## 3 System Model  
NR [24] is the new OFDM-based air interface designed for 5G systems. Orthogonal Multiple Access (OMA) is the NR basic multiple access scheme for both downlink and uplink data transmissions, where time and frequency physical resources of different users/devices do not overlap.  
NR supports optimized OFDM-based waveforms, thanks to scalable numerology and Transmission Time Interval (TTI). This brings to different values of Subcarrier Spacing (SCS), scaling from 15 to 480 KHz. As highlighted in Equation (1), the SCS \(\Delta f\) values depend on the numerology \(\mu\).  
\[\Delta f=15 KHz\times 2^{\mu} \tag{1}\]  
Downlink and uplink transmissions are organized in frames. Each frame consists of 10 subframes, each lasting at maximum 1 ms. With the introduction of SCS, the number of slots in a frame depends on the numerology, and a slot can last from 31.25 \(\mu\)s to 1 ms. More details are shown in Table 1. A slot is 14 OFDM symbols with 61 available configurations [24]. OFDM symbols in a slot can be classified as _downlink_ (denoted D), _flexible_ (denoted X), or _uplink_ (denoted U). In a slot in a downlink frame, downlink transmissions only occur in \(D\) or \(X\) symbols. In a slot in an uplink frame, uplink transmissions only occur in \(U\) or \(X\) symbols.  
NR is designed to support a wide variety of 5G services and devices, deployments and spectrum ranges. The available radio spectrum is managed in terms of Resource Blocks (RBs). In the frequency domain, each RB corresponds to 12 consecutive and equally spaced subcarriers. Differently from Long Term Evolution (LTE), where the subcarrier spacing is 15 KHz and a RB spans 180 KHz (15 KHz \(\times\) 12), in NR the RB bandwidth varies with the numerology (i.e., with \(\mu=0\), RB = 180 KHz; with \(\mu=1\), RB = 360 KHz; with \(\mu=2\), RB = 720 KHz; and so on).  
In NR, the new base station is named as next-generation Node B (simply gNodeB or gNB). Each MTC device or sensor/machine node transmits its channel quality indicator (CQI) to the gNodeB that performs scheduling procedures, by setting the MCS transmission parameters and assigning radio resources to the scheduled MTC device at every TTI.  
Each MTC device can support two transmission modes: the _cellular mode_, when the MTC device communicates through the gNodeB; and the _D2D mode_, when the MTC device bypasses  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mu\) & \(\Delta f\) & No. Symbols Per Slot & No. Slots Per Frame & No. Slots Per Subframe & Time Slot \\ \hline
0 & 15 KHz & 14 & 10 & 1 & 1000 \(\mu\)s \\
1 & 30 KHz & 14 & 20 & 2 & 500 \(\mu\)s \\
2 & 60 KHz & 14 & 40 & 4 & 250 \(\mu\)s \\
3 & 120 KHz & 14 & 80 & 8 & 125 \(\mu\)s \\
4 & 240 KHz & 14 & 160 & 16 & 62.5 \(\mu\)s \\
5 & 480 KHz & 14 & 320 & 32 & 31.25 \(\mu\)s \\ \hline \hline \end{tabular}
\end{table}
Table 1: NR numerology, Subcarrier Spacing, Number of OFDM symbols per slot, Number of slots per frame, Number of slots per subframe and Time Slot.  
the gNodeB and exploits direct connections (D2D link or sidelink). In this paper, we assume that D2D communications take place in the uplink subframe. This assumption guarantees a more efficient radio resources reuse [25]. By doing so, some downlink resources are destined for other services (i.e., unicast  requests). The performance of the proposed EED2D-SF scheme is also affected by the considered frame configuration, since each configuration implies a different number and position of Uplink and Downlink subframes within the frame.