# A Light-Weighted Machine Learning Approach to Channel Estimation for New-Radio Systems
## 4 Proposed ML Method  
### Network Architecture  
#### 4.1.1 Structure  
To compensate for the shortcomings of LS, MMSE, and existing ML-based channel estimation, we propose a CIR estimation that is closer to the actual channel than the LS method and requires no prior information, unlike the MMSE method. Figure 4 shows the structure of the proposed ML-based channel estimation, which includes a DNN architecture. To propose the low-complexity ML, it is designed with only one hidden layer and estimates a CIR shorter than CFR.  
The receiver receives transmission signals coming through channels in various directions. Therefore, the reception signal can be expressed as the convolution product of the channel impulse response and the transmission signal, and the first part of the reception signal is affected by the reception signal of the previous symbol, resulting in Inter-Symbol Interference. Accordingly, the communication system prevents Inter-Symbol Interference by adding a CP in front of the transmission signal. In general, since the length of the channel impulse response is smaller than the CP, ISI prevention is possible. Long pilot signals are transmitted for more accurate channel estimation, but too-long pilot signals generate overhead. The pilot signal has an appropriate length and thus occurs longer than  
Figure 4: The structure of the proposed ML-based channel estimator.  
the length of the channel impulse response. Consequently, the \(L\)-length CIR output from the proposed ML is shorter than the \(N\)-length CFR output from the existing ML, and a simpler ML can be designed.  
It is necessary to distinguish between real and imaginary parts of the complex signal because the current ML platform only allows real numbers. Therefore, the input data of the ML for the \(d\)-th data \(\mathbf{X}_{\text{in},d}\) are given as follows  
\[\mathbf{X}_{\text{in},d}=\begin{bmatrix}Re(Z_{d}(0))\\ Im(Z_{d}(0))\\ \vdots\\ Re(Z_{d}(N-1))\\ Im(Z_{d}(N-1))\\ \end{bmatrix}. \tag{12}\]  
The number of nodes in the output layer is \(2L\) according to the length of CIR \(L\), and the output value of the ML for the \(d\)-th data \(\mathbf{Y}_{\text{out},d}\) is given as follows  
\[\mathbf{Y}_{\text{out},d}=\begin{bmatrix}Re(\hat{h}_{d}(0))\\ Im(\hat{h}_{d}(0))\\ \vdots\\ Re(\hat{h}_{d}(l))\\ Im(\hat{h}_{d}(l))\\ \vdots\\ Re(\hat{h}_{d}(L-1))\\ Im(\hat{h}_{d}(L-1))\\ \end{bmatrix}, \tag{13}\]  
where \(\hat{h}_{d}(l)(l=0,\dots,L)\) is the output of the neural network for the \(l\)-th tap of the \(d\)-th data. The number of nodes in the hidden layer is less than the number of pilot signals \(N\) and the largest is the power of \(2\), and it is represented by \(Q=2^{\lfloor\log_{2}(N)\rfloor}\). Since the objective of ML-based estimation is to minimize the MSE between the estimated channel and the actual channel, the loss function \(\mathcal{L}\) used in the training step is defined as follows  
\[\mathcal{L}(\mathcal{W},\mathcal{B})=\frac{1}{DL}\sum_{d=1}^{D}\sum_{l=0}^{L-1 }\|h_{d}(l)-\hat{h}_{d}(l)\|^{2}, \tag{14}\]  
where \(D\) is the number of data used for training, and \(h_{d}(l)\) is the actual channel value associated with \(\hat{h}_{d}(l)\). From a set of initial values, the weights and biases are updated by minimizing the loss function shown in Equation (13) with the forward and backward propagation.  
The proposed method estimates the CIR, so the CIR is converted into the CFR to derive the pilot symbol-based CFR \(\hat{\mathbf{G}}_{\text{ML}}\) as follows  
\[\begin{split}\hat{\mathbf{H}}_{\text{ML}}=\mathbf{F}_{N_{\text{ flip}}}\cdot[\hat{\mathbf{h}}_{\text{ML}},\mathbf{0}_{N_{\text{in}}-L}]^{T},\\ \hat{\mathbf{G}}_{\text{ML}}=\hat{\mathbf{H}}_{\text{ML}}(\text{ idx}(\mathbf{S})),\end{split} \tag{15}\]  
where \(\mathbf{0}_{N_{\text{in}}-L}\) is the \((N_{\text{fft}}-L)\times 1\) zero vector, and \(\mathbf{F}_{N_{\text{in}}}\) is the \(N_{\text{fft}}\)-point FFT matrix. \(\text{idx}(\mathbf{S})\) refers to the location where the pilot signal is placed on the subcarrier.