# Downlink Training Design for FDD Massive MIMO Systems in the Presence of Colored Noise
## 7 Results and Findings
The results in Figures 3 and 4 show respectively plots of the normalized MSE and the achievable sum rate versus SNR using the one ring channel model, based on ULA BS with different levels of correlations, i.e., with an azimuth angular spread of \(\alpha_{\rm A}=\{5^{\circ},15^{\circ}\}\). In particular, the results in Figures 3 and 4 were obtained with \(d=1/2\), \(\tau=100\) symbols, \(N=128\) and \(K=8\) users. The curves for the normalized MSE are plotted based on Equations (27) and (30), while the curves for the achievable sum rate are plotted based on Equations (4) and (45). The number of pilot sequence lengths are selected based on the threshold-based selection criteria, which is given as \(T_{\rm s}=14\) and \(T_{\rm s}=34\) for the one ring channel model with \(\alpha_{\rm A}=5^{\circ}\) and \(\alpha_{\rm A}=15^{\circ}\), respectively. The results in Figure 3 show that the normalized MSE with proposed DTS design is decreased significantly with increasing the spatial correlation. i.e., with \(\alpha_{\rm A}=5^{\circ}\). This indicates that increasing the spatial correlation would reduce the power requirement to achieve the same MSE. In particular, increasing the spatial correlation would allow the power to be focused into the most relevant eigendirections, and thus, these eigendirections become easy to be estimated. In addition, the results demonstrate that the proposed DTS design with colored noise achieves a significant improvement in the MSE performance in comparison to the conventional design with white noise. Figure 4: Achievable sum rate versus SNR using the one ring channel model based on ULA BS with different levels of correlations, i.e., with an azimuth angular spread of \(\alpha_{\rm A}=\{5^{\circ},15^{\circ}\}\). Figure 3: Normalized mean square error (MSE) versus signal-to-noise-ratio (SNR) using the one ring channel model based on uniform linear array (ULA) BS with different levels of correlations, i.e., with an azimuth angular spread of \(\alpha_{\rm A}=\{5^{\circ},15^{\circ}\}\). Figure 4 demonstrates that remarkable improvement in the achievable sum rate performances are achieved for different level of correlations. Specifically, the results show that in order to obtain a rate of 10 bits/s/Hz with relatively high spatial correction, the proposed DTS design achieves a 5 dB gain compared with the conventional designs with white noise. In addition, the results demonstrate that this gain is increased to almost 10 dB in with relatively low spatial correction in comparison to the conventional designs. The results show that the gab between the proposed DTS design and the conventional designs is reduced. This can be justified due to the fact that as the SNR increases, the mutual interference is increased, and thus, the ability of RZFBF precoding to mitigate the users interference is reduced. Nonetheless, the proposed DTS design achieves a noticeable gain of approximately 2 dB in comparison to the conventional designs. Figures 5 and 6 examine respectively the normalized MSE and the achievable sum rate versus SNR using the Laplacian channel model based on UPA BS with different levels of correlations, i.e., with an azimuth angular spread of \(\alpha_{\mathrm{A}}=\{5^{\circ},15^{\circ}\}\). The number of pilot sequence lengths are selected based on the threshold-based selection criteria, which is given as \(T_{\mathrm{s}}=15\) and \(T_{\mathrm{s}}=24\) for the Laplacian channel model with \(\alpha_{\mathrm{A}}=5^{\circ}\) and \(\alpha_{\mathrm{A}}=15^{\circ}\), respectively. The other salient system parameters remain unchanged. The results show that using the Laplacian channel model with a UPA, the MSE of the proposed DTS design with colored noise is significantly reduced compared with the conventional training designs with white noise. Further, the results demonstrate that using the proposed training design, a noticeable improvement in the DL achievable sum rate is achieved in comparison to the conventional training designs.