# Social-Aware Relay Selection for Cooperative Multicast Device-to-Device Communications
## 3 System Model  
We focus on a cooperative multicast context, in which end users receive the requested content not directly from the BS but via other users acting as a relay in D2D communications. In the considered social-physical scenario, the users can communicate directly with other multicast users and exchange shared content mainly if they are friends and according to the quality of the D2D connection links. In particular, we refer here to the classical social-physical architecture, which entails two layers, as in Figure 1. In this context, the source (either the eNodeB or a D2D node) can deliver the same content to a group of D2D devices in a small area, and as the node density increases, various devices can act as relays to forward multicast traffic to the end-devices of the social communities and vice versa. The devices selected as relays may also be interested in receiving the same data content because they could belong to the multicast group. According to the multicast concept, data is delivered if all the destinations have received it. Moreover, we assume that the D2D multicast group can be very far from the BS and that the direct path cannot exist or suffers from a deep attenuation due to path-loss and shadowing effects. A device can leave or join the multicast community according to his mobility. However, we assume that the D2D devices remain in the same location during a D2D communication transmission period (e.g., in the order of milliseconds), while their positions can change across different periods because of users' mobility. The D2D social-trust levels and the forwarding metric related to the channel quality are known at the source and D2D/relays. We consider a relay-assisted network in which a source \(S\) transmits to many destinations \(D_{i}\) with \(i=1....M\) through different relays \(R_{j}\) with \(j=1,...N\), as in Figure 2. We assume flat block fading on all the links, such that the channel coefficients can be assumed to be constant during one time transmission period and can change from one period to the next. One relay is selected among \(N\) to serve the multiple destinations according to the best joint quality of the social and physical layers. The relay nodes use HD decoding and the forward relaying mode. The nodes can retrieve their social relationships information, for example, from the BS, reporting the analysis of content sharing or account information by accessing online social websites such as Facebook, Twitter, YouTube, Instagram, and so forth. These social trust values tend to be stable over the time reporting friendships and acquaintances among users. Moreover, for example, Twitter associates with each tweet the exact location (latitude and longitude), and this might allow the nodes the possibility to know their related positions and also discover their neighbors in mobility. As in [18], the social trust impacts the transmission power of the relay node: if a stronger social-trust relationship exists between the source and relay, the relay provides more power resources to help the source node in retransmission. Therefore, the selected relay \(R_{j}\) transmits to the multiple destinations with a power proportional to the strength of the social-trust value \(\beta_{j}\). For each relay-destination link, the \(\gamma\) signal-to-noise ratio (SNR) at the destination \(D_{i}\) is related to the path-loss, the Rayleigh flat fading, and the zero-mean additive white Gaussian noise (AWGN) with variance \(\sigma_{n}^{2}\), and it can be expressed as  
\[\gamma_{R_{j},D_{i}}=\frac{P_{R_{j}}|h_{R_{j},D_{i}}|^{2}}{\sigma_{n}^{2}d_{R_ {j},D_{j}}^{R}} \tag{1}\]  
where \(P_{R_{j}}\) is the transmit power of the \(j\)th relay, \(d_{R_{j},D_{i}}\) stands for the distance of relay \(R_{j}\) from destinations \(D_{i}\), \(\alpha\) is the path-loss coefficient, and \(h_{R_{j},D_{i}}\) are the Rayleigh fading coefficients. In the multicast transmission mode, minimizing the delivery latency necessary to receive the data to all the destinations is the main objective.