# Hybrid Precoding Design for Wireless Fading Channels
## 4 Simulation Results
From these results, it can be seen that the computation time of the SLP-2 scheme is much longer than that of the linear MMSE precoding technique and that the computation time of the proposed scheme is longer than that of the linear MMSE precoding scheme and shorter than that of the SLP-2 scheme. The reason for this is that the MMSE precoding scheme is an average-based precoding technique, so the precoding matrix is obtained only once during the block length period, but the SLP-2 scheme is a symbol-based precoding technique, so the precoding result must be obtained for each block length. \begin{table}
\begin{tabular}{c c c c c} \hline
**K** & **MMSE (s)** & **SLP-2 (s)** & **Proposed (s)** & **Pro./SLP-2 (\%)** \\ \hline
2 & \(3.1369\times 10^{-5}\) & \(2.1784\times 10^{-1}\) & \(2.1581\times 10^{-1}\) & 99.1 \\ \hline
4 & \(3.1369\times 10^{-5}\) & \(2.1784\times 10^{-1}\) & \(2.0712\times 10^{-1}\) & 95.1 \\ \hline
6 & \(3.1369\times 10^{-5}\) & \(2.1784\times 10^{-1}\) & \(1.9234\times 10^{-1}\) & 88.3 \\ \hline
8 & \(3.1369\times 10^{-5}\) & \(2.1784\times 10^{-1}\) & \(1.7032\times 10^{-1}\) & 78.2 \\ \hline
10 & \(3.1369\times 10^{-5}\) & \(2.1784\times 10^{-1}\) & \(1.5319\times 10^{-1}\) & 70.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Computation complexity comparison in terms of the execution time when block length L = 1000, M = 14, and K + J = 12. Figure 3: SER comparison of the proposed scheme and conventional ones when M = 28 and K + J = 26. (SLP-1 and SLP-2 refer to the schemes in [21] and [22], respectively). \begin{table}
\begin{tabular}{c c c c c} \hline
**K** & **MMSE (s)** & **SLP-2 (s)** & **Proposed (s)** & **Pro./SLP-2 (\%)** \\ \hline
4 & \(8.0797\times 10^{-5}\) & \(6.1286\times 10^{-1}\) & \(5.1434\times 10^{-1}\) & 83.9 \\ \hline
10 & \(8.0797\times 10^{-5}\) & \(6.1286\times 10^{-1}\) & \(3.8130\times 10^{-1}\) & 62.2 \\ \hline
16 & \(8.0797\times 10^{-5}\) & \(6.1286\times 10^{-1}\) & \(2.7781\times 10^{-1}\) & 45.3 \\ \hline
22 & \(8.0797\times 10^{-5}\) & \(6.1286\times 10^{-1}\) & \(2.1152\times 10^{-1}\) & 34.5 \\ \hline \end{tabular}
\end{table} 
Table 2: Computation complexity comparison in terms of the execution time when block length L = 1000, M = 28, and K + J = 26.  
symbol, so the calculation time of the SLP-2 technique takes much longer. Meanwhile, since the proposed technique applies the MMSE precoding technique to the data for K users belonging to group 1, the precoding matrix is obtained only once during the block length period, so the calculation time is reduced compared to that of the SLP-2 technique. In this table, Pro./SLP-2 (%) is the result of comparing the calculation time of the proposed method with that of the SLP-2 method. From these results, it can be seen that as K increases, the calculation time of the proposed method decreases significantly compared to that of the SLP-2 method. Table 2 shows the performance for the case of M = 28 and K + J = 26. In this case, similar results are shown in Table 2.  
Combining the results in Figures 1 and 2 and Tables 1 and 2, it can be seen that the proposed technique shows better SER performance than the MMSE precoding technique and requires much less computation than the SLP-2 technique. It can be seen that the SER performance and computational complexity performance of the proposed method can be appropriately controlled by adjusting the value of K.