## 3 Method: Massive MIMO Network Design
### Problem Description
#### 3.1.1 Tri-Objective Fitness Function  
The tri-objective fitness functions accounting for the power consumption, the downlink exposure and the uplink exposure are defined as follows:  
1. Power consumption fitness function The power consumption fitness function is defined as follows: \[f_{1}^{3}=\min_{\{\mathbf{y},\mathbf{p}\}}~{}~{}~{}\left(1-\frac{\sum\limits_{k\in \mathcal{K}}P_{\text{calc}}\left(y_{k}p_{k}\right)}{P_{\text{max}}}\right)\] (6) where \(P_{\text{calc}}(\,)\) is the power consumption of the designed network in W consisting of the powers consumed by the analog, the baseband and the circuit components [30]; \(P_{\text{max}}=K\times P_{\text{calc}}\left(p_{t}\right)\)is the power consumption of the entire network when all BSs are assumed active and transmitting at maximum power (43 dBm). Figure 2: Selected area in Ghent, Belgium and the possible location of the base stations. Downlink exposure fitness function  
The below formula accounts for the downlink EMF exposure:  
\[f_{2}^{3}=\min_{\{y,p\}}\quad\left(1-\frac{E_{\text{e}\in\mathcal{K}}(y_{k}p_{k}) }{E_{\text{max}}}\right) \tag{7}\]  
where \(E(\,)\) is the electric field in (V/m) within the designed network-covered area due to the downlink EMF exposure. This latter is modeled similarly to [31; 32] in terms of the total EMF exposure \(E\) as the weighted average (over the area and the 40 simulations) of the median value \(E_{50}\) of the electric field strengths in the area and the 95 th percentile \(E_{55}\) of the electric field strengths in the same area:  
\[E=\alpha_{1}\cdot E_{50}+\alpha_{2}\cdot E_{95} \tag{8}\]  
\(E_{max}\) is the maximum DL exposure in [V/m] obtained when all BSs are assumed active and transmitting at maximum power with the maximum number of antenna elements mounted on each BS. This approach has been adopted since the favorable propagation conditions of the massive MIMO are assumed, in which the individual antenna's propagation channels are mutually uncorrelated. \(\alpha_{1}\) and \(\alpha_{2}\) are the weighting coefficients related to \(E_{50}\) and \(E_{95}\) respectively and have been chosen of equal importance (\(\alpha_{1}=\alpha_{2}=0.5\)). From a practical point of view, with the use of multiple antenna elements, the BS does not always transmit at maximum power since the power is split among different directions depending on the locations of the users within the area of interest [9]. So, in 5G massive MIMO BS, the realistic power level EIRP per antenna element contributing to the EMF exposure is significantly lower compared to the theoretical maximum radiated power \(\text{EIRP}_{\text{th}}\) since the duty cycles are applied (\(\text{EIRP}_{\text{real}}=\text{EIRP}_{\text{th}}\)[in W] \(\ast\text{DC}_{\text{TDD}}\ast\text{DC}_{\text{SPA}}\)). Even for very large degrees of system utilization, the authors in [9] proved that the realistic power level can take values between 7-22%, based on the user distributions considered in both azimuth and elevation. In this analysis, since the users are uniformly distributed in azimuth, the corresponding spatial duty cycle is set to 15% [9]. To evaluate the electric field created by an antenna element A of a massive MIMO 5G base station, we evaluate the DL exposure at a grid as in [32] with constant distances between two different grid points in both x-and-y axes.