# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 2 System Model  
### Satellite Network Description  
A typical radio access network (RAN) supports a set of MODCODs spectral efficiencies \(M=\{M_{1},M_{2},\ldots,M_{\rm K}\}\), each associated with monotonously increasing function \(T:M\rightarrow\mathbb{R}\), where \(T(M_{i})\) represents minimal SNR value needed to operate in the MODCOD \(M_{i}\), also called the threshold. If we denote the instantaneous SNR in the channel by \(\gamma\) then the _optimal MODCOD_ is the greatest element in a set \(S_{\gamma}\subseteq M,\ S_{\gamma}=\{M_{i}|T(M_{i})\leq\gamma\}\), i.e., supremum of \(S_{\gamma}\) denoted as \(\sup(S_{\gamma})\). In a special case, when \(S_{\gamma}=\varnothing\), the lowest spectral efficiency \(M_{1}\) will be used for transmission.  
Let us enumerate all of the total \(N\) RANs that the end-user can use to establish communication by a set \(I=\{1,2,\ldots,N\}\). At a time interval \((t_{j-1}t_{j}]\), the end-user measures instantaneous SNRs for all the currently available RANs, i.e., RANs from a set \(I_{j}\in I\). The principle of forming the \(I_{j}\) set is discussed later. The measured values form a set, \(\Gamma_{j}=\{\hat{\gamma}_{j,i}|i\in I_{j}\}\), where \(\gamma_{j,i}\) represents measured SNR in [dB] of the \(i\)-th RAN during time interval \((t_{j-1}t_{j}]\). Then, a prediction function \(f:\mathbb{R}^{3}\to M\) is executed, which for all the available RANs produces the MODCODs that will potentially be used until the next SNR measurements are completed, i.e., in the time interval \((t_{j}t_{j+1}]\). The goal of the function \(f()\) is to make predictions regarding the optimal MODCOD based on the current and previous SNR measurements. Let \(S\subseteq M\) be a set of MODCOD efficiencies formed in the following way  
\[P=\big{\{}M_{m}\big{|}g\big{(}\hat{\gamma}_{j,i},\hat{\gamma}_{j-1,i},\hat{ \gamma}_{j-2,i}\big{)}\geq T(M_{m})\big{\}}, \tag{1}\]  
where \(\gamma_{j,i}\in\Gamma_{j}\), while \(g:\mathbb{R}^{3}\rightarrow\mathbb{R}^{+}\) produces a prediction of channel state information (i.e., SNR value). Thus we have  
\[f\big{(}\hat{\gamma}_{j,i},\hat{\gamma}_{j-1,i},\hat{\gamma}_{j-2,i}\big{)}= \sup(P). \tag{2}\]  
The end-user simply chooses the RAN that will produce the MODCOD with the highest spectral efficiency, i.e.,  
\[f\big{(}\hat{\gamma}_{j,n_{j}},\hat{\gamma}_{j-1,n_{j}},\hat{\gamma}_{j-2,n_{ j}}\big{)}\geq f\big{(}\hat{\gamma}_{j,i},\hat{\gamma}_{j-1,i},\hat{ \gamma}_{j-2,i}\big{)},\ \forall i\in I_{j}. \tag{3}\]  
In the case where there are multiple RANs that achieve maximal efficiency, and the previously used RAN is among them, the end-user does not perform a handover. Otherwise, the least-used RAN in the current time window is selected in order to reduce the possibility that the selected RAN leaves a set of available RANs. If \(n_{j}\
eq n_{j-1}\), the handover procedure is triggered, and the information of the preferred RAN is sent to the network core via reverse link.  
In our previous work [29], we optimized the threshold margin; however, our further findings revealed that the prediction of SNR could be directly made by state-of-the-art machine learning models, as discussed in the subsequent section.