# On the Spectral Efficiency for Distributed Massive MIMO Systems
## 3 Power Unbalance on Sub-6 Ghz D-MIMO Systems
### Power Balance Analysis  
In order to analyze the effect of the power balance in a D-MIMO system, the balance of the measurements must be assessed. For that purpose, Table 1 shows the normalized power balance (NPB) over the maximum value for the \(i\)-MIMO system. Since all scenarios are normalized, it can be seen that scenario A reaches the maximum power in the receivers. As stated in [22; 23], this scenario lacks absorbers, so it is logical to expect maximum received power. The higher the number of absorbers, the lower the received power due to the absorption effect.  
Once the power allocation is known, we can establish a D-MIMO system formed by the first transmitter of the scenarios from A to E and all three receivers from every scenario. This leads to a D-MIMO whose channel matrix \(\mathbf{H}\) has the dimensions 5 TX \(\times\) 3 RX. In this new \(\mathbf{H}\), the average value of the normalized power is 0.65. Scenarios A and B are modified by applying the balance factors \(Att_{1}\) and \(Att_{2}\) Equation (2) to the first two rows of \(\mathbf{H}\) to see the effect of the power balance. Figure 3a shows the spectral efficiency of the D-MIMO when it is modulated with both balance factors simultaneously. As it can be seen, the higher the \(Att_{2}\) value is, the higher the spectral efficiency obtained. Since \(Att_{2}\) modulates \(\mathbf{H}_{2}\) (NPB = 0.48) and the average NPB for the full matrix \(\mathbf{H}\) is 0.65, it is intended to obtain an \(Att_{2}\) value as close as possible to 1. This fact provides an NPB in the \(\mathbf{H}_{2}\) row that is the closest to the average NPB. Observing the effect of \(Att_{1}\), the spectral efficiency rises from 0.01 to 0.6, where it reaches a maximum. From that value, the metric tends to decrease. Since \(\mathbf{H}_{1}\) NPB is 1, the value of \(Att_{1}\) that provides a NPB similar to the average NPB is 0.65. It is clearly observed that the maximum spectral efficiencies are reached for these values. In short, the D-MIMO is able to maximize its spectral efficiency when the \(i\)-MIMO systems tend to be balanced due to the balance factor inclusion.  
In order to validate this reasoning, a second experiment was carried out. The first transmitter from the scenarios C, D, E, F and G were chosen. Therefore, a D-MIMO with channel matrix \(\mathbf{H}\) (5 TX \(\times\) 3 RX) was created. In this case, the average NPB is 0.42 and the balance factors \(Att_{3}\) and \(Att_{4}\) are applied to the scenarios C (\(\mathbf{H}_{3}\)) and D (\(\mathbf{H}_{4}\)), respectively. Figure 3b presents the spectral efficiency when both balance factors are included. First, the NPB in scenario C is 0.36. Therefore, larger values of \(Att_{3}\) obtain a NPB closer to the average NPB of the D-MIMO. Consequently, the spectral efficiency increases as \(Att_{3}\) increases. Based on the modulation of scenario D (\(Att_{4}\)), the NPB is 0.85. In order to maximize the spectral efficiency, the NPB must tend to values around the average NPB. This is obtained for values of \(Att_{4}\) around 0.5. Note that \(Att_{4}\) values above 0.5 do not increase the spectral efficiency even when it implies increasing the transmission power of scenario C. This fact is due to the power unbalance when \(Att_{4}\) is too high.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **A (\(\mathbf{H_{1}}\))** & **B (\(\mathbf{H_{2}}\))** & **C (\(\mathbf{H_{3}}\))** & **D (\(\mathbf{H_{4}}\))** & **E (\(\mathbf{H_{5}}\))** & **F (\(\mathbf{H_{6}}\))** & **G (\(\mathbf{H_{7}}\))** \\ \hline Power allocation & 1 & 0.48 & 0.36 & 0.85 & 0.58 To conclude this section, it was proven that the spectral efficiency of a D-MIMO system is directly proportional to the power balance. Therefore, the received power variance between the TX-RX pair should be reduced in order to provide satisfactory UE services.