## 2 SNR Definition and Channel Models
By applying discrete Fourier transformation (DFT) to \(y[m]\), the frequency-domain representation of the received signal at OFDM symbol \(n\) and subcarrier \(k\) is given by  
\[Y[n,k]=X[n,k]H[n,k]+W[n,k] \tag{6}\]  
where \(Y[n,k]\), \(X[n,k]\), \(H[n,k]\), and \(W[n,k]\) are transformed results of \(y[m]\), \(x[m]\), \(h[m]\), and \(w[m]\), respectively. In this paper, we assume that perfect side information, such as channel impulse response, signal power, and noise power, is available to the receiver. The transmitted signal power in Figure 1 is calculated as  
\[P_{\text{signal}}=\lim_{M\rightarrow\infty}\frac{1}{2M+1}\sum_{m=-M}^{M}|x[m ]|^{2}. \tag{7}\]  
For finite-length signals, the limiting process is omitted. The transmitter-side SNR can then be computed as the ratio of the transmitted signal power \(P_{\text{signal}}\) to the noise power, as shown in (1), assuming the channel gain is unity. However, since the mentioned channel models are probabilistic, the channel power gain  
\[\sum_{l=0}^{L-1}h_{l}{h_{l}}^{*} \tag{8}\]  
varies from one channel realization to another. Only by averaging over an infinite number of channel realizations can the channel gain be normalized to unity, as per the procedure in (4). In typical simulation scenarios, with a large number of trials (e.g., 50 trials), the averaged channel power gain approaches one. Thus, the SNR is usually calculated under the assumption of a unity channel gain [11; 15; 16]. It has been demonstrated that the resulting experimental BER performance aligns with the analytical predictions well [15; 16]. Since this SNR is calculated based on the ensemble average of the channel gain, it is appropriately referred to as the ensemble-average SNR. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**EPA Model**} & \multicolumn{2}{c}{**EVA Model**} & \multicolumn{2}{c}{**ETU Model**} \\ \hline
**Tap \(l\)** & \(\tau_{l}\) **(ns)** & \(P_{l}\) **(dB)** & \(\tau_{l}\) **(ns)** & \(P_{l}\) **(dB)** & \(\tau_{l}\) **(ns)** & \(P_{l}\) **(dB)** \\ \hline
1 & 0 & 0.0 & 0 & 0.0 & 0 & \(-1.0\) \\
2 & 30 & \(-1.0\) & 30 & \(-1.5\) & 50 & \(-1.0\) \\
3 & 70 & \(-2.0\) & 150 & \(-1.4\) & 120 & \(-1.0\) \\
4 & 90 & \(-3.0\) & 310 & \(-3.6\) & 200 & 0.0 \\
5 & 110 & \(-8.0\) & 370 & \(-0.6\) & 230 & 0.0 \\
6 & 190 & \(-17.2\) & 710 & \(-9.1\) & 500 & 0.0 \\
7 & 410 & \(-20.8\) & 1090 & \(-7.1\) & 1600 & \(-3.0\) \\
8 & N/A & N/A & 1730 & \(-12.0\) & 2300 & \(-5.0\) \\
9 & N/A & N/A & 2510 & \(-16.9\) & 5000 & \(-7.0\) \\ \hline \end{tabular}
\end{table} 
Table 1: Channel profiles. It is also possible to use the individual channel gain of each realization to compute the receiver-side SNR. First, we compute the signal power \(r[m]\) at the receiver side (referring to Figure 1) as:  
\[P_{\rm r}=\frac{1}{|\mathbf{M}|}\sum_{m\in\mathbf{M}}|x[m]\bigotimes h[m]|^{2} \tag{9}\]  
where \(\mathbf{M}\) is the set of sample indexes in a codeword, and \(|\mathbf{M}|\) is its cardinality. The SNR is then computed as the ratio of \(P_{\rm r}\) to the noise power, as shown in (2). Since this SNR is calculated based on a specific channel realization, and typically the codewords are short, we refer to it as short-term SNR. It is important to note that in an experiment, if we aim to generate channel realizations based on a given short-term SNR value and a fixed noise power (and thus a fixed \(P_{\rm r}\)), \(h_{L-1}\) will depend on \(h_{0}\), \(h_{1}\), \(..\), \(h_{L-2}\), which violates the assumption of uncorrelated scattering in the channel model. Additionally, the theoretical BER analysis developed in [15; 16] cannot be directly applied in this case. In terms of user experience, the short-term SNR is a more accurate indicator as it determines the short-term BER at the user's device. A technique known as effective exponential SNR mapping (EESM) [17; 18] has been proposed to convert the instantaneous SNR values on subcarriers to an equivalent SNR in an AWGN environment, from which the packet error rate can be derived.