# Intelligent Transmission Control Scheme for 5G mmWave Networks Employing Hybrid Beamforming
## 4 Proposed Work
### Optimized Beam Training for Adaptive mmWave Communication
#### 4.4.1 Digital and Analog Hybrid Beam Training (DAH-BT) Approach
This phase-one OMP-based DAH-BT greatly minimizes the search space, improves precision, and optimizes beam alignment with low computational complexity, thus making it suitable for dynamic and high-mobility mmWave networks. DAH-BT-LSTM combines the long-term and short-term pattern analysis of signal patterns to maximize beam training to minimize noise and the necessity of recalibration. DAH-BT-LSTM employs a two-phase beam training technique with OMP for AoA and AoD estimation. LSTM modifies beam direction from previous and current beam training signals, which results in better accuracy and lowered overhead in training. ```
Step 1: The hybrid module transmits \(\mathrm{x}^{\mathrm{DL}}\) in all directions through the BS. Step 2: This inexpensive DBF module provides the MS with omnidirectional reception of the signal \(\mathrm{r}=\frac{\mathrm{DL}}{\mathrm{ADC}}\,\eta\,\frac{\sqrt{\mathrm{N}_{t}}}{ \mathrm{Gt}}\,\mathrm{X}_{\mathrm{ms}}\underline{\mathrm{\Delta}}_{\mathrm{r}}\, \mathrm{h}_{\mathrm{v}}^{\mathrm{DL}}+\mathrm{n}_{\mathrm{e}}^{\mathrm{DL}}\). Step 3: Estimating the AoAs using OMP. Input: \(\mathrm{r}=\frac{\mathrm{DL}}{\mathrm{ADC}}\), \(\Phi=\eta\frac{\sqrt{\mathrm{N}_{t}}}{\mathrm{Gt}}\,\mathrm{X}_{\mathrm{ms}}\)\(\underline{\mathrm{\Delta}}_{\mathrm{r}}\) and stopping criterion Establishing over: \(\mathrm{r}^{0}=\mathrm{r}=\frac{\mathrm{DL}}{\mathrm{ADC}},\ \mathrm{x}^{0}=0,\ \mathrm{ \Lambda}^{0}=\mathrm{\mathcal{O}},\mathrm{t}=0\)
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Match: \(\mathrm{V}^{t}=\Phi^{\mathrm{T}}\mathrm{r}^{t}\)  
Identify: \(\mathrm{\Lambda}^{t+1}\)= \(\mathrm{\Lambda}^{t}\,\bigcup\left\{\mathrm{argmax}_{\mathrm{j}}\Big{|} \mathrm{u}^{t}(\mathrm{j})\Big{|}\right\}\) (where \(\mathrm{u}^{t}(\mathrm{j})\) is the \(\mathrm{j}\)-th entry of \(\mathrm{u}^{t}(\mathrm{j})\) is the \(\mathrm{j}\)-th entry of \(\mathrm{V}^{t}\)). Update: \(\mathrm{X}^{t+1}=\mathrm{argmin}\left\|\mathrm{r}-\Phi\underline{\mathrm{ \Delta}}\right\|_{2}\) \(Z:\mathrm{supp}(z)\subseteq\mathrm{\Lambda}^{t}\) \(\mathrm{r}^{t+1}=\mathrm{r}-\Phi\,\mathrm{X}^{t+1}\) \(\mathrm{t}=\mathrm{t}+1\) conclude While Results: \(\hat{\mathrm{h}}_{\mathrm{v}}^{\mathrm{DL}}\ =\ \mathrm{x}^{t}\) Step 4: Identify the greatest \(\mathrm{L}_{\mathrm{est}}\) values in \(\hat{\mathrm{h}}_{\mathrm{v}}^{\mathrm{DL}}\), compute the matching angles by Equation (28), and note them in the designated SAoA. ```  
**Algorithm 3**The Initial Stage of OMP-Based DAH-BT. In summary, Algorithm 4 summarizes the beam training phase 2 procedures and emphasizes the estimation of angles of departure (AoD) for beam alignment maximization in mmWave communication. Once the angles of departure (AoAs) have been determined, the AoDs should be estimated. Procedures: MS sends out directed beams. DBF is how BS obtains it. The strongest AoDs are found using OMP. Ideal transmit-receive beam pairs should be formed by combining with earlier AoAs. This is beneficial because it minimizes the computation required to finish the hybrid beamforming beam alignment procedure. Following the AoA estimations of the initial phase, the hybrid beamforming module now sends directional signals sequentially from the mobile station (MS), whereas the base station (BS) receives them omnidirectionly via a cost-effective digital beamforming (DBF) circuit. The OMP algorithm is then utilized to retrieve the most dominant AoD values by iteratively choosing the maximum-energy transmission angles. Estimated AoDs are stored in addition to the already established AoAs, and an optimized beam pair choice for increased transmission efficiency is created. This OMP-based DAH-BT in the second phase continues to reduce beam training overhead, improves beam alignment, and lessens interference; hence, it is optimized for high-speed and adaptive mmWave networks. We ultimately determine which beam pairs, transmission and being received, are documented in \(S_{AoD}\) and \(S_{AoD}\), respectively, following phases 1 and 2 of the DAH-BT.