# 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  
Once the two types of propagation channels are known, two MIMO systems are acquired. The first one has a BS with 11 TX pointing the UE in the semi-anechoic part. The transmitters are arranged at 90\({}^{\circ}\) amplitude in the azimuth angle, with an angle separation between consecutive transmitters of 9\({}^{\circ}\). The UE is composed by 5 RX in a 20 cm lineal array, where the separation between consecutive RX is 5 cm. The frequency range of the measurement goes from 40 GHz to 50 GHz for 101 frequency samples (100 MHz frequency spacing) and the distance on the LoS is 150 cm. The second MIMO measured is similar to the first one. The main difference lies on the BS pointing angle. In this case, the BS points directly to the metallic wall in the semi-reverberation part, which makes a NLoS scenario where the signal reaches the RX through several reflections. In this case, the shortest path from the TX to the RX is 720 cm. Figure 5: Spectral efficiency of a D-MIMO (50 \(\times\) 10) system for two frequencies (10 GHz and 28 GHz) and LoS and NLoS visibility conditions. SINR is fixed to 15 dB. (**a**) UMa scenario and (**b**) UMi scenario. Due to the peculiarities of the scenarios, several conclusions can be drawn. The anechoic channels are expected to achieve lower attenuations due to the proximity between the pair TX/RX. However, the correlation between channels will be high due to the low spatial diversity of the scenario. On other hand, the reverberation channels are expected to obtain higher attenuations due to the TX-RX distance. Nevertheless, the channels tend to be independents. Once the previous facts were known, we created a D-MIMO system formed by both MIMO systems. A matrix channel \(\mathbf{H}=\left[\mathbf{H}_{1}^{\mathrm{T}},\mathbf{H}_{2}^{\mathrm{T}}\right]^{T}\) with dimensions 22 TX \(\times\) 5 RX for 101 frequency samples was obtained. The normalized power balance for the submatrix \(\mathbf{H}_{1}\) and \(\mathbf{H}_{2}\) is 1 and 0.158, respectively. As previously stated, the anechoic channels achieve the maximum power, and the reverberation channels are attenuated in a factor 6.325 in average. Without the application of a normalization factor, reverberation channels will be masked by the anechoic channels. Therefore, as shown in Section 3, \(Att_{1}\) and \(Att_{2}\) factors multiply the anechoic and reverberation channels in order to modulate the D-MIMO balance power. Figure 6 shows a parametric sweep of both factors for the spectral efficiency. \(Att_{1}\) moves in the range from 0 to 2 and \(Att_{2}\) in the range from 0 to 5. Moreover, a black line with slope 6.325 is shown. This line represents those operating points where the D-MIMO is balanced in terms of power. On the right side of this line, the D-MIMO system is dominated by anechoic channels, while the reverberation channels prevail in the left side. The higher the prevalence of the anechoic channels, the lower the spectral efficiency due to the high correlation between these channels. As we approach the equilibrium line, the presence of the significantly less correlated reverberation channels becomes higher, which increases the efficiency. In the balanced region, the efficiency is maximized around 45 bps/Hz. On the left side, the values remain around the maximum because the reverberation channels are the predominant ones over the anechoic channels. Finally, to further explore this scenario, three key operating points were studied in terms of SINR. Figure 7 illustrates the spectral efficiency of the MIMO subsystem formed by the anechoic channels, the unbalanced D-MIMO and the balanced D-MIMO. The first curve takes into account only the \(\mathbf{H}_{1}\) channel matrix. For 30 dB SINR, it reaches a spectral efficiency of 24.5 bps/Hz. This operating point is shown in Figure 6 for \(Att_{1}=1\) and \(Att_{2}=0\). If we include the reverberation channels, the unbalanced D-MIMO is formed.