# 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
### Preliminary Phase for 5G NR L2S Mapping  
To perform L2S mapping, data of post-processing SINRs corresponding to allocated REs and BLERs is required. The procedure to extract raw data of post-processing SINRs and BLER from LLS is considered as a preliminary phase for L2S mapping. In AWGN environment, methods to extract raw data for L2S mapping are almost the same as the performance evaluation of stand-alone LLS. However, methods to extract raw data for L2S mapping in the fading channel environment are different from existing LLS evaluation methods. The preliminary phase for 5G NR L2S mapping is discussed in this subsection. We consider fading channel models such as CDL or TDL specified in 3 GPP TR 38.900 under downlink. As mentioned in Section 3.1, 4200 symbols are transmitted through 4200 REs for a sub-frame. Whenever one TB is generated every sub-frame, 4200 received SNRs corresponding 4200 REs can be measured on a UE side. Since a wide bandwidth of 5 MHz is used, the channel is varying on the frequency-axis domain but it does not change much on the time-axis. Therefore, we consider the received signal of 300 sub-carriers (i.e., 25 RBs \(\times\) 12 sub-carriers \(\times\) 1 symbol = 300 REs) at the first symbol-time to eliminate redundancy and reduce calculation complexity. The received signal from the \(k\)th sub-carrier (\(1\leq k\leq 300\)) at the first symbol-time in a sub-frame is expressed as follows:  
\[\mathbf{y}_{k}=\mathbf{H}_{k}\mathbf{W}_{k}\mathbf{s}_{k}+\mathbf{n}_{k}, \tag{1}\]  
where \(\mathbf{y}_{k}\in\mathbb{C}^{N_{R}\times 1}\) is a received signal vector on the \(k\)th sub-carrier, \(\mathbf{H}_{k}\in\mathbb{C}^{N_{R}\times N_{T}}\) is the MIMO channel matrix on the \(k\)th RE, \(\mathbf{W}_{k}\in\mathbb{C}^{N_{T}\times N_{T}}\) is the precoder matrix on the \(k\)th sub-carrier, \(\mathbf{s}_{k}\in\mathbb{C}^{N_{T}\times 1}\) is a transmitted symbol vector on the \(k\)th sub-carrier, and \(\mathbf{n}_{k}\sim\mathcal{CN}(0,\sigma^{2}\mathbf{I}_{N_{R}})\) is a Gaussian noise vector on the \(k\)th sub-carrier. \(N_{T}\) denotes the number of transmit antenna and \(N_{R}\) denotes the number of receiver antennas. A receiver filter on the \(k\)th sub-carrier by zero-forcing (ZF) and minimum mean square error (MMSE), \(\mathbf{G}_{k}\), is given as follows:  
\[ \begin{split}\mathbf{G}_{k}&=(\mathbf{H}_{k}^{H} \mathbf{H}_{k})^{-1}\mathbf{H}^{H},\ \ \text{for ZF},\\ \mathbf{G}_{k}&=(\mathbf{H}_{k}^{H}\mathbf{H}_{k}+ \sigma^{2}\mathbf{I}_{N_{R}})^{-1}\mathbf{H}_{k}^{H},\ \ \text{for MMSE},\end{split}  \tag{2}\]  
where \(\mathbf{G}_{k}\in\mathbb{C}^{N_{L}\times N_{R}}\) denotes a receiver filter matrix, and \(N_{L}\) denotes the number of spatial transmission layers. The estimated received symbol vector on the \(k\)th sub-carrier by a receiver filter, \(\mathbf{x}_{k}\), is expressed as follows:  
\[\mathbf{x}_{k}=\mathbf{G}_{k}\mathbf{y}_{k}=\mathbf{G}_{k}\mathbf{H}_{k} \mathbf{W}_{k}\mathbf{s}_{k}+\mathbf{G}_{k}\mathbf{n}_{k}, \tag{3}\]  
where \(\mathbf{x}_{k}\in\mathbb{C}^{N_{L}\times 1}\). Post-processing SINR of the \(k\)th sub-carrier at the \(m\)th layer is calculated as follows:  
\[ \begin{split} SINR_{k}(m)=\frac{\mid\left[\mathbf{G}_{k}\mathbf{ H}_{k}\mathbf{W}_{k}\right]_{(m,m)}\mid^{2}}{\sum\limits_{i=1,j\
eq m}^{N_{ l}}\mid\left[\mathbf{G}_{k}\mathbf{H}_{k}\mathbf{W}_{k}\right]_{(m,j)}\mid^{2} +\sigma^{2}\sum\limits_{i=1}^{N_{R}}\mid\left[\mathbf{G}_{k}\right]_{(m,i)} \mid^{2}}\end{split}  \tag{4}\]  
where \(\left[\cdot\right]_{(m,i)}\) is a signal in row \(m\) and column \(i\) of matrix. The numerator term is the desired signal at the \(m\)th layer, whereas the first term of denominator is the sum of the inter-stream interference signals and the second term is the filtered noise. Since each layer is independent and identically distributed, in the case of a large number of simulation, it does not matter to collect raw data from how many layers or which layer. For simplicity of experiment, raw data of post-processing SINRs and BLER is collected at the firstlayer.