# An Efficient Precoding Algorithm for mmWave Massive MIMO Systems
## 4 Numerical Simulation Analysis
Comparing Figures 2 and 3, it can be found that the effect is better when \(N_{\rm RF}^{\rm t}=N_{\rm RF}^{\rm r}\geq N_{s}\), because in this case, the dimensions of baseband precoding \(F_{\rm BB}\) and RF precoding \(F_{\rm RF}\) are higher, and the precoding matrix contains more information, so the effect is better. Therefore, the proposed algorithm can achieve better results for \(N_{\rm RF}^{\rm t}=N_{\rm RF}^{\rm r}\geq N_{s}\). Figure 3: Comparison of spectral efficiency under different SNR levels of the proposed algorithm with other state-of-the-art algorithms with \(N_{\rm RF}^{\rm t}=N_{\rm RF}^{\rm r}\geq N_{s}\). (**a**) \(N_{s}=3\); (**b**) \(N_{s}=4\). Figure 4a,b shows the spectral efficiency with the number of RF links for different precoding algorithms with \(N_{t}=64\) antennas at the transmitter, \(N_{r}=16\) antennas at the receiver, \(N_{s}=1\),3, and \(SNR=0\) dB. As can be seen from Figure 4a,b, since full-digital precoding is precoded only at the baseband, the analog precoding is precoded only at the radio frequency, so they are not affected by the change in the number of RF links. With the increase of the number of RF links, the proposed algorithm has better spectral efficiency than the traditional OMP-based hybrid precoding scheme. When \(N_{s}=1\), the proposed algorithm and the traditional OMP-based hybrid precoding algorithm have approximately similar performances (Figure 4a). When \(N_{s}=3\), the proposed algorithm shows a better performance than the traditional OMP-based hybrid precoding algorithm (Figure 4b). Therefore, the proposed algorithm performance gets better when the number of RF links and the number of data streams are relatively large. However, if the difference is too large, then the meaning of hybrid precoding is lost. So, the number of RF links is generally twice that of the data streams for better performance. Therefore, the proposed algorithm can achieve better results for different number of RF link. Figure 4: Comparison of spectral efficiency under different number of RF links with other state-of-the-art algorithms with \(N_{r}=16\), \(N_{s}=[1,3]\) and \(SNR=0\) dB. (**a**) \(N_{s}=1\); (**b**) \(N_{s}=3\). Figures 5 and 6 show the different BERs with \(N_{t}=64\) antennas at the transmitter end, \(N_{r}=16\) antennas at the receiving end, \(N_{\mathrm{RF}}^{\mathrm{t}}=N_{\mathrm{RF}}^{\mathrm{r}}=4\), and \(N_{s}\) at 1 and 3, respectively. As can be seen from Figures 5 and 6, the BER of the full-digital precoding, the proposed algorithm, and the traditional OMP-based hybrid precoding algorithms decrease with the increase of SNR, while the analog precoding BER remains unchanged. This is because the analog precoder selects the \(N_{s}\) column array response vector with the largest channel gain, and its selection is independent of the SNR. Comparing Figure 5 with Figure 6, it can be found that when \(N_{s}=1\), the full-digital precoding algorithm, the proposed BSAMIBOMP, and the traditional OMP-based hybrid precoding algorithm achieved the best BER performance, that is, with no error rate. When \(N_{s}=3\), the full-digital precoding algorithm can be optimized at 5 dB, while the OMP-based hybrid precoding and the proposed algorithm tend to be stable after 5 dB SNR, and a closer observation can be found in this paper. The proposed algorithm shows better BER performance than the traditional OMP-based hybrid precoding, and also its performance is closer to the full-digital precoding scheme. We also conclude that the proposed algorithm is especially suitable when there is a difference between the number of RF links and the number of data streams. From the above results, it is clear that the proposed algorithm also shows better performance in terms of BER. Figure 7 compares the computational complexity of the proposed BSAMIBOMP algorithm with another existing algorithm under a different number of RF chains. As can be seen from Figure 7, when the number of RF chains increases, the number of multiplications and additions required for all the algorithms increases.