# An Efficient Precoding Algorithm for mmWave Massive MIMO Systems
## 4 Numerical Simulation Analysis  
In order to verify the performance of the proposed hybrid precoding Algorithm 1, this section gives the simulation results of full-digital precoding, analog precoding, and OMP-based hybrid precoding, and compares them with the proposed Algorithm 1 in mmWave massive MIMO systems. The simulation parameters are shown in Table 2. We used MATLAB R2017a for simulations, while the results are averaged over 1000 random channel implementations. Figure 2 shows the difference in spectral efficiency (SE) with SNR for different precoding algorithms with \(N_{t}=64\) antennas at the transmitter, \(N_{r}=16\) antennas at the receiver, and \(N_{\rm RF}^{\rm t}=N_{\rm RF}^{\rm r}=N_{s}=[2,3]\). It can be seen from Figure 2a,b that as the SNR increases, the spectral efficiency of the different precoding algorithms in improved to different degrees, and as the data streams increase, the spectral efficiency of different precoding will be improved to varying degrees. For digital data streams, the full-digital precoding algorithm performs best because it is optimal precoding, and all precoding is aimed at \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Computational Complexity (\(\mu\)s)** \\ \hline OMP Algorithm [15] & \(\mathcal{O}\Big{(}N_{t}^{2}N_{RF}^{t}N_{s}\Big{)}\) \\ Proposed Algorithm & \(\mathcal{O}\Big{(}N_{t}N_{RF}^{t}\Big{)}^{2}\Big{)}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complexity Comparison. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of clusters \(N_{\rm cl}\) & 5 \\ Number of propagation paths per cluster \(N_{\rm ray}\) & 10 \\ Antenna array deployed & ULA \\ Azimuth Angle-of-Arrival (AoA) and & \\ Angle-of-Departure (AoD) cluster angles distribution & Uniform \([0,2\pi]\) \\ Angular spread & \(10^{\circ}\) \\ Number of transmitter antennas \(N_{t}\) & 64 \\ Number of transmitter antennas \(N_{r}\) & 16 \\ SNR & 10 dB \\ Number of RF chains & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. approaching it. The proposed BSAMIBOMP algorithm performs better than the traditional OMP-based hybrid precoding algorithm as it eliminates the matrix inversion operation and candidate matrix requirement. Also, the proposed algorithm outperforms traditional hybrid OMP precoding as it utilizes the BSA algorithm to search for the global optimal solution, while the traditional OMP-based precoding algorithm uses the candidate matrix to select the column with the highest correlation. However, there is an interval between the angles of each column in the candidate matrix, so the selected array response vector is not necessarily the global optimal solution. The analog precoding performance is the worst because the analog precoding is constant modulus; only the phase characteristics are utilized, and the amplitude characteristics are not utilized. Therefore, the proposed algorithm can achieve better results under \(N_{\text{RF}}^{\text{t}}=N_{\text{RF}}^{\text{r}}=N_{s}\). Figure 2: Comparison of spectral efficiency under different SNR levels of the proposed algorithm with other state-of-the-art algorithms with \(N_{\text{RF}}^{\text{t}}=N_{\text{RF}}^{\text{r}}=N_{s}\). (**a**) \(N_{s}=2\); (**b**) \(N_{s}=3\). Figure 3a,b shows the spectral efficiency versus SNR for different precoding algorithms with \(N_{t}=64\) antennas at the transmitter, \(N_{r}=16\) antennas at the receiver, \(N_{\rm RF}^{\rm t}=N_{\rm RF}^{\rm r}=4\), and \(N_{s}=3\) and \(4\), respectively. As can be seen from Figure 3a,b, as the SNR and data streams increase, the spectral efficiency of different algorithms improves to different degrees. Similarly, for all data streams, the performance of the fully-digital precoding algorithm is the best. The performance of the proposed BSAMIBOMP algorithm is close to the full-digital algorithm and better than the traditional OMP-based hybrid precoding algorithm. The analog precoding performance is the worst of all precoding schemes.