## 4 Results
### Discussion
#### 4.2.2 Impact of the Number of Antenna Elements on the EMF Exposure  
Figure 8 shows that when an equal importance is given to the tri-objective optimization problem (power consumption, DL exposure and UL exposure), the increase of the number of BS antenna elements leads to a decrease of the number of BSs deployed in the network (from 48 to 36 BSs, when the antenna elements is increased from 16 to 256, Table 3). This increase of antenna elements at the BS yields to lower power level at each antenna element, as the total radiated power of BS is spread among these multiple antenna elements. Despite this low per-antenna output power level which would have required more BSs with smaller cells' range, the massive MIMO BS benefits from the additional beamforming (BF) gain that helps extend the range of the cells. The BF gain is defined as \(10\cdot\log_{10}\left(A\right)\). This results into the deployment of fewer number of BS in the network, which lowers the DL exposure and augments of the UL exposure.  
The DL exposure decreases by 12% (from 93.5 (mV/m) with 48 BSs to 82.3 (mV/m) with 36 BSs) when the number of BS antenna elements vary from 16 to 256 respectively (Table 3). This is explained by the low transmit power of the antenna elements used at the BS and the fewer BSs needed to provide the coverage to the users (in Table 3, with 256 antenna elements, 25% less BSs are needed in comparison with the scenario with 16 antenna elements). However, the increase of the UL exposure is related to the fact that the number of BSs deployed in the area of interest decreases with the number of antenna elements until it reaches an optimal value (with 256 antenna elements) requiring the user to transmit with high powers.  
The same behavior can be observed when the DL and UL exposure effects are combined into a single metric in terms of dose (Figure 9). The increase of the number of antenna elements leads to a 32% reduction of the DL dose (from \(1.88\times 10^{-4}\) with 16 antenna elements to \(1.28\times 10^{-4}\)\((\frac{\text{W-S}}{\text{Kg}})\) with 256 antenna elements, Table 4) given the low input power per antenna element. As the coverage improves with the beamforming gain, the more antenna elements the BS is equipped with the fewer number of BSs the network requires to provide a good coverage to the users who will have to adjust their transmit power accordingly to maintain a good radio link with the BS. This results into a 70% increase of the UL dose: from \(0.9\times 10^{-4}\)\((\frac{\text{W-S}}{\text{Kg}})\) with 16 antenna elements to \(1.53\times 10^{-4}\)\((\frac{\text{W-S}}{\text{Kg}})\) with 256 antennas (see Table 4).  
Figure 8: Impact of the number of antenna elements on the DL and UL exposure (scenario 2, tri-objective optimization).  
The above results, summarized in Tables 3 and 4, have been obtained with an approach to solve multi-objective optimization problem that assigns the same weight or importance to each objective for a simultaneous optimization in order to assess the influence of both the number of users and BS antenna elements. To this regards, the values of the individual fitness functions (\(f_{1},f_{2}\)_and_\(f_{3}\) for the tri-objective optimization and \(f_{1}^{{}^{\prime}}\)_and_\(f_{2}^{{}^{\prime}}\) for the bi-objective one) have been evaluated and reported on the tables as well. It can be observed that, under the assumption of equal importance of the objective functions, \(f_{2}\)_and_\(f_{3}\) are higher compared to \(f_{1}\), meaning that the DL exposure (E-field) and the uplink exposure (UL SAR) have a large impact on the optimization since more BSs with low input power are needed to obtain low levels of EMF exposure.