D2D discovery
In this system model, decision of pairing was performed by a centralized entity (i.e. D2D controller) based on SINR measurement of each D2D link. Therefore, in D2D discovery phase, every device calculates the SINR for every potential pair based on exchanged discovery signals. After that, measured SINRs were transmitted to the D2D controller.

also D2D controller selected the device that will act as the relay node (BS?Device?Device). Bolded word Device means connected device to the serving BS plays the role of relay. Thus, each device transmits the SINR of its serving BS to D2D controller. Transmitted information was used to select the relay node by D2D controller.
The procedure below was performed by each device that compute SINR related to all potential D2D pairs in addition of serving BS. Based on measurement of exchanged discovery signals, that transmitted in predefined OFDM subcarriers (e.g. Physical Side link Discovery Channel).
total power received by a Device u from the Device v over the discovery channel k was given by the sum of: useful signal P_k^((v) ) (u) g_k^((v) ) (u), interference from other Devices ?_(d?D.d?u)??P_k^((v) ) (u) g_k^((v) ) (u)?,interference from BSs ?_(i?M)??P_(bs.k)^((i)) (u)g_(bs.k)^((i) ) (u)? and thermal noise Nth. In case of the 3D BF scenario, we suppose serving BS was not transmitted directly to the evaluated device through the discovery phase, thus, the SINR ?_k^((v) ) (u) could be expressed as follows:

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The received SINR at Device u from a serving BS i can be expressed as follows:

Then, the SINR of serving BS for a Device u transmitted through discovery channel k could be expressed as ?_k^’ (u). When D2D controller receive the measurements, therefore Algorithm 1 was used for peering devices. SINR threshold? ??_D2D needs to be satisfied by the two devices to allocate channel k to a D2D link. The threshold? ??_D2D let us guarantee a minimal throughput level.

In Algorithm 1, a device u sends SINR of potential D2D pairs ?_k^((v) ) (u)?v?D and SINR of serving server?_k^’ (u) to the D2D controller in order to evaluate each potential D2D connection j ? D. Initially, it check each measured SINR between devices u and v (u ?v and u ? v) and chooses the minimum SINR (D2D) for comparing it with required SINR threshold? ??_D2D. A D2D connection was not possible when D2D was small than ? ??_D2D, else case a D2D connection was established. Next that, relay node is selected in order to possessing best connection between device and serving BS (?_BS) taking into account the SINR measurement ?_k^’ (u) and ?_k^’ (v).
At last, the D2D controller makes signaling procedure in order to set up a D2D connection between devices u and v. This algorithm is applied once new device is linked to the network or when new SINR are received by the D2D controller.


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