## 2 Background  
Hereafter, we describe the LTE-A protocol stack, as well as point-to-multipoint (P2 MP) D2D communications. An LTE-A network is composed of cells, under the control of a single eNB. UEs are attached to a eNB, and can change the serving eNB through a handover procedure. The eNBs can communicate between themselves using the X2 interface, a logical connection generally implemented on a wired network. The LTE-A protocol stack incorporates a suite of four protocols, shown in Figure 1, which collectively make up layer 2 (i.e., the Data-link layer) of the OSI (Open System Interconnection) stack. The stack is present on both the eNB and the UE. Traversing the LTE-A stack from the top down, and assuming the viewpoint of the eNB, we first find the Packet Data Convergence Protocol (PDCP), which receives IP (Internet Protocol) datagrams, performs cyphering and numbering, and sends them to the Radio Link Control (RLC) layer. RLC Service Data Units (SDUs) are stored in the RLC buffer, and they are fetched by the underlying MAC (Media Access Control) layer when the latter needs to compose a subframe transmission. The RLC may be configured to work in three different modes: transparent (TM), unacknowledged (UM) or acknowledged (AM). The TM mode does not perform any operation. The UM, instead, segments and concatenates RLC SDUs to match the size requested by the MAC layer, on the transmission side. On the reception side, RLC-UM reassembles SDUs, it detects duplicates and performs reordering. The AM adds an ARQ (Automatic Repeat Request) retransmission mechanism on top of UM functionalities. The MAC assembles the RLC Protocol Data Units (PDUs) into Transmission Blocks (TB), adds a MAC header, and sends everything through the physical (PHY) layer for transmission. In LTE-A resources are scheduled by the eNB's MAC layer, at periods of a Transmission Time Interval (TTI) (1 ms). On each TTI, a vector of Resource Blocks (RBs) is allocated to backlogged UEs according to the desired scheduling policy. A TB may occupy a different number of RBs, depending on the Modulation and Coding Scheme (MCS) chosen by the eNB. The latter is selected based on the CQI reported by the UE, which is computed by the UE using proprietary algorithms, and corresponds to the Signal to Interference to Noise Ratio (SINR) perceived by the latter, over a scale of 0 (i.e., very poor) to 15 (i.e., optimal). Each CQI corresponds to a particular MCS, which in turn determines the number of bits that one RB can carry. Hereafter, we will often use the term CQI to refer to the (one and only) MCS that is determined by the former, trading a little accuracy for conciseness. In the downlink (DL), the eNB transmits the TB to the destination UE on the allocated RBs. In the uplink (UL), the eNB issues transmission grants to UEs, specifying which RBs and which MCS each UE can use. In the UL, UEs need means to signal to the eNB that they have backlog. This is done both in band, by transmitting a Buffer Status Report (BSR) when scheduled, or out band, by starting a Random Access (RAC) procedure, to which the eNB reacts by issuing transmission grants in a future TTI. RAC requests from different UEs may collide at the eNB. To mitigate these collisions, the UEs select at random one in 64 preambles, and only RAC requests with the same preamble collide. After a RAC request, a UE sets a timer: If the timer expires without the eNB having sent a grant, that UE waits for a backoff period and re-iterates the requests. The 3 rd Generation Partnership Project (3 GPP) has standardized Network-controlled D2D communications for LTE-A in release 12 [11]. These are point-to-multipoint (or one-to-many) communications having proximate UEs as the endpoints, i.e., without the need to use a two-hop path having the eNB as a relay. A D2D link is also called sidelink (SL). The SL is often allocated in the UL spectrum in a Frequency Division Duplex (FDD) system, since the latter can be expected to be less loaded than the DL one, due to the well-known traffic asymmetry [9].