## 6 Performance Evaluation
In both figures, we evaluate various TS designs under a high channel and comparatively weak correlations, specifically, at \(\omega_{\mathrm{H}}=5^{\circ}\) and \(\omega_{\mathrm{H}}=15^{\circ}\), respectively. The analyses of the results demonstrate that the proposed TS method outperforms the existing methods, especially at high SNR values. This performance enhancement is significantly increased when \(N\) is increased, as clearly indicated by the results in Figures 8 and 9. The results indicate that a remarkable improvement in the rate performances is achieved using the proposed pilot sequence. The findings indicate that when the horizontal angle \(\omega_{\mathrm{H}}=5^{\circ}\), the suggested design results in a \(30\,\mathrm{bits/s/Hz}\) rate with a \(7\,\mathrm{dB}\) improvement over existing designs. On the other hand, when the horizontal angle is \(\omega_{\mathrm{H}}=15^{\circ}\), the proposed pilot sequence yields a \(30\,\mathrm{bits/s/Hz}\) \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Number of BS antennas & \(N\) & 128, 256 \\ Number of users & \(K\) & 10 \\ Azimuth angular spread & \(\omega_{\mathrm{H}}\) & \(\{5^{\circ},15^{\circ}\}\) \\ Antenna element separation & \(D_{\mathrm{H}}=D_{\mathrm{V}}=D\) & \(\lambda/2\) \\ Coherence block length & \(\tau_{\mathrm{c}}\) & 100 symbols \\ Training power & \(\rho_{\mathrm{tr}}\) & \(-15\,\mathrm{dB}\) to 20 dB \\ BS height & \(h\) & 30 m \\ Ring radius & \(s\) & 30 m \\ Users distance & \(d_{k}\) & 200 m \\ BS configurations & BS & UPA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The simulated parameters considered. Figure 5: Rate as a function of SNR based on OR model with different spatial channel correlations, i.e., \(\omega_{\rm H}=\{5^{\circ},15^{\circ}\}\), with \(N=256\) and \(\tau_{\rm c}=100\). (a) \(\omega_{\rm H}=5^{\circ}\); (b) \(\omega_{\rm H}=15^{\circ}\)[36, 41]. Figures 10 and 11 show, respectively, plots of the sum rate using Laplacian and OR channel models as a function of a number of BS antenna with CCT \(\tau_{\mathrm{c}}=100\) and SNR = 15 dB. The results demonstrate a significant improvement in the sum rate performance can be achieved with the proposed training sequence design. Overall, the results indicate clearly that our proposed TS design outperforms the state-of-the-art training designs in all the scenarios considered. The physical interpretation of the proposed idea is that each eigenvector of the \(\mathbf{R}_{\mathrm{tot}}\) represents the transmit direction where the users are located, and the associated eigenvalue \(\mathbf{\Lambda}_{\mathrm{tot}}\) indicates the channel gain in that direction. As such, more power should be assigned to the signals transmitted along with the directions with larger channel gains. In particular, at low SNR values, training only a few directions (corresponding to the largest eigenvalues of the \(\mathbf{R}_{\mathrm{tot}}\) is enough to achieve acceptable performance and zero power could be allocated to the weakest eigenvalues. As the SNR values increase, additional directions corresponding to smaller eigenvalues could be included to be trained to improve the channel estimation accuracy. Our proposed method exploits the waterfilling power allocation algorithm and achieves a significant improvement in the rate compared to the existing methods. The results presented in this paper also indicate that a feasible DL pilot sequence for the FDD systems with very limited CCT can be achieved without increasing the system complexity and overhead. The analyses of the results support the main contribution of this work.