# Resource Allocation for GBR Services in D2D-Enabled Communication
## 3 Resource Allocation for GBR Services
### Channel Bandwidth for Arbitrary Matching, \(B_{n,m}^{l}\) and Channel Sharing Mode Selection  
When the channel is divided into two orthogonal resources in a dedicated mode:  
The channel bandwidth of channel \(l\), \(\mathrm{B}_{n,m}^{l}\) (\(ns\)) is divided into \(B_{n_{C}}^{l}\) and \(B_{m_{D}}^{l}\) exclusively for CU \(n\) and DU \(m\), respectively. Note that since there is no co-channel interference between CU and DU, SINR can be simply reduced to SNR. The transmit power \(P_{n_{C}}^{l}\) of CU \(n\) is controlled to meet the SNR target \(\gamma_{T}\) at the BS. Since the transmit power is power-limited at its maximum, it is determined as follows:  
\[P_{n_{C}}^{l}\ =\ \left\{\begin{array}{cc}\gamma_{T}\rho_{n,0}^{l}N_{0}B_{n_{C} }^{l}&,\ P_{n_{C}}^{l}\leq P_{max}\\ P_{max}&,otherwise\end{array}\right., \tag{1}\]  
where \(B_{n_{C}}^{l}\) is the channel bandwidth allocated to CU \(n\) on channel \(l\) and \(N_{0}\) is the noise power density. Generally, \(D_{max}\) is much shorter than the cell radius. And hence, it is assumed that the transmit power of DT \(m\), \(P_{m_{D}}^{l}\) is not limited by the maximum transmit power and can be expressed as  
\[P_{m_{D}}^{l}\ =\ \gamma_{T}N_{0}h_{m,m}^{l}B_{m_{D}}^{l}, \tag{2}\]  
where \(B_{m_{D}}^{l}\) is the channel bandwidth allocated to DU \(m\) on channel \(l\). For simplicity, the CU and DU are assumed to have the same SNR target for transmit power control.  
When the transmit power is enough to compensate for the channel loss (the channel loss is the inverse of the channel gain), the CU can meet the SNR target. However, as the channel loss increases, the received SNR may be less than \(\gamma_{T}\) because of the maximum power limit. Then, the bandwidth should be increased so that the data rate of CU \(n\) meets \(R_{T}\). The bandwidth for CU \(n\) on channel \(l\) to meet the target data rate is expressed as  
\[B_{n_{C}}^{l}\ =\ \frac{R_{T}}{\log_{2}\Bigl{(}1+\gamma_{n_{C}}^{l}\Bigr{)}}. \tag{3}\]  
On the other hand, since the channel loss between DT and DR is assumed to be small enough, the SNR can always be kept at \(\gamma_{T}\). So, the bandwidth for DU \(m\), \(B_{m_{D}}^{l}\) can be given by replacing \(\gamma_{n_{C}}^{l}\) with \(\gamma_{T}\) in (3). Now, the channel bandwidth for a dedicated mode, \(B_{n,m}^{l}(ns)\) can be obtained by adding the two bandwidths for CU \(n\) and DU \(m\);  
\[B_{n,m}^{l}(ns)\ =\ \ B_{n_{C}}^{l}+B_{m_{D}}^{l}. \tag{4}\]  
When the channel is shared in a shared mode:  
Only a single channel bandwidth, \(B_{n,m}^{l}(s)\) is allocated to both CU \(n\) and DU \(m\) on channel \(l\). Then, the transmit powers in (1) and (2) are determined with \(B_{n_{C}}^{l}\ =\ B_{m_{D}}^{l}\ =\ B_{n,m}^{l}(s)\). Since the same channel is shared by both CU and DU, a co-channel interference exists between them. The SINR for CU \(n\) matched with DU \(m\) on channel \(l\), \(\gamma_{(n),m}^{l}\) can be expressed as  
\[\gamma_{(n),m}^{l}\ =\ \frac{p_{n_{C}}^{l}/p_{n,0}^{l}}{N_{0}+p_{m_{D}}^{l}/h_ {m,0}^{l}}, \tag{5}\]  
where \(p_{n_{C}}^{l}\) is the power density of CU \(n\) on channel \(l\) and is obtained by dividing the transmit power by the channel bandwidth, i.e., \  
the channel bandwidth \(B_{n,m}^{l}(s)\) can be obtained from the above relations while guaranteeing the target rate for both users:  
\[B_{n,m}^{l}(s)\ =\ max\Bigg{\{}\frac{R_{T}}{\log_{2}\!\left(1+\gamma_{(n),m}^{l} \right)^{\prime}}\!,\frac{R_{T}}{\log_{2}\!\left(1+\gamma_{n,(m)}^{l}\right)} \Bigg{\}}. \tag{6}\]  
A user requiring a wider channel bandwidth can exactly meet the target rate, while other users may achieve a data rate higher than \(R_{T}\) since the channel bandwidth becomes wider than required.  
Channel bandwidth and channel sharing mode selection:  
The channel sharing mode requiring a smaller channel bandwidth is selected for channel \(l\) matched to CU \(n\) and DU \(m\). Then, the channel bandwidth is decided as  
\[B_{n,m}^{l}\ =\ \min\!\left\{B_{n,m}^{l}\ (ns),B_{n,m}^{l}(s)\right\}. \tag{7}\]