## 5 Experiments  
In this section, we present experimental results for the prediction of multi-antenna and/or frequency-selective channels. Numerical examples for single-antenna frequency-flat channels for both offline and online learning scenarios can be found in the conference version of this paper [45]. For all the experiments, we compute the normalized mean squared error (NMSE) \(||h_{l+\delta,f}-h_{l+\delta,f}||^{2}/||h_{l+\delta,f}||^{2}\), which is averaged over 100 samples for 200 new frames. To avoid discrepancies between the evaluation measures used during the training and testing phase, we also adopt the NMSE as the training loss function by normalizing the training dataset for the new frame \(f^{\text{new}}\) as (cf. (3))  
\[\mathcal{Z}_{f^{\text{new}}}^{\text{tr}} =\{(x_{i,f^{\text{new}}},y_{i,f^{\text{new}}})\}_{i=1}^{L^{\text{ tr}}}\] \[\equiv\Big{\{}\Big{(}\text{vec}(H_{l,f^{\text{new}}}^{N})/||h_{ l+\delta,f^{\text{new}}}||,h_{l+\delta,f^{\text{new}}}/||h_{l+\delta,f^{\text{ new}}}||\Big{)}\Big{\}}_{l=N}^{L^{\text{tr}}+N-1}, \tag{57}\]  
and similarly redefine the datasets from previous frames \(f=1,\dots,F\) for transfer and meta-training as (cf. (58))  
\[\mathcal{Z}_{f} =\{(x_{i,f},y_{i,f})\}_{i=1}^{L}\] \[\equiv\Big{\{}\Big{(}\text{vec}(H_{l,f^{\text{new}}}^{N})/||h_{l+ \delta,f}||,h_{l+\delta,f}/||h_{l+\delta,f}|\big{|}\Big{)}\Big{\}}_{l=N}^{L+N-1}. \tag{58}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Learning Type** & \(\mathbf{O(\cdot)}\) **for Naive Approach** & \(\mathbf{O(\cdot)}\) **for LSTD-Based Approach** \\ \hline Conventional learning & – & – \\ Transfer learning & \(O(S^{3}N^{3}+S^{2}N^{2}FL)\) & \(O(KI_{\text{LNS}}(FL(S^{3})+S^{2})+N^{3}+S^{3})\) \\ Meta-learning & \(O(F(S^{3}N^{3}+S^{2}N^{2}L\) & \(O(KF_{\text{LPLP}}IA_{\text{LS}}(L(S^{2}N^{2}+S^{2})+N^{3}+S^{3}))\) \\  & \(+S^{2}NL^{\text{tr}}(L^{\text{tr}}+SN)))\) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational complexity analysis during meta-training.  
As summarized in Table 3, we consider a window size \(N=5\) with lag size \(\delta=3\). All of the experimental results follow the 3 GPP 5G standard SCM channel model [46] with variations of the long-term features over frames following Clause 7.6.3.2 (Procedure B) [46], under the Umi-Street Canyon environment, as discussed in Section 2.2. The normalized Doppler frequency \(\rho=\gamma_{d,f}/\gamma_{\text{SRS}}\in[0,1]\) within each frame \(f\), defined as the ratio between the Doppler frequency \(\gamma_{d,f}\) (4) and the frequency of the pilot symbols \(\gamma_{\text{SRS}}\), or sounding reference signal (SRS) [46], is randomly selected in one of the two following ways: (i) for slow-varying environments, it is uniformly drawn in the interval \([0.005,0.05]\); and (ii) for fast-varying environments, it is uniformly distributed in the interval \([0.1,1]\). In the following, we study the impact of (i) the number of antennas \(N_{R}N_{T}\), (ii) the number of channel taps \(W\), (iii) the number of training samples \(L^{\text{new}}\), and (iv) the number of previous frames \(F\), for various prediction schemes: (a) conventional learning, (b) transfer learning, and (c) meta-learning, where each scheme is implemented by using either the naive or the LSTD parametrization. We set \(\lambda=0\), \(\lambda_{1}=0\), and \(\lambda_{2}=0\) for conventional learning [9, 45], whereas \(\lambda=1\), \(\lambda_{1}=1\), and \(\lambda_{2}=1\) for transfer and meta-learning.