# Multicell Interference Management in Device to Device Underlay Cellular Networks
## 6 Performance Evaluation
### Proposed Approach Properties and Operation  
#### 6.1.1 RB Allocation  
In this subsection, the effectiveness and efficiency of the first step of our approach i.e., Algorithm 1 is shown. The simulation setup and the corresponding parameters considered are shown in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of evolved NodeBs (eNBs) & 3 \\ Number of available Resource Blocks (RBs) per eNB & 10 \\ Number of Device to Device (D2D) cells per eNB & 16 \\ Number of cellular users per eNB & 8 \\ Cellular Cell Radius & 300 m \\ D2D Cell Radius & 30 m \\ Channel Gains Loss Exponent & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Setup.  
Similarly, in Figure 3, the final RB allocation as the outcome of the application of the first step of our approach (i.e., Algorithm 1) to all users of the network is shown. It is clearly demonstrated that the RB reuse efficiency has been significantly improved. Specifically, considering as metric of such efficiency the achieved reuse distance of a common RB--denoting the distance between a transmitter and a different D2D receiver who share the same RB--it is observed that the reuse distance of all RBs increases drastically. Precisely, the average minimum reuse distance of every RB, before the application of Algorithm 1, was approximately 15 m and after the application of Algorithm 1 it increases to approximately 35 m, corresponding to an improvement of 133%.  
In Figure 4, the evolution of the total interference in the network is demonstrated with respect to the number of iterations needed for Algorithm 1 to converge. It is shown that Algorithm 1 always reduces the total interference after each step of its execution. This also verifies experimentally the respective theoretical property of potential games [32], as the one considered in this paper. The required number of iterations for convergence was quite low with respect to the total number of players of the game. Precisely, the required number was about 3-4 times the total number of players involved in the game. The total interference reduction compared to the corresponding value based on the initial random allocation is approximately 80%. It is noted that we have also verified experimentally that Algorithm 1 converges to a stable outcome under any initial RB allocation, while the range of the optimal values of the total interference was within 5% difference of the observed maximum value.  
Subsequently, in Figure 5, we show the average interference reduction for every user of the network after the application of Algorithm 1. For clarity reasons, it is mentioned that users 1-24 in all figures represent cellular users, while the users 25 and beyond represent D2D users.  
Figure 4: Total Interference Evolution.  
Based on these results, we observe that Algorithm 1 achieves a significant reduction to the interference, sensed at every user of the network. Precisely, the mean interference reduction is on average 93%. This in turn can be translated to significant improvements in the achievable transmission rate as well, as it is observed in Figure 6, where the achieved transmission rate per used bandwidth unit (i.e., spectral efficiency) is shown for every user of the network. The mean rate increase with respect to the initial achievable transmission rate is calculated at approximately 34%.