# A Light-Weighted Machine Learning Approach to Channel Estimation for New-Radio Systems
## 2 System Model  
This paper considers the comb-type pilot arrangement-based OFDM system [19; 20; 21; 22] with \(K_{\text{TC}}\) intervals for subcarriers of length \(N_{sc}\), as shown in Figure 1. Figure 2 shows a typical block \begin{table}
\begin{tabular}{l l} \hline \hline
**Perspective** & **Contents** \\ \hline \multirow{4}{*}{Input data type in ML} & \(\cdot\) Machine learning using received signal [6] \\  & \(\cdot\) Machine learning using estimated channels [7; 8; 9; 10; 11; 12; 13] \\  & \(\cdot\) Machine learning using transmitted and received signals [14] \\  & \(\cdot\) Machine learning using transmitted signal, received signal, and estimated channels [15; 16] \\ \hline \multirow{4}{*}{Design the number of usage symbols according to channel types} & \(\cdot\) ML to estimate instantaneous channels from one symbol [6; 7; 8; 9; 16] \\  & \(\cdot\) ML to estimate the channel for the current symbol using the channel estimated \\  & \(\cdot\) from the previous symbol [10; 11; 14; 15] \\  & \(\cdot\) ML to perform interpolation to estimate the channel of the slot where pilot symbols are \\  & located not only that of the pilot symbol [12; 13] \\ \hline \multirow{2}{*}{Channel estimation by domain types} & Estimation of Channel Impulse Response in time domain [14; 16] \\  & Estimation of Channel Frequency Response in frequency domain [6; 7; 8; 9; 10; 11; 12; 13; 15] \\ \hline \multirow{4}{*}{Complexity and MSE performance} & \(\cdot\) Low complexity and low MSE performance due to the use of simple ML structure \\  & (with or without one hidden layer) [8; 16] \\ \cline{1-1}  & \(\cdot\) High complexity and high MSE performance from leveraging complicated ML structure \\ \cline{1-1}  & (MNN or CNN, LSTM, and so on) [6; 7; 9; 10; 11; 12; 13; 14; 15] \\ \hline \multirow{2}{*}{Our work} & \(\cdot\) Estimation of channel impulse response using received signal in the frequency domain \\ \cline{1-1}  & \(\cdot\) Single slot design for channel estimation with a one-time symbol \\ \cline{1-1}  & \(\cdot\) Low complexity and high MSE performance with the simple ML structure \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A concise comparison of our work with the existing ML-based channel estimations. diagram of the OFDM system with the pilot signal assisted. \(\mathbf{\tilde{S}}=[S_{0},\ \ldots,\ S_{N-1}]^{T}\) is an \(N\times 1\) pilot signal vector known by both transmitters and receivers, and \(\mathbf{\tilde{X}}=[X_{0},\ \ldots,\ X_{N_{\mathrm{sc}}-1}]^{T}\) is an \(N_{\mathrm{sc}}\times 1\) transmission signal vector in a frequency domain where pilot signal \(\mathbf{\tilde{S}}\) is placed at regular intervals in subcarriers, and symbols without pilot signals are set to 0. After pilot insertion, \(\mathbf{\tilde{X}}\) adds the \(N_{\mathrm{zp}}\times 1\) Zero Padding (ZP) vector \(\mathbf{0}_{N_{\mathrm{zp}}}\) to both sides to expand to the \(N_{\mathrm{fft}}\times 1\) vector, and as shown in Equation (1), \(\mathbf{\tilde{X}}\) with ZP added is sent to an \(N_{\mathrm{fft}}\)-point Inverse Fast Fourier Transform (IFFT), which is modulated into \(\mathbf{x}\) in the time domain as  
\[\mathbf{x}=\mathbf{F}_{N_{\mathrm{fft}}}^{-1}[\mathbf{0}_{N_{\mathrm{zp}}},\ \mathbf{\tilde{X}},\ \mathbf{0}_{N_{\mathrm{zp}}}]^{T}, \tag{1}\]  
where \(\mathbf{F}_{N_{\mathrm{fft}}}^{-1}\) is an \(N_{\mathrm{fft}}\)-point IFFT matrix and \(N_{\mathrm{zp}}=\frac{1}{2}(N_{\mathrm{fft}}-N_{\mathrm{sc}})\). The transmission signal \(\mathbf{x}\) places a cyclic-prefix (CP) of length \(N_{\mathrm{cp}}\) at the front of the signal to prevent Inter-Symbol Interference (ISI), and then a \((N_{\mathrm{fft}}+N_{\mathrm{cp}})\times 1\) vector \(\mathbf{x}_{\mathrm{cp}}\) is transmitted to the receiver.