# A Novel Link-to-System Mapping Technique Based on Machine Learning for 5G/IoT Wireless Networks
## 3 Methodology for 5G NR Link-to-System Mapping
### Schematic of 5G NR L2S Mapping  
L2S mapping method has two aims to map various SNRs over allocated REs to one averaged SNR as well as to reduce system overload in SLS. The overall procedure of the L2S mapping is shown in Figure 2 where L2S mapping method basically receives raw data of \(\gamma_{1}\), \(\cdots\), \(\gamma_{N_{RE}}\) and \(BLER\) from the LLS and then delivers two mapping parameters of (\(\alpha_{1}\), \(\alpha_{2}\)) and 5G NR AWGN to the SLS. Our L2S mapping is composed of four modules: \(M_{1}\), loading raw data; \(M_{2}\), AWGN curve; \(M_{3}\), Effective SNR (ESM); and \(M_{4}\), exponential ESM (EESM) L2S mapping. The operation and function of each module are explained below. 1. _Module \(M_{1}\):_ _Loading raw data_ \(M_{1}\) module reads stored data on the preliminary phase in Section 3.2. The format of raw data is composed of \(x\) rows and \(y\) columns for each CQI. The value of \(x\) is the number of input \(SNRs\)\(\times\) the number of simulations (\(Sim\)) and the value of \(y\) is \(N_{RE}\)+2. As mentioned in Section 3.1, the number of allocated sub-carriers per sub-frame is \(N_{RE}\). The first column is a given _input SNR_, the last column is \(BLER\), and the rest of columns mean \(\gamma_{1}\), \(\cdots\), \(\gamma_{N_{RE}}\). The data loading is performed for AWGN channel and all fading channels, respectively. _Module \(M_{2}\): AWGN curve_  
\(M_{2}\) module only applies to AWGN channel. It gets AWGN raw data from \(M_{1}\) module and makes AWGN fitting curve for SNR versus BLER in the range of all CQIs. The AWGN fitting curve is generated from the relation of \((\gamma_{1},\cdots,\gamma_{N_{BE}})\) and \(BLER\). Generally, the fitting curve is induced from an exponential function or regression curve of machine learning. 3. _Module \(M_{3}\): Effective SNR_  
\(M_{3}\) module calculates an effective SNR applying \(\alpha_{1}\) and \(\alpha_{2}\) when a UE measures \(\gamma_{1},\cdots,\gamma_{N_{BE}}\), and it is expressed as follows [5; 6]:  
\[\gamma_{\text{eff}}\left(\alpha_{1},\alpha_{2}\right)=-\alpha_{1}\ln\left( \frac{1}{N}\sum_{k=1}^{N}\exp(-\frac{\gamma_{k}}{\alpha_{2}})\right), \tag{8}\]  
where \(\alpha_{1}\) and \(\alpha_{2}\) are determined after optimization in \(M_{4}\). In fact, SLS only measures \(\{\gamma_{1},\gamma_{2},\cdots,\gamma_{N_{NE}}\}\) without decoding. To estimate error for a received TB, SLS calculates an effective SNR from Equation (8) using \(\alpha_{1}\) and \(\alpha_{2}\). The values of \(\alpha_{1}\) and \(\alpha_{2}\) are already reported to SLS through a L2S mapping method. 4. _Module \(M_{4}\): EESM based L2S Mapping_  
\(M_{4}\) module finds optimal mapping parameters of \(\alpha_{1}\) and \(\alpha_{2}\) for a given CQI and a channel type. After performing \(M\) snapshots, we calculate mean square error (MSE) as follows [5; 6]:  
\[\text{MSE}(\alpha_{1},\alpha_{2})=\sum_{i=1}^{M}\Big{[}\log_{10}BLER_{i}-\log _{10}BLER_{R}\left(\gamma_{\text{eff}}^{i}(\alpha_{1},\alpha_{2})\right)\Big{]} ^{2}. \tag{9}\]  
where \(M\) denotes the total number of simulated snapshots and \(BLER_{i}\) denotes the BLER measured from the \(i\)th post-processing SINR values. In addition, \(\gamma_{\text{eff}}^{i}(\alpha_{1},\alpha_{2})\) is calculated by Equation (8) at the \(i\)th snapshot, and \(BLER_{R}\) is the value of BLER on AWGN channel. Furthermore, \(BLER_{R}(x)\) denotes output \(BLER\) corresponding to input \(x\) from AWGN fitting curve. (It is plotted in module \(M_{2}\))  
To find optimal \(\alpha_{1}^{*}\) and \(\alpha_{2}^{*}\), we minimize MSE for the entire range of (\(\alpha_{1}\), \(\alpha_{2}\)) as follows:  
\[(\alpha_{1}^{*},\alpha_{2}^{*})=\underset{(\alpha_{1},\alpha_{2})}{\arg\min} \ \ \text{MSE}(\alpha_{1},\alpha_{2}). \tag{10}\]  
Since the BLERs vs. SNR varies depending on the modulation method, code block size and code rate, we should find \(\alpha_{1}^{*}\) and \(\alpha_{2}^{*}\) for a given condition. Figure 2: Schematic of 55 NR L2S mapping.