## 1 Introduction
If the network is configured to have just one MBSFN subframe per frame (a frame being 10 subframes), then unicast transmission capacity in the downlink is reduced by 10%, and the worst-case delay for a multicast relaying is still 10 ms, which is non negligible. Clearly, this mechanism is tailored to a continuous, periodic traffic, rather than a sporadic, infrequent one. Second, MBSFN transmissions reach a tracking area, which corresponds to a set of cells. There is no way to geofence the broadcast to smaller, user-defined areas. Third, a single transmission format is selected for the whole tracking area: depending on their channel conditions, some--possibly many--UEs may not be able to decode the message, hence reliable delivery is not guaranteed. eNB-driven relaying using unicast transmissions solve all the above three problems: assuming that the eNB possesses the location of the target UEs (something which is achievable through localization services, empowered by Mobile-edge Computing (MEC) [8]), the eNB may select which UEs to target (hence defining its own geofence), use different transmission formats in order to match their channel conditions, and allocate capacity only on demand. The downside, however, is that this may be too costly in terms of downlink resources: in fact, the resource occupancy grows linearly with the number of UEs. If a 40-byte message has to be relayed to 100 UEs, and the average Channel Quality Indicator (CQI) is 5, three Resource Blocks (RBs) per UE are needed, which means 300 RBs in total, i.e., six subframes entirely devoted to relaying the message within the cell in a 10-MHz bandwidth LTE deployment. This deprives other UEs of bandwidth for a non-negligible time, and consumes energy in the network. Starting from the latest releases, the LTE-A standard has incorporated network-controlled device-to-device (D2D) transmissions, i.e., broadcast transmissions where both endpoints are UEs. These are also foreseen in the upcoming 5G standard. The eNB still allocates the resources for D2D transmission on the so-called sidelink (SL), which is often physically allocated in the UL (uplink) frame [9]. D2D transmissions have a number of attractive features: they do not increase the operator'senergy bill, since data-plane transmissions do not involve the eNB. Moreover, they can occur at reduced power, hence exploit spatial frequency reuse. However, the main downside is that their coverage area is limited to a UE's transmission radius, which is often too small. This paper, which extends our previous work [10], advocates using multihop D2D transmissions to support geographically constrained broadcast services. Multihopping allows these services to scale up to a larger geographical reach, while retaining all the benefits of D2D. In order to engineer a Multihop D2D-based broadcast (MDB) service, it is necessary to enlist the cooperation of both the UE and the eNB, which are interdependent. In fact, UEs must define the broadcast domain, and--being the only nodes that can use the SL--decide if and when to relay messages, keeping into account that an aggressive relaying policy may waste resources or even induce collisions. On the other hand, the network--and, specifically, the eNBs--must allocate resources to allow the diffusion of the broadcast, and possibly coordinating with neighboring eNBs. Resource allocation can be either static or dynamic (i.e., on demand) [11], and both solutions have pros and cons. Our goal is to prove that an MDB service can be realized by using minimal, standard-compliant cooperation from the network infrastructure (which need not even be aware of the very existence of the MDB service), and only running relatively simple application logic within UEs. While several other papers have investigated multihop D2D transmissions in LTE-A (e.g., [12; 13; 14; 15; 16; 17]), this work and its predecessor [10] have been the first paper to propose multihop D2D as a building block for geofenced broadcast services.