# The Role of Correlation in the Performance of Massive MIMO Systems
## 6 Numerical Results
### Performance Evaluation Based on Spectral Efficiency  
So far, the results have been presented in order to evaluate the system performance based on MSE performance. This section evaluates the system performance considering spectral efficiency.  
Figures 8 and 9 examine the spectral efficiency performance for the RZF precoding technique vs. the SNR in dB for the ULA and URA topologies, respectively. In particular, Figure 8 shows that at a typical SNR value, i.e., 10 dB, the spectral efficiency is increased by almost 50 bit/s/Hz when the number of service antennas is increased from \(M=16\) to \(M=256\). However, the performance gap is reduced when the number of service antennas is increased to above \(M=64\). Furthermore, the results in Figure 8 show that a 15 dB gain is achieved by using \(M=256\) in comparison with \(M=16\) using the same transmit power. Interestingly, to achieve the same spectral efficiency performance, we can increase the number of service antennas from \(M=16\) to \(M=64\). As such, a 10 dB transmit power gain is achieved by adding extra service antennas. This is a reasonable price to pay for saving the transmit power. As can be observed from Figures 8 and 9, the spectral efficiency benefits significantly from increasing the number of base station antennas. This is due to the fact that the signal intended for different UEs is spatially focused when the number of antennas at the base station increases, which results in a significant improvement in spectral efficiency. Clearly, deploying the ULA topology at the base station achieves a considerable gain in the spectral efficiency in comparison with the URA-based configuration.  
Figure 8: Spectral efficiency vs. SNR in dB for the ULA topology, \(U=10\) UEs, \(\alpha_{\rm A}(AS)=5\), with different numbers of base station antennas.  
Figures 10 and 11 plot the spectral efficiency vs. the number of base station antennas \(M\), for the ULA and URA configurations, respectively, comparing different correlation levels by using various standard deviations \(\alpha_{A}\) (AS). An important insight that can be drawn from the plots in Figures 10 and 11 is that increasing the level of correlation by decreasing the azimuth standard deviation \(\alpha_{A}\) (AS) results in reducing the spectral efficiency. In addition, deploying the ULA topology at the base station results in improving the spectral efficiency significantly in comparison with the URA-based configuration. This is due to the fact that increasing the interference between the covariance matrices of the UEs would lead to reducing the received signal strength and, thus, reducing the spectral efficiency performance.  
Figure 10: Spectral efficiency vs. SNR in dB for the ULA topology, \(U=10\) UEs, \(M=128\), with different values of angular spread \(\alpha_{\rm A}(AS)\).  
Figure 9: Spectral efficiency vs. SNR in dB for the URA topology, \(U=10\) UEs, azimuth standard deviation \(\alpha_{\rm A}(AS)=5\), with different numbers of base station antennas.  
The analysis of the results provides a clear insight into the operation and interference characteristics of an m-MIMO system when different levels of correlations at the base station are considered. Overall, we identify a set of scenarios under which the m-MIMO system can achieve a minimum MSE and a maximum SE. The results confirm that minimizing the MSE of the channel estimate would not necessarily maximize the SE for the m-MIMO systems under consideration.