# On the Spectral Efficiency for Distributed Massive MIMO Systems
## 5 D-MIMO System on a Semi-Anechoic and Semi-Reverberation Chamber in the mmWave Band
### Anechoic and Reverberation Channel Analysis
In this case, diversity is added to the scenario, although reverberation channels are masked  
Figure 6: Spectral efficiency for a parametric sweep of \(Att_{1}\) and \(Att_{2}\). The black line stands for the region where both MIMO subsystems are balanced in terms of power. The SINR is fixed to 30 dB and the values are averaged over the 101 frequency samples. due to unbalancing. The effect can be seen in the second curve, where the spectral efficiency is slightly improved. This operating point corresponds to \(Att_{1}=1\) and \(Att_{2}=1\), where the spectral efficiency is 30.9 bps/Hz in Figure 6. Finally, the channel power balance can improve further the scenario. This effect is shown in the third curve, where the spectral efficiency is significantly improved (\(Att_{1}=0.158\) and \(Att_{2}=1\)). Due to this fact, values up to 45 bps/Hz are achieved. This means an improvement of 45.6% compared with the unbalanced case and 83.7% compared with the anechoic subsystem. Once the previous case was studied, a second set of measurements was acquired. On the one hand, 33 TX points the UE in the semi-anechoic chamber. As in previous case, TXs are arranged at a 90\({}^{\circ}\) amplitude in the azimuth angle with a separation of 9\({}^{\circ}\) (11 locations). However, we added 11 TX 5 cm on the left and 11 TX 5 cm on the right to form a ULA. Each position includes 11 TX that varies in the azimuth angle, for a total of 33 TX. On the other hand, the UE is composed of 25 RX in a 20 cm uniform rectangular array (URA), where the separation between the consecutive RX is 5 cm in both axes. The second MIMO is similar to the first one, but pointing the semi-reverberation chamber. The distances and frequency ranges are the same as in the previous example. After the acquisition, the D-MIMO channel matrix is formed by combining both MIMO system, whose size is 66 TX \(\times\) 25 RX. The normalized power balance for the anechoic MIMO and reverberation MIMO is 1 and 0.091, respectively. This means the reverberation MIMO is even more unbalanced than in Figure 6. Specifically, reverberation channels are attenuated in an 11.042 factor compared with the anechoic channels. Figure 8A presents a sweep parameter for \(Att_{1}\) and \(Att_{2}\) factors, where we can extract similar conclusions as in Figure 6. Note that the black line which indicates the balance power equilibrium is shifted to the left. This is due to the larger unbalance from the reverberation chamber. The slope of this equilibrium point is 11.042. In the balance region, the spectral efficiency is maximized around 205 bps/Hz. Figure 8B shows the operation points previously illustrated in Figure 7. When the number of propagation channels increases and the power distribution is balanced, the spectral efficiency is also expected to increase. For a 30 dB SINR, the anechoic MIMO obtains 60.7 bps/Hz, the unbalanced D-MIMO gets 94.3 bps/Hz and the balance D-MIMO achieves 205.8 bps/Hz. In relative terms, the balanced D-MIMO system has an improvement of 118.3% compared with the unbalanced case and 238.9% compared with the anechoic subsystem. These results show how critical a proper assignation of the power resources is for massive D-MIMO systems. Figure 7: Spectral efficiency for the anechoic MIMO (blue line), unbalanced D-MIMO (red line) and balanced MIMO (black line). For each value of SINR, the spectral efficiency is averaged over the 101 frequency samples. The analysis made in this section shows that decorrelation of channels in a D-MIMO, as well as channel power balance, imply the improvement of propagation channel conditions, ensuring both conditions induce optimal physical channel performance. Furthermore, by comparing both D-MIMOs, it was shown that the higher the number of propagation channels are, the more noticeable this improvement is.