## 4 D2D Group Communication Scheme with Bidirectional and InCrentental A-Star (BICA*) Routing
### Path Selection Algorithm
We compare the performance of four approaches based on a number of performance metrics, including throughput, delay time, average hop-count, and satisfaction rate. We also examine the effects of different factors, such as the number of UEs, speed of movement, longest D2D link, and group size. Figure 11 presents the throughput for different numbers of UEs when the UEs remain stationary. A* and our approach, which take into account the channel conditions, outperform Greedy and TSRS, which consider only geographic information. The interference is less severe when there are only a small number of UEs. Therefore, there is less performance difference among different approaches. As the number of UEs increases, the performance difference is displayed. Figure 12 shows the throughput for different group sizes. There are 40 UEs in each group. There is a greater chance for path rupture for a larger group radius and, therefore, more immense group expanse. The A* algorithm needs to recalculate a new path from scratch, resulting in a comparative degradation in throughput. Our approach has a 12% improvement over A*. With bidirectional search, the proposed approach is more capable of finding a path within the delay budget. For Greedy and TSRS, a larger group size implies a longer distance between UEs. The received power and the throughput decrease accordingly. \begin{table}
\begin{tabular}{c c} \hline
**Type of File** & **Value** \\ \hline \multirow{3}{*}{Text/HTML} & QCI: 9 \\  & Packet Delay Budget: 300 ms; Resource Type: non-GBR \\  & Minimum File Size: 1 K bytes; Maximum File Size: 4000 K bytes \\ \hline \multirow{3}{*}{Video} & QCI: 4 \\  & Packet Delay Budget: 150 ms; Resource Type: GBR \\  & Minimum File Size: 72.5 M bytes; Maximum File Size: 225 M bytes \\ \hline \multirow{3}{*}{Music} & QCI: 6 \\  & Packet Delay Budget: 300 ms; Resource Type: non-GBR \\  & Minimum File Size: 2.4 M bytes; Maximum File Size: 12 M bytes \\ \hline \end{tabular}
\end{table} 
Table 2: Types and parameters of contents. Figure 13 depicts the throughput for different maximal D2D link lengths. There are 40 UEs in a group. The group radius is 100 m. For all approaches, as the length of the maximal D2D link increases, the received signal strength and therefore the throughput lessen accordingly. When the link length is short, there is more chance for link rupture. The A* algorithm needs to recalculate the entire search tree, and it might exceed the delay budget. Figure 11: Throughput vs. number of UEs. Figure 12: Throughput vs. group radius. Figure 15 shows the results of delay when UEs are on the move. Greedy and TSRS cannot react quickly enough and therefore have more chances of picking up inferior paths. On the other hand, A* and the proposed approach can adapt themselves better to the topological change. There is a slight performance difference between A* and the proposed approach. The A* algorithm recalculates a new path in response to topological change. Figure 14: Delay vs. number of UEs. Figure 13: Throughput vs. D2D link length. However, as the moving speed increases, A* may fail to catch up with the changes. On the other hand, the BICA* search endows the proposed approach with the rapid reaction capability to topological changes, as expected. Figure 16 shows the relationship between the average hop count and the number of UEs. It can be seen that A* and the proposed approach tend to have paths with a higher hop count. The path selection is biased by the utility function. Although there may be many hops, all hops are of high throughput and low delay, resulting in configuring paths of good QoS. Figures 17 and 18 show the utility values of delay and throughput when UEs are on the move. For all approaches, delay and throughput degrade as the moving speed increases. A*

Figure 16: Hop count vs. number of UEs. Figure 15: Delay vs. UE’s moving speed. and our proposed approach have superior performance to Greedy and TSRS since channel conditions are considered. The proposed approach has performance improvement over A* because of its BICA* algorithm.