# Instantaneous Beam Prediction Scheme against Link Blockage in mmWave Communications
## 3 System Model
### Blockage Model  
Blockage occurs when obstacles of different dimensions are present in the established direct link between the MS and BS that use the beamforming and combining vectors that \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Variable** \\ \hline \(f_{\alpha}\) & Carrier frequency \\ \(\phi_{n}\) & The \(n\)-th antenna angular position \\ \(\varphi_{t}^{j}\) & Principal radiation at MS affiliated with \(c_{i}^{t}\) vector at (\(t\)) th time step \\ \(G_{\text{MS}}\) & Array gains at the MS \\ \(G_{\text{BS}}\) & Array gains at the BS \\ \(g_{n}\) & Gain for one antenna \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._resulted in the highest signal level. Now these beams are blocked, and the channel gain is changed accordingly in the form of an increased path loss. This is modeled as [31],  
\[\Gamma_{bl}=\mathbb{I}[\mathrm{p}\left(d\right)]\ \Gamma_{\mathrm{LoS}}(d)+ \mathbb{I}[1-\mathrm{p}\left(d\right)]\ \Gamma_{\mathrm{NLoS}}(d), \tag{5}\]  
where the symbol \(\mathbb{I}\) represents an indicator function for status of the link (e.g., LoS or NLoS). Namely, if blockage occurs then \(\mathbb{I}(x)=1\)_iff_\(x=1\), whereas \(\mathbb{I}(x)=0\) in the absence of blockage effects. Moreover, \(\Gamma_{\mathrm{LoS}}(d)\) and \(\Gamma_{\mathrm{NLoS}}(d)\) symbolize LoS and NLoS path loss parameters, respectively, and are calculated as [32],  
\[\Gamma_{\mathrm{LoS}}(d)=10\log_{10}(\ d_{\mathit{nf}})+10\ g_{\mathrm{LoS}} \log_{10}\left(d\right),\ for\ \mathrm{LoS}, \tag{6}\]  
\[\Gamma_{\mathrm{NLoS}}(d)=10\log_{10}(\ d_{\mathit{nf}})+10\ g_{\mathrm{NLoS}} \log_{10}\left(d\right),\ for\ \mathrm{NLoS}. \tag{7}\]  
Here, variable \(d\) denotes the separation distance between BS and MS, whereas variable \(d_{\mathit{nf}}\) is the reference distance. Additionally, the symbols \(g_{\mathrm{LoS}}\) and \(g_{\mathrm{NLoS}}\) account for the path loss exponent (PLE) for the different link status (LoS and NLoS, respectively) In addition, variables \(\mathrm{p}\left(d\right)\) and (\(1-\mathrm{p}\left(d\right)\)) represent LoS and NLoS probabilities at a separation distance \(d\). This probability is calculated as \(\mathrm{p}\left(d\right)=exp(-\rho d)\), where \(\rho\) denotes the blockage parameter for objects of varying dimensions. See Table 4 for the list of notations for the channel models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Variable** \\ \hline \(P_{\mathrm{nr}}\) & Transmitted power level \\ H & mmWave channel block \\ \(z\) & Control or data signal \\ \(w\) & Additive white Gaussian noise \\ \(\sigma_{w}^{2}\) & Noise variance \\ \(\Gamma_{bl}\) & Blockage path loss \\ \(h_{I}\) & Channel gain from path \(l\) \\ \(L\) & Total paths (rays) \\ \(K\) & Clusters \\ \(\zeta\) & Power ratio between first arriving LoS ray and subsequent rays \\ \(\theta_{\mathrm{MS}}\) & Azimuth angle at MS \\ \(\phi_{\mathrm{MS}}\) & Elevational MS \\ \(\mathbb{I}\) & Indicator function \\ \(\Gamma_{\mathrm{LoS}}(d)\) & LoS path loss parameter \\ \(\Gamma_{\mathrm{NLoS}}(d)\) & NLoS path loss parameter \\ \(d\) & Separation distance between the BS and MS \\ \(d_{\mathit{ref}}\) & Reference distance \\ \(g_{\mathrm{LoS}}\) & Path loss exponent for LoS link status \\ \(g_{\mathrm{NLoS}}\) & Path loss exponent for NLoS link status \\ \(\mathrm{p}(d)\) & LoS probability at distance \(d\) \\ \(1-\mathrm{p}(d)\) & NLoS probability at distance \(d\) \\ \(\rho\) & Blockage parameter for objects of varying dimensions \\ \(\left(c_{i}^{l}\right)_{\mathit{bst}}\) & Beam index at MS that yields highest signal at (\(t\))_th_ time step \\ \(\left(p_{j}^{l}\right)_{\mathit{bst}}\) & Beam index at BS that yields highest signal at (\(t\))_th_ time step \\ \(y_{\mathrm{MS}}\) & Highest signal at (\(t\))_th_ time step \\ \(\delta_{\mathit{inst}}\) & Instantaneous \\ \(\Omega\) & Loss factor \\ \(\delta_{\mathit{max}}\) & Maximum spectral efficiency \\ \(\Psi\) & Boltzmann constant \\ \(\Gamma_{0}\) & Operating temperature \\ \(b\) & Bandwidth \\ \hline \hline \end{tabular}
\end{table}