## 6 Performance Evaluation and Discussion
### Simulation Results
#### 6.2.2 MTC Power Allocation and Battery Energy State  
Extensive simulations are performed by considering different user densities and with changing levels of interference and battery energy levels to evaluate the impact of proposed power control scheme. The results of the simulation were analyzed by varying the MTC user densities present in service area of the cell for three particular cases. Case-I: low density scenario (150 nodes), Case-II: medium density scenario (300 nodes) and Case-III: high density scenario (500 nodes). Figure 8 shows the results obtained as a result of different simulations performed on described MTC user scenarios. The allocated power is compared for different energy levels of the batteries of these devices.  
Figure 8a depicts power allocation pattern for Case-I with 150 MTC users in the cell along with a random number of HTC users. The convergence condition for this simulation setup is taken as the point of satisfaction of the reliability condition for MTC users. Higher initial battery energy allocate higher initial transmit power to the MTC users and devices with lower initial battery energy tend to conserve energy by allocating lower transmit powers. The allocated transmit power is adapted to a lower level after sometime for high battery energy devices owing to battery discharge cycle and the reliability condition. Lower energy level devices are allocated lower transmit power at the start of the MFG which is gradually increased with the progression of the game. This is partially due to lower MTC node density which incurs less interference on MTC users as compared to more dense scenarios and partially due to the decreasing powers allocated to MTC users having higher initial battery energy. It is observed that the effect of the interference state is simpler due to the relatively lower MTC user density. The results are shown in Figure 8b, which were obtained when the MTC user density (300 nodes) is increased to observe the effect on the power allocation. More power is allocated to each MTC node because of increased interference due to the increased MTC device numbers. Similar to the low MTC density case, higher initial battery level devices are allocated more transmission power. After some time, the allocated amount of power declines because the available energy in the batteries of MTC devices decreases and the interference increases as a result of relatively higher MTC device density. Figure 8c depicts the case with the highest MTC user density causing increased interference experienced by MTC devices and the consequent need for a higher amount of allocated power to reach the SINR threshold. MTC users with high initial battery energy levels perform the same way as the low and medium device density cases with higher power allocations initially with an eventual decline with the progression of the MFG. The MTC devices with lower levels of battery energy initially allocate power levels required to be within the SINR threshold. So, the transmit power increases until they satisfy the defined criterion with the power levels being held constant until the end of the game simulation maintained for the duration of the game or upon a significant drop in the battery level of the MTC devices.  
Figure 7: Power distributions at varying time instances with equilibrium evolution, (**a**) T = 2 s, (**b**) T = 3.5 s, (**c**) T = 5 s.