# Energy Efficient IoT Data Collection in Smart Cities Exploiting D2D Communications
## 3 Reference System Model
### Energy Efficient IoT Data Uploading  
Since most IoT applications are characterized by transmitting small amounts of data, the objective of reducing the power consumption in the uplink can be reached by adopting a more robust MCS which requires a lower transmit power for the device. A more robust MCS guarantees a smaller TBS, which is however acceptable as long as it can contain the data to upload. On the other hand, it might also happen that adopting a very robust MCS over multiple RBs is also more energy efficient. For an energy efficient _cellular mode_ IoT data uploading, an optimal MCS selection has been proposed in [14] where IoT data are transmitted to the eNodeB with the lowest energy consumption is possible. To evaluate the power savings with the optimal MCS selection, we first report the standard transmission power \(P_{tx}\) formulation [48] for a generic UE in a subframe:  
\[P_{tx}=\min(P_{max},P_{0}+10\cdot log(r)+\alpha\cdot PL+\delta_{mcs}+f(\Delta_{ i})) \tag{2}\]  
where \(P_{max}\) is the maximum transmitted power of the UE, \(r\) is the number of Physical RBs (PRBs) allocated per user, \(P_{0}\) is the target power in one RB as specified by the eNodeB to reliably demodulate and decode the data, \(\alpha\) is the path loss compensation factor specified by the eNodeB in a [0,1] range, \(PL\) is the estimated UE Path Loss in uplink, \(\delta_{mcs}\) is an MCS dependent offset which can be seen as the ratio between the target MCS and the basic MCS according to the UE feedback, and \(f(\Delta_{i})\) is the closed loop correction function. In particular, according to the \(\delta_{mcs}\) when using a higher/lower MCS level, the corresponding transmit power should be increased/decreased. As the authors in [14] discuss, when the number of RBs is fixed to \(r\), the optimal MCS to be adopted for an energy efficient solution, _i.e._, \(MCS_{r}^{*}\), is the one maximizing the TBS utilization rate:  
\[MCS_{r}^{*}=\operatorname*{arg\,max}_{MCS} \left(\frac{D}{TBS(MCS,r)}\right)\] s.t. \[D\leq TBS(MCS,r) \tag{3}\]  
where \(TBS(MCS,r)\) is the TBS determined by the MCS and the number of allocated resources \(r\). With reference to Figure 1(a), when the proposed optimization is implemented in subframe \(n+1\) a lower MCS is being adopted w.r.t. the MCS adopted in subframe \(n\). This maximization guarantees that the data is actually sent with the minimum TBS is needed, and an energy saving can be obtained due to a power decrease related to a lower MCS level. However, having a fixed value for \(r\) means that a UE needs to necessarily use all the allocated resources \(r\). Removing this constraint, so that the number of RBs is not fixed, we can determine the most energy efficient MCS as:  
\[MCS^{*}=\operatorname*{arg\,min}_{MCS;}(\delta_{mcs}(MCS_{r}^{*})\cdot r) \tag{4}\]  
where \(\delta_{mcs}(MCS_{r}^{*})\) is the power offset of each optimal MCS to the basic MCS. In such a situation, as represented in Figure 1(b) (see final configuration in subframe \(n+1\) after the optimization is implemented, compared to subframe \(n\)), the proposed minimization allows to find the MCS with the smallest transmit power as this is equal to: \(P=Pbasic\cdot\delta_{mcs}\cdot r\), where \(Pbasic\) is the power per RB for the basic MCS, \(\delta_{mcs}\) is the power offset between MCS and the basic MCS. Thus, a simple though effective solution to find the most energy efficient combination of MCS and number of RBs needed is:  
* select for each RB number \(n=[1,r]\) the MCS according to Equation (3);
* from all the resulting MCS values, select the one minimizing the power transmission according to Equation (4). In particular, in our problem setting, the value for \(r\) is the maximum number of allocated resources to the single device according to the radio resource allocation implemented by the eNodeB, _i.e._, the Round Robin policy in our case.