}\), addressing a different MMV issue. ```
Input: Overall matrix \(Y\) for measurements
1: Step 1: Give back the calculated row-sparse matrix \(H_{row}\)\({}^{e}\) line from \(Y\) with the \(A_{1}\)-generated LAMP network. 2: Step 2: Bring back the approximate angular cascaded channel \(\overset{\sim}{H_{c}}\) calculated by \(H_{row}\)\({}^{e}\) using the LAMP network built from \(A_{1}\). 3: Step 3: \(H_{c}^{e}=A_{B}\overset{\sim}{H_{c}}\overset{e}{\sim}{A_{S}}\)\({}^{H}\)
4: Provide the predicted combined channel \(H_{c}^{e}\)
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**Algorithm 1**Two-stage LAMP (TS-LAMP) Network. The two-stage learned approximate message passing (TS-LAMP) network is a sophisticated channel estimation technique that aims to increase accuracy while minimizing computational overhead in mmWave communication systems. The conventional cascaded channel estimation techniques tend to have excessive overhead stemming from the mmWave channels' multi-dimensional characteristics, thus causing real-time processing difficulty. To mitigate this, the TS-LAMP network splits the estimation process into two separate steps. The algorithm uses, during the initial step, a Learned Approximate Message Passing (LAMP) network to approximate the row-sparse channel matrix structure and estimate key channel parameters via a soft-thresholding operator to remove noise while retaining salient channel parameters. This leaves only the most important rows of the channel structure that contribute predominantly to the overall structure of the channel, omitting unnecessary calculations. When the row-sparse matrix is produced, it then goes through row compression, and non-essential information is dropped to maximize efficiency. In stage two, there is another LAMP network, which conducts more precise channel estimation but only for the compressed rows determined in stage one, such that accuracy can be maximized without too much computational load. In contrast to traditional methods that try to estimate the whole channel matrix at one time, the two-stage method focuses on important components first, which leads to reduced training overhead, improved convergence, and better estimation accuracy. This method is especially helpful in intelligent reflecting surface (IRS)-aided mmWave networks, where both direct and indirect channels need to be estimated efficiently. Through the utilization of deep learning optimizations, the TS-LAMP network learns optimal thresholding and row selection parameters dynamically, continuing to improve its performance with multiple iterations of training. This approach significantly improves channel clarity, reduces latency, and promotes spectral efficiency, making it an efficient option for next-generation wireless communication systems.