# Resource Allocation for GBR Services in D2D-Enabled Communication
## 4 Numerical Results  
We consider a single cell for D2D-enabled cellular communications. Unless otherwise stated, the numbers of CUs, DUs, and channels are set to the same value, i.e., \(N=M=L\). CUs and DTs are randomly located within a cell. Different path loss formulas are used for device-to-BS and device-to-device based on the 3 GPP TR36.814 specification [30]. The remaining parameters are summarized in Table 1.  
To better understand the operation of the proposed rate-guarantee scheme, snapshots of channel bandwidths and data rates are shown in Figure 3. For comparison, the sum rate-maximization scheme with a constraint of SINR 11.3 dB is also investigated, where the channel bandwidth is fixed. The proposed scheme changes the channel bandwidth according to the varying channel capacity to guarantee the target data rate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Cell radius & 100 m \\ Maximum distance between DT and DR (\(D_{max}\)) & 10 m, 30 m, 50 m \\ Target data rate(\(R_{T}\)) & 1 Mbps \\ Target SNR (\(\gamma_{T}\)) & 15 dB \\ Maximum transmit power (\(P_{max}\)) & 23 dBm \\ Path loss for BS\(\leftrightarrow\)device & 15.3 + 37.6 log10 (d[m]) \\ Path loss for device\(\leftrightarrow\)device & 28 + 40 log10 (d[m]) \\ \hline \hline \end{tabular}
\begin{tabular}{c} \hline \hline
**Fading** & i.i.d. Rayleigh \\ i.i.d. Racian with K = 7 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Snapshots of channel bandwidths and data rates for six sample points matches. For a fair comparison, the average channel bandwidth was calculated in the proposed scheme and then the same amount of channel bandwidth was allocated for the sum-rate maximization scheme. As expected, the data rate in the sum rate-maximization scheme varied while it was always higher than or equal to the target data rate in the proposed rate-guarantee scheme. On the other hand, in Figure 3a the channel bandwidth is fixed, but it must be varied to guarantee the target rate in Figure 3b. When the channel bandwidth is drawn with two colors, the channel is operated in a dedicated mode due to severe co-channel interference, e.g., see samples 2 and 5 in Figure 3a and sample 6 in Figure 3b. In this case, the proposed rate-guarantee scheme allocates a wider channel bandwidth to meet the target rate, while the sum rate maximization scheme halves the channel bandwidth for CU and DU. Then, the SINR is guaranteed but the data rate becomes lower than the target data rate. Figure 4 investigates the average channel bandwidth by varying the number of CUs for \(D_{max}\) = 10 m and 50 m. As the number of CUs, \(N\), increases, a better match for CU-DU-channel can be found with a higher probability, and then the required channel bandwidth can be reduced. If the distance between devices is short, e.g., 10 m, there is a very high possibility of a Line of Sight (LoS) path. Then, the fading should follow the Rician distribution. We also simulated the proposed scheme under Rician fading for \(D_{max}~{}=~{}10\) m. We assume K factor is 7 dB. Owing to the LoS path component, DUs experience comparatively better channel quality. Then, DTs tend to transmit with a lower power, which results in reduced interference. The average channel bandwidth decreases compared with the Rayleigh fading case but the impact is marginal. The proposed sub-optimal algorithm based on a Lagrangian relaxed algorithm can achieve almost the same performance as that of the optimal algorithm. The optimal 3-D matching problem can be solved by an exhaustive search with huge computational complexity. On the other hand, in the proposed sub-optimal algorithm, the 3-D matching problem is converted into two 2-D matching problems to obtain an approximate solution based on the Hungarian method. With a computational complexity of \(O\!\left(N^{3}\right)\) for each iteration, this computational complexity is much lower than that of the optimal algorithm.