# A Light-Weighted Machine Learning Approach to Channel Estimation for New-Radio Systems
## 5 Simulation Analysis  
### Simulation Environment  
In this paper, the environment for channel estimation is based on the pilot signal generated through the 5G NR Sounding Reference Signal (SRS) [24]. In 5G NR, the OFDM system is almost the same as the OFDM system in LTE [25], so it is possible to follow the system model in Section 2. SRS is generated based on the Low Peak to Average Power Ratio (PAPR) sequence as follows  
\[r_{u,v}^{(\alpha,\beta)}(n)=e^{j\alpha n}r_{u,\
u}(n),\quad 0\leq n\leq M_{sc}^{ RS}, \tag{17}\]  
Figure 6: The structure of the weight quantization algorithm. Figure 7: CDF of weights for the proposed ML. where \(M_{sc}^{RS}=mN_{sc}^{RB}/2^{\delta}\) is the length of the SRS, and \(m\) is the number of resource blocks (RBs) occupied by the SRS. \(N_{sc}^{RB}\) is the number of subcarriers contained in one RB, and \(\delta\) is \(\delta=log_{2}(K_{TC})\) according to transmission comb number \(K_{TC}\in\{2,4,8\}\). The base sequence \(r_{u,v}(n)\) depends on the group number \(u\) and the number of base sequences \(v\), and multiple orthonormal SRS can be generated using different cyclic shift \(\alpha\) even with the same base sequence. For \(M_{\text{ZC}}\geq 3N_{sc}^{RB}\), the base sequence \(r_{u,v}(n)\) (\(0\leq n\leq M_{sc}^{RS}\)) is given by  
\[ \begin{split}& r_{u,v}(n)=x_{q}(n\ modN_{ZC}),\\ & x_{q}(m)=e^{-j\frac{\pi\text{nm}(m+1)}{N_{\text{ZC}}}},\end{split}  \tag{18}\]  
where \(q\) is given by  
\[ \begin{split}& q=\lfloor\bar{q}+1/2\rfloor+v\cdot(-1)^{\lfloor 2 \bar{q}\rfloor},\\ &\bar{q}=N_{\text{ZC}}\cdot(u+1)/31.\end{split}  \tag{19}\]  
The length \(N_{ZC}\) is given by the largest prime number such that \(N_{ZC}<M_{sc}^{RS}\). To evaluate the performance of the proposed ML-based channel estimation in this paper, an algorithm for channel estimation was designed using MATLAB (R2021b)-based simulation [26], and the parameters used in the simulation are shown in Table 3. The correlation matrices of the MMSE method design an ideal MMSE using the actual CFR \(\mathbf{G}\). Parameters required for the proposed ML are shown in Table 4. As an additional technique, ML utilizes an Adam optimizer to quickly reach global optimum points without converging to local optimum points [27]. The structure of the layer in the proposed ML is designed as shown in Table 5. The performance of the ML is verified after the training is completed. In this simulation, the CIR was set in consideration of the AWGN channel with \(L=1\) and the multipath channel with \(L=6\), wherein the power of each component of the CIR is the same and the sum is 1. The trained ML performs weight quantization for the weights in the ML, and quantized weights are stored in memory. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline SRS size \((N)\) & 48 \\ Subcarrier size \((N_{sc})\) & 216 \\ FFT size \((N_{\text{fft}})\) & 256 \\ Tap size \((L)\) & 1, 6 \\ Channel model & Gaussian channel \\ Noise model & Gaussian noise \\ SNR & \([-10:5:20]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The parameters for proposed ML. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of hidden layer & 1 \\ Input layer size \((2N)\) & 96 \\ Hidden layer size \((Q)\) & 32 \\ Output layer size \((2L)\) & 2, 12 \\ Batch size & 8 \\ Learning rate & \(10^{-4}\) \\ Training epochs & 100 \\ Activation function & tanh \\ Optimizer & Adam \\ Loss function & Mean squared error \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The parameters for OFDM system.