# User-Information-Aware D2D Multicast File Distribution Mechanism
## 6 Cluster Head Selection Mechanism
### D2D Multicast Utility Metric  
As shown in Figure 1, several service requesters and potential service requesters are randomly distributed in the grid. In the fourth section, with consideration of the user's willingness and other information, the potential service requesters are selected to form the users set \(U_{C}\) of D2D multicast cluster together with the service requesters. As shown in Figure 3, CU denotes the cellular user, DU denotes D2D user, and CH denotes the cluster head of the D2D multicast cluster. D2D users can reuse the uplink channel resource with cellular user, so the D2D multicast receivers will be disturbed by cellular user's transmit signals. In this paper, the channel model follows path fading and Rayleigh fading, each channel obeys one-mean Rayleigh fading independently [31]. When the cluster head CH and cellular user CU transmit signals with constant power \(P_{h}\) and \(P_{c}\) respectively, the SINR for any D2D multicast receiver \(u_{i}\) in the set \(U_{C}\) can be expressed as:  
\[SINR_{h,i}=\frac{P_{h}d_{h,i}^{-a}h_{0}}{P_{c}d_{c,i}^{-a}h_{0}+\sigma^{2}} \tag{18}\]  
where, \(d_{h,i}\) is the distance between the cluster head CH and the D2D multicast receiver \(u_{i}\), \(d_{c,i}\) is the distance between the cellular user CU and the D2D multicast receiver \(u_{i}\), \(\alpha\) is the path loss exponent, \(h_{0}\) is the Gaussian channel coefficient constant, \(\sigma^{2}\) is zero-mean the Gaussian noise. The CH and \(u_{i}\) are members of the user set \(U_{C}\), and each user in the set \(U_{C}\) may be selected as cluster head. Due to the differences of channel quality for users, the received SINR of D2D multicast users have very differences when select different user as cluster head. Assuming that the relative distance between all users in set \(U_{C}\) are known by the system, and let \(\mathbf{D}\) denotes the distance matrix about the user set \(U_{C}\), it can be expressed as:  
\[\mathbf{D}=\left[ \begin{array}{ccc}d_{1,1}&\ldots&d_{1,|U_{C}|}\\ \ldots&\ldots&\ldots\\ d_{|U_{C}|,1}&\ldots&d_{|U_{C}|,|U_{C}|}\end{array} \right]\ |U_{C}|\times|U_{C}| \tag{19}\]  
Notably, if \(i=j\), then \(d_{i,j}=0\). According to Equations (18) and (19), when user \(u_{i}\in U_{C}\) is selected as cluster head, and its transmission power is \(P_{h}\), the SINR for each D2D multicast receiver can be calculated easily. Thereby, the channel quality matrix about the user set \(U_{C}\) can be denoted by:  
\[\mathbf{\Gamma}_{simr}=\left[ \begin{array}{ccc}\infty&\ldots&SINR_{1,|U_{C}| }\\ \ldots&\ldots&\ldots\\ SINR_{|U_{C}|,1}&\ldots&\infty\end{array} \right]_{|U_{C}|\times|U_{C}|} \tag{20}\]  
where \(SINR_{i,j}\) is the receive signal to interference and noise ratio of user \(u_{j}\) when user \(u_{i}\) is selected as cluster head. Obviously, if \(i=j\), then \(SINR_{i,j}=\infty\), because the transmission distance is 0, the signal power does not attenuate. According to Equation (2), the total throughput of D2D multicast communication is related to the number of D2D multicast receivers and the worst receive signal to interference and noise ratio. The number of D2D multicast receivers is \(|U_{C}|-1\), and the worst receive signal to interference and noise  
Figure 3: D2D multicast communication interference diagram. ratio \(SINR_{i}^{min}\) can be achieved easily by traversing the channel quality matrix \(\Gamma_{sint}\). The \(SINR_{i}^{min}\) is the receive signal to interference and noise ratio with the lowest channel quality's user in the set \(U_{C}\) when user \(u_{i}\) is selected as cluster head. Therefore, when selected user \(u_{i}\) as cluster head, the total throughput of D2D multicast communication can be calculated as:  
\[C_{i}=B(|U_{C}|-1)\log_{2}\Bigl{(}1+SINR_{i}^{min}\Bigr{)} \tag{21}\]  
where \(B\) is the channel bandwidth. In fact, the throughput model shown in Equation (21) ignores the transmission performance influence by the strength of social relationships among users.