## 6 Results and Discussion
### Computational Complexity Evaluation
Overall, the results show that the proposed training algorithm maximizes the achievable sum rate performance, while delivering a lower overall computational complexity owing to a faster convergence rate in comparison to the state-of-the-art iterative algorithms. Table 8 presents a comparison of the fundamental characteristics of the proposed method with the state-of-the-art-methods. Figure 4: Overall computational complexity versus the number of BS antennas \(N\) comparing different training sequence methods corresponding to the pilot length in BF and RZF precoding in the OR model with \(\omega=2.5^{\circ}\), \(D=1/2\), \(T=100\) symbols, \(\rho_{\rm d}=10\) dB and \(K=10\) users. Figure 5: Overall computational complexity versus the number of BS antennas \(N\) comparing different training sequence methods corresponding to the pilot length in BF and RZF precoding in the OR model with \(\omega=25^{\circ}\), \(D=1\), \(T=100\) symbols, \(\rho_{\rm d}=10\) dB and \(K=10\) users. Figure 6: Overall computational complexity versus the number of BS antennas \(N\) comparing different training sequence methods corresponding to the pilot length in BF and RZF precoding in the OR model with \(\omega=5^{\circ}\), \(D=1/2\), \(T=100\) symbols, \(\rho_{\rm d}=5\) dB and \(K=10\) users. Figure 7: Overall computational complexity versus the number of BS antennas \(N\) comparing different training sequence methods corresponding to the pilot length in BF and RZF precoding in the OR model with \(\omega=5^{\circ}\), \(D=1/2\), \(T=100\) symbols, \(\rho_{\rm d}=10\) dB and \(K=6\) users. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{N}\) & \multicolumn{2}{c}{**SCMI**} & \multicolumn{2}{c}{**SMSE**} & \multicolumn{2}{c}{**CGD**} & \(\mathbf{N}\) & \multicolumn{2}{c}{**SCMI**} & \multicolumn{2}{c}{**SMSE**} & \multicolumn{2}{c}{**CGD**} \\ \hline \multicolumn{6}{c}{**(a) BF precoding**} \\ \hline
10 & 85 & 120 & 66 & 10 & 151 & 40 & 66 \\ \hline
50 & 3151 & 767 & 201 & 50 & 3151 & 413 & 54 \\ \hline
100  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(N\) & \multicolumn{2}{c}{**SCMI**} & \multicolumn{2}{c}{**SMSE**} & \multicolumn{2}{c}{**CGD**} & \(N\) & \multicolumn{2}{c}{**SCMI**} & \multicolumn{2}{c}{**SMSE**} & \multicolumn{2}{c}{**CGD**} \\ \hline \multicolumn{6}{c}{(**a**) BF precoding} \\ \hline \(10\) & \(316\) & \(25\) & \(23\) & \(10\) & \(163\) & \(3\) & \(3\) \\ \hline \(50\) & \(13742\) & \(394\ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(N\) & **SCMI** & **SMSE** & **CGD** & \(N\) & **SCMI** & **SMSE** & **CGD** \\ \hline \multicolumn{6}{c}{(**a**) BF precoding} & \multicolumn{6}{c}{**(b) RZF precoding} \\ \hline
10 & 49 & 55 & 50 & 10 & 209 & 60 & 24 \\ \hline
50 & 1763 & 288 & 117 & 50 & 1763 & 155 & 73 \\ \hline
100 & 4545 & 318 & 140 & 100 & 2177 & 188 & 102 \\ \hline
150 & 2689 & 747 & 155 & 150 & 2281 & 747 & 155 \\ \hline
200 & 2391 & 1091 & 165 & 200 & 2679 & 853 & 161 \\ \hline
250 & 5800 & 1041 & 200 & 250 & 4789 & 1225 & 264 \\ \hline
300 & 5831 & 1355 & 280 & 300 & 4776 & 1126 & 263 \\ \hline
350 & 5627 & 1428 & 298 & 350 & 6494 & 1580 & 263 \\ \hline
400 & 7380 & 1763 & 303 & 400 & 8822 & 1490 & 346 \\ \hline
450 & 9942 & 1739 & 403 & 450 & 9942 & 1739 & 403 \\ \hline
500 & 6266 & 1633 & 347 & 500 & 7171 & 1917 & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of iterations per each training sequence algorithm required to converge with respect to the number of BS antennas \(N\) for the pilot length in BF and RZF precoding in the OR model with \(\omega=5^{\circ}\), \(D=1/2\), \(T=100\) symbols, \(\rho_{\rm d}=10\) dB and \(K=6\) users.