## 5 Simulation Results
### SE Bounds Achieved by Type I Codebook
In general, for low SNR values, it is better to concentrate the energy in a single very directional path to the UE. In this example, the values of \(N_{s}\) that achieve the highest performance averaging over all the SNR range, for the single-panel ULA, UPA, and multi-panel ULA are \(N_{s}=3,N_{s}=1\), and \(N_{s}=2\), respectively. According to these figures, the best performance is obtained with the ULA configuration. The reason for this is that, in this case, the UPA layout has few antennas in each dimension, which does not properly exploit the spatial characteristics of the channel. Figure 4: Average SE vs. SNR for SU-MIMO systems assuming \(N_{t}=8,N_{r}=4\), and different values of \(N_{s}\). The gNB is implemented assuming a single-panel ULA with four DP polarized antenna elements in the horizontal dimension (\(N_{1}=4\) and \(N_{2}=1\)). Figure 5: Average SE vs. SNR for SU-MIMO systems assuming \(N_{t}=8,N_{r}=4\), and different values of \(N_{s}\). The gNB is implemented assuming a single-panel UPA with two DP polarized antenna elements in the horizontal and vertical dimensions (\(N_{1}=2\) and \(N_{2}=2\)). Figure 7 shows the robustness of the 5G-NR precoding matrices in the presence of channel estimation errors. This result is obtained by adding an error matrix \(\mathbf{E}_{j}\in\mathbb{C}^{N_{s}\times N_{t}}\) to the true channel \(\mathbf{H}_{j}\) as \(\mathbf{\hat{H}}_{j}=\mathbf{H}_{j}+\mathbf{E}_{j}\). Each element of \(\mathbf{E}_{j}\) follows a Gaussian distribution with zero mean and variance \(\sigma_{e}^{2}\). The performance loss is evaluated for two different error variances, \(\sigma_{e}^{2}=10^{-3}\) and \(\sigma_{e}^{2}=10^{-2}\), which are common values for channel estimation algorithms. The gNB is configured following the ULA layout used in Figure 4. According to the results of Figure 4, the number of parallel layers is now fixed to \(N_{s}=3\). It can be noted that the channel estimation error affects the 5G-NR precoding performance in the same proportion as the optimal SVD solution. The performance degradation is negligible for \(\sigma_{e}^{2}=10^{-3}\). In the case of \(\sigma_{e}^{2}=10^{-2}\), the performance loss is only noticeable for high values of SNR. This is due to the fact that the effect of noise is more relevant than the channel estimation errors for low SNR. Figure 6: Average SE vs. SNR for SU-MIMO systems assuming \(N_{t}=8,N_{r}=4\), and different values of \(N_{s}\). The gNB is implemented assuming a multi-panel ULA with \(N_{g}=2,N_{1}=2\), and \(N_{2}=1\). Figure 7: Average SE vs. SNR for SU-MIMO systems assuming \(N_{t}=8,N_{r}=4\), and \(N_{s}=3\). The gNB is implemented assuming a single-panel ULA with four DP polarized antenna elements in the horizontal dimension (\(N_{1}=4\) and \(N_{2}=1\)). Figure 8 depicts the average SE for a higher number of transmit antennas given by \(N_{t}=32\) ( i.e., 32 CSI-RS antenna ports). The performance is evaluated for several values of \(N_{s}\). Similar to the previous figures, three types of different antenna configurations are considered, including both single and multi-panel arrays. A single-panel ULA and UPA are considered with \(N_{1}=16,N_{2}=1\), and \(N_{1}=4\), \(N_{2}=4\), respectively. Furthermore, a multi-panel is considered with \(N_{g}=2,N_{1}=8\), and \(N_{2}=1\). This figure shows the SE gain obtained with respect to Figures 4-6 when increasing from 8 to 32 antenna ports. The performance loss due to channel estimation error is also evaluated considering \(\sigma_{e}^{2}=10^{-3}\). Similar to Figure 7, the degradation in SE is only slightly noticeable for SNR values higher than 10 dB. Regarding the overhead between linear and planar arrays, ULA demands lower overhead because the subindex \(i_{12}\) is not reported. For this particular example, the single-panel ULA requires a PMI with a total of 20 bits while single-panel UPA needs 22 bits. It must be pointed out that the multi-panel ULA also needs to report the subindex \(i_{141}\) and hence, 22 bits of overhead are used as in the case of single-panel UPA [25; 39].