# A New Design of Codebook for Hybrid Precoding in Millimeter-Wave Massive MIMO Systems
## 4 Simulation Results
### Comparison and Analysis of Spectral Efficiency Performance  
Figure 3 indicates that the spectral efficiency achieved by different algorithms varying with SNR and the number of RF chains at the transmitter \(N_{\text{t}}^{\text{RF}}\) is 8. Figure 3 clearly shows that the spectral efficiency of the proposed codebook design algorithm is higher than that of the OMP-based joint codebook algorithm in [4] and the hybrid precoding algorithm with quantization in [1] in the SNR interval [\(-\)5, 30]. The specific simulation results are shown in Table 2. When SNR is 0 dB, the spectral efficiency of the hybrid precoding with quantification algorithm [1] is 14.4082 bps/Hz, the OMP-based codebook algorithm [4] is 15.3462 bps/Hz, the proposed codebook algorithm is 15.8109 bps/Hz, and the optimal unconstrained precoding algorithm is 15.3462 bps/Hz. Compared with the previous two algorithms, the proposed algorithm improves the spectral efficiency by 9.74% and 3.02%, respectively. However, compared with the last algorithm, the proposed algorithm reduces the spectral efficiency by 4.43%. When SNR is 5 dB, the proposed algorithm improves the spectral efficiency by 6.96% and 2.56%, respectively, and reduce by 6.30%. When SNR is 10 dB, the proposed algorithm improves the spectral efficiency by 5.68% and 2.27%, respectively, and reduce by 8.97%. When SNR is between \(-\)5 dB and 30 dB, although our algorithm is lower than the last algorithm (optimal unconstrained precoding algorithm) in spectral efficiency performance, the last algorithm is executed in an ideal state, which is not realizable. We only compare it as a benchmark. In addition, through the analysis of \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of clusters \(N_{\text{cl}}\) & 4 \\ Number of propagation paths per cluster \(N_{\text{ray}}\) & 20 \\ Antenna array deployed & USPA \\ AoA and AoD cluster angles distribution & Uniform\([0,2\pi]\) \\ Angular spread & \(6^{0}\) \\ Number of transmitter antennas \(N_{\text{t}}\) & 64 \\ Number of receiver antennas \(N_{\text{r}}\) & 32 \\ Number of of RF chains \(N_{\text{t}}^{\text{RF}}\) & 8 \\ Number of data streams \(N_{\text{s}}\) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. the data in Table 2, we can see that compared with the current two better algorithms, our hybrid precoding design algorithm has a significant improvement in spectral efficiency performance when the signal-to-noise ratio (SNR) is low. At the same time, Figure 3 shows that when the SNR is relatively high, the spectral efficiency of our proposed algorithm is not greatly improved compared with the other two algorithms; especially, when the SNR is higher than 25 dB, it almost coincides with the corresponding curves of the two compared algorithms. The reasons are as follows. The algorithms involved in this paper are hybrid precoding codebook design schemes based on the compressed sensing (CS) reconstruction algorithm. The algorithms generally need some prior knowledge of the reconstructed signal, which is some channel state information (CSI) obtained from channel estimation. When SNR is low, the channel estimation result is not accurate enough. The proposed algorithm selects multiple column vectors instead of a single-column vector to form the initial analog codebook at each iteration. When reconstructing the signal, it avoids the error accumulation effect. Compared with other algorithms, the reconstructed signal can be obtained more accurately. So, the spectral efficiency of proposed algorithm is better than other algorithms. However, when SNR is high, the channel estimation result is accurate enough and all algorithms will not accumulate too much error in iterations. This is the reason why the spectral efficiency of the new proposed algorithm is the same as the other previous algorithms for higher SNR regimes. In Figure 4, the spectral efficiency of different precoding methods are simulated and compared under different numbers of RF chains.