# On the Spectral Efficiency for Distributed Massive MIMO Systems
## 4 Correlation and Los on Emulated D-MIMO Systems above 6 Ghz
### Correlation and LoS Analysis  
The first test consists of studying the TX/RX antenna spacing in the BS/UE to determine its effect on spectral efficiency. For that purpose, a D-MIMO system with 50 TX and \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Simulation Parameters**} \\ \hline Frequency & 10 GHz, 28 GHz, 40 GHz and 78 GHz \\ Bandwidth & 800 MHz \\ Frequency samples & 1601 (500 kHz frequency spacing) \\ Propagation environment & Urban macrocell (UMa) and urban microcell (UMi) \\ Visibility & Line-of-sight (LoS) and non-line-of-sight (NLoS) \\ UE-BS distance & 50 to 1000 m \\ TX antennas in the BS & 200 antennas (Lineal array) \\ RX antennas in the UE & 20 antennas (Lineal array) \\ TX antenna separation & \(\lambda/10\), \(\lambda/2\) and \(\lambda\) \\ RX antenna separation & \(\lambda/10\), \(\lambda/2\) and \(\lambda\) \\ EIRP & 30 dBm \\ Iterations & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NYUSIM simulation parameters. Figure 3: Spectral efficiency of a D-MIMO when the power balance is modulated with two balance factors. SINR is fixed to 15 dB. The \(i\)-MIMO systems that form the D-MIMO are the scenarios (**a**) A (\(Att_{1}\) ), B (\(Att_{2}\)), C, D, E, and (**b**) C (\(Alt_{3}\)), D (\(Att_{4}\)), E, F, G.  
10 RX was created. The D-MIMO is formed by 3 BS which are 100 m, 120 m, and 140 m away from the receiver. The relative distance between BSs is set to be the largest BS-UE distance (140 m). On each BS the transmission is made with 17 TX, 17 TX, and 16 TX, respectively. The simulations are made for two environments (UMa and UMi) and three frequencies (28 GHz, 40 GHz, and 78 GHz). Since the goal is to study the TX/RX antenna spacing effect, three distances are considered for the TX/RX spacing: \(\lambda/10\), \(\lambda/2\), and \(\lambda\). For the sake of clarity, the spacing is set to the same value on both sides of the communication. Theoretically, the closer the antennas are to each other, the lower the benefit from spatial diversity is due to the higher correlation between channels. Figure 4a,b show the results for this test. We define \(\Theta\) as the difference between the Shannon theoretical limit and the spectral efficiency simulated. The Shannon theoretical limit establishes the spectral efficiency for completely decorrelated channels. Therefore, the Shannon limit cannot be exceeded and \(\Theta\) provides an idea of how far the scenario is from the theoretical limit. Looking at both scenarios, UMa (Figure 4a) and UMi (Figure 4b), the UMa scenario tends to obtain similar results for all frequencies, while the UMi scenario shows differences up to 3 bps/Hz due to the frequency band. However, the main effect is induced by the TX/RX spacing. The farther apart the TX and RX are spaced in the ULA, the closer the theoretical limit of spectral efficiency is. In this case, the propagation channel looks different for the receivers and the propagation channels become independent from each other. Therefore, we can take advantage of the spatial multiplexing and the spectral efficiency to be closer to the Shannon limit. It is remarkable that curves between \(\lambda/10\) and \(\lambda/2\) are more separated than curves between \(\lambda/2\) and \(\lambda\). This fact shows that a \(\lambda/10\) spacing significantly affects the channel due to the high correlation. However, spacing values above \(\lambda/2\) are enough decorrelated to take advantage of the channel diversity. In absolute terms, the improvement from \(\lambda/10\) to \(\lambda/2\) is 13 bps/Hz (UMa) and 12 bps/Hz (UMi). Nevertheless, the improvement from \(\lambda/2\) to \(\lambda\) is only 2 bps/Hz (UMa) and 5 bps/Hz (UMi). In conclusion, a wider spacing between BS antennas allows an increase in spectral efficiency for the user by decreasing the antenna correlation and increasing the independence of the communication channels. The second test studies the influence of LoS and NLoS on the communication channels of a D-MIMO system.