# Multicell Interference Management in Device to Device Underlay Cellular Networks
## 6 Performance Evaluation
### Comparative Results  
In this subsection our proposed approach is compared against a state of the art approach in the recent literature [26]. The latter concerns the RB allocation in a multicell D2D underlay network, with the objective of optimizing the total sum of transmission rates of all users of the network, through an approximate better response algorithm under a potential game formulation. In the following, we refer to this approach as Rate Max approach. The comparative process and evaluation is performed in a gradual manner in order to clearly demonstrate and quantify the benefits obtained by the application of each step of our approach, while maintaining fairness in the comparisons. Our approach aims at total interference minimization while the approach of [26] aims at throughput maximization in the RB allocations space. The first step of our approach i.e., Algorithm 1 achieves on average better results with respect to the interference at  
Figure 7: Transmit Power Convergence for a random RB. the receiver of each user compared to [26]. This gives the users the opportunity as it will be shown next, by applying Algorithm 2 to transmit at lower levels on average while a larger number of them satisfies their SINR requirements. Specifically, the following four scenarios are considered and compared:  
* the application of only Algorithm 1 i.e., our proposed algorithm for the RB allocation phase of the problem
* the application of approach [26] for the RB allocation phase of the problem
* the combined application of Algorithms 1 and 2
* the combined application of approach [26] and Algorithm 2 of our approach (for power control). In this subsection, the above approaches are tested and evaluated under the simulation setup used in previous Section 6.1.2, that is the one presented in Table 1 with the SINR requirement equal to 10. As mentioned before, all the numerical results presented in the following refer to statistical average values, as they are obtained by several repetitions of the simulation, with the locations of the cellular and D2D users varying uniformly and randomly in the network topology. The combined application concerns the sequential application of a RB allocation approach and then the application of our proposed power control approach (i.e., Algorithm 2). In Figure 8, the first step of our approach i.e. Algorithm 1 is compared directly to approach [26] in terms of observed interference. As clearly indicated by the corresponding results Algorithm 1 achieves a considerable interference reduction compared to [26]. Specifically, the average reduction of our approach with respect to [26] is calculated as approximately 50% per user. It should be clarified that this value refers to the net value of interference, while the vertical axis of Figure 8 is expressed in decibel Watts (dBWatts). It can be seen that the largest benefit concerns the cellular users, where the respective reduction is almost 80%. In Figure 9, the respective transmission rates per Hertz for each user are shown. It can be seen that although Algorithm 1 targets at interference minimization, under fixed transmission power obtains comparable to [26] performance with respect to the achievable transmission rate. By applying Algorithm 2 after the execution of Algorithm 1 and approach [26] respectively, we compare and analyse the averaging results with respect to the transmission power and the number of users satisfying their SINR requirements. In Figure 10, it is demonstrated that the required transmission power under our proposed approach reduces radically, i.e., by 70% on average with respect to the initial transmission power values and by 30% with respect to the combined approach (Rate Max + Algorithm 2). Lastly, the number of users in the system who are able to satisfy their SINR requirement also increases following both approaches, with our approach outperforming by 12% the (Rate Max + Algorithm 2) (Figure 11). Figure 10: Comparison of the transmission power for the combined approaches.