# Capacity Bounds for Dense Massive MIMO in a Line-of-Sight Propagation Environment
## 6 Simulation Results and Discussion  
In this section, we present the results of several simulations that were designed to assess the findings we have reported in this work. Initially, we assess the tightness of the derived exact and lower/upper bounds for the sum-capacity in favorable propagation against the actual capacity as the number of antennas grows. Next, we evaluate the tightness of the derived capacity equations over the variation of the average SNR. Then, we show that the sum-capacity for low- and high-SNR regimes can be accurately described by the derived approximated closed-form equations. In the sequence, we demonstrate the power scaling law for different values of \(\alpha\) and show that the transmit power can be reduced as the number of antennas grows. Next, we prove that the total power gain of the channel matrix can be approximated by a Gamma distribution. To conclude, the remaining simulation results present approximations for distribution of the instantaneous sum-capacity in low- and high-SNR regimes and show that by employing those distributions, the outage probabilities can be accurately calculated for these two cases as the number of devices and antennas grows, respectively. All results presented here have the following simulation setup parameters \(R=100\) [m], \(R_{min}=10\) [m], and \(\lambda=0.01070687\) [m], which is equivalent to a carrier frequency of 28 GHz. Figure 2 has the following simulation setup parameters \(K=10\) and \(\rho=80\) [dB]. As can be seen, the simulated capacity is within the lower and upper bound ranges as expected. It is also possible to see that the simulated and analytical capacities in favorable propagation match each other, showing that the derived analytical closed-form is tight for the favorable propagation case. Moreover, the simulated capacity asymptotically approaches the capacity in favorable propagation as the number of antennas, \(M\), grows, proving that favorable propagation is asymptotically achieved as \(M\) grows. It is also important to highlight that the analytical capacity in favorable propagation,given by Equation (12), provides a good approximation for the capacity. For example, for \(M=100\) the simulated capacity is equal to 21.53 bits/s/Hz and the analytical capacity in favorable propagation is equal to 22.3 bits/Hz. Figure 2 also presents on the right x-axis the average distance from favorable propagation as defined in Equation (35). As can be noticed, the average distance asymptotically decreases as the number of antennas grows, starting at 0.13 for \(M=10\) and decreasing to 0.005049 for \(M=1000\). This result is another indication that favorable propagation is asymptotically achieved as \(M\) grows. Figure 3 compares the sum-capacity over the variation of the average SNR, \(\rho\), for the same simulation parameters used for the results in Figure 2 and \(M\) constant and equal to 300 antennas. As expected, the sum-capacity, simulated and analytical, stays within the lower and upper capacity bounds. For low-SNR values the sum-capacity is closer to the upper bound and as the SNR increases, we see that both lower and upper bounds converge to the sum-capacity. In Figure 4 we present the results of the sum-capacity for low- and high-SNR regimes in favorable propagation condition versus the average signal-to-interference ratio, \(\rho\), with \(M\) constant and equal to 300 antennas. As can be seen, Equations (24) and (26) represent the sum-capacity fairly well for the low- and high-SNR regimes, respectively. In the upper part of the figure, we show the sum-capacity for the low-SNR regime and it is possible to see that the approximated expression given by Equation (24) closely follows the sum-capacity until around 60 [dB]. In the lower part of the figure, we show the sum-capacity for the high-SNR regime and we also see that the approximated expression given by Equation (26) closely follows the sum-capacity for SNR values greater than 80 [dB].