# Resource Allocation for GBR Services in D2D-Enabled Communication
## 2 System Model  
Figure 1 shows an example of channel assignments for the CU, DU, and channel, where \(N\) CUs and \(M\) DUs are serviced with \(L\) channels over a cellular uplink in a single cell environment. Different colors imply different channels and hence, different matchings. The solid blue lines indicate the desired signals and the red dashed lines are co-channel interference. A DU is formed between a D2D transmitter (DT) and a D2D receiver (DR). The DR is located uniformly within a circle with a radius of \(D_{max}\) and its center is at the DT. For each matching of 3-tuple (CU \(n\), DU \(m\), channel \(l\)), the SINR of the CU and DU are different, depending on the channel gain in the links as well as the channel sharing mode. On channel \(l\), the channel gain between CU \(n\) and the BS is denoted as \(\rho_{n,0}^{l}\), and it is \(\rho_{n,m}^{l}\) between CU \(n\) and DR \(m\). Channel gain includes path loss and fading, where fading follows an independent and identically distributed (i.i.d.) Rayleigh distribution. Similarly, the channel gains from DT \(m\) to DR \(m\) and to the BS are denoted as \(h_{m,m}^{l}\) and \(h_{m,0}^{l}\), respectively.  
Figure 2a shows a comparison of the channel bandwidth needed to guarantee the target data rate in relation to matching the CU and DU in each channel. The size of the box corresponds to the bandwidth required for the CU-DU matching to guarantee the target data rate. When CU \(n\) and DU \(m\) are matched on channel \(l\), the required channel bandwidth is determined by whether it is in either a shared mode or a dedicated mode. If there is one box for one matching, the CU and DU share the channel resource in a shared mode, where a single channel bandwidth \(B_{n,m}^{l}(s)\) is allocated. If there are two boxes, it is in a dedicated mode where the matched CU and DU use orthogonal resources \(B_{n_{C}}^{l}\) and \(B_{m_{D}}^{l}\) for CU \(n\) and DU \(m\), respectively and the channel bandwith comes to their sum, \(B_{n,m}^{l}(ns)~{}=~{}B_{n_{C}}^{l}+B_{m_{D}}^{l}\).  
Figure 1: System Model.  
Two matching samples A and B were selected and are described in more detail in Figure 2b. For sample A, channel \(I\) is matched for CU \(N\) and DU \(I\). The channel bandwidth for the dedicated mode, \(B_{N,1}^{1}(ns)\) is smaller than the channel bandwidth for the shared mode, \(B_{N,1}^{1}(s)\). Accordingly, the dedicated mode was chosen and its channel bandwidth denoted as \(B_{N,1}^{1}\). For sample B, the shared mode is more beneficial than the dedicated mode in terms of channel bandwith. The channel bandwidth becomes \(B_{1,1}^{1}(s)\) for a matching of CU \(I\) and DU \(I\).  
Figure 2c shows a number of matching combinations, together with their total channel bandwidth. The matching combination represents a collection of all the CUs, DUs matchings, and channels without multiple assignments.  
In this study, we aim to find a resource allocation method that minimizes the total channel bandwidth while all users have data rates greater than or equal to the target data rate. Accordingly, we should compare the total channel bandwidths of all the matching combinations to find the optimal one with the smallest total bandwidth. This exhaustive search requires a huge computational complexity of \(O\left(N^{N}N!\right)\) when the numbers of CUs, DUs, and channels are all equal to \(N\)[23].