# Analysis and Evaluation of Performance Gains and Tradeoffs for Massive MIMO Systems
## 5 Simulation Results
Secondly, in reality the separation between antenna elements are not well (as in massive MIMO), so spatial correlation may occur which means the large number of degree of freedom will not be offered by propagation environment and this will limit the multiplexing gain under imperfect CSI. With massive MIMO, extra antennas may boost the transmission SNR and increases the multiplexing gain. For comparing massive MIMO and conventional MIMO in terms of multiplexing gain, large scale system \"Massive MIMO\" outperforms better than conventional MIMO due to increase the number of antennas and the number of terminals that are served simultaneously within the same coherence interval. Figure 5: Array gain vs. number of antennas in multi-cell system with K = 15 users, L = 7 and transmit power = 10 dB. In Figure 7, as the number of antennas increases, outage probability of \(k\)th user improves also. This result can be expected for the large scale system under perfect propagation conditions, i.e., (independent, identically distributed i.i.d flat fading channels), where such system offers a large degree of freedom but practically with multi-cell massive MIMO systems, base station depends on channel state information to make estimation of channel matrix and due to non-orthogonal interfering channels among cells outage probability degraded. This deterioration rises as the number of served users \(K\) increases proportionally with rising number of antennas \(M\) in massive MIMO. Figure 7 studies also the relation between increasing the number of served terminals and outage probability occurrence with a different number of antennas (\(M\)). From the plotted figure, increasing the number of served users coherently will raise the likelihood of occurrence for outage probability, this returns to the interference among neighboring cells that use the same non-orthogonal pilot sequences. As a result with massive MIMO system, the increment in number of base station's antennas without limits can enhance the possibility of outage probability occurrence, which leads to improved spatial diversity gain. In Figure 8, the transmitted SNR is plotted with outage probability in a multi-cell system, increasing the number of antennas will improve the outage probability through the high SNR regime. From the plotted graph, increasing the number of propagation channels will increase the number of  
Figure 6: Spatial multiplexing gain vs. the number of BS antennas in multi-cell system with L = 7, K = 10, transmit power =10 dB. Figure 7: Outage Probability vs. number of users in multi-cell system with L = 7, transmit power = 10 dB and Y\({}_{\ell\text{th}}\) = 10 dB. served terminals which means the system will suffer interference from other cells due to the reuse of non-orthogonal pilot signals in a multi-cell system. In addition, Figure 8 discusses the tradeoff between the spatial diversity gain and spatial multiplexing gain if a number of users is fixed, increasing the number of antennas will improve the outage probability which means increasing the degree of freedom or enhancing the diversity gain for user. On another hand, increasing the number of propagation channels, it will increase the achievable sum rate, i.e., \"spectral efficiency\", which leads to improve the multiplexing gain. However, in multi-cell large scale systems with an unlimited number of propagation channels, the number of served users differs every coherent interval will worsen the outage probability due to inter-cell interference and degrade diversity gain, while increasing the number of served terminals will increase the spectral efficiency and enhancing the multiplexing gain. However, with a multi-cell massive MIMO system under the effect of pilot contamination, the achievable sum rate will degrade due to inter-user interference among cells which leads to decrease the multiplexing gain. In Figure 9, spectral efficiency is plotted vs. energy efficiency with various circuit power conditions under the effect of pilot contamination in multi-cell system.