# Energy Efficient IoT Data Collection in Smart Cities Exploiting D2D Communications
## 3 Reference System Model
### LTE Standard IoT Data Uploading  
Let us consider an LTE-A eNodeB that receives data from a set of IoT devices within a single TTI. If the data to be sent to the eNodeB requires multiple TTIs, the same solution is applied in the consecutive TTIs. Data uploading in the standard _cellular mode_ occurs through the activation of separate links from each UE to the eNodeB after the CQI collection procedure.  
Formally, let \(\mathcal{K}\) be the set of \(K\) LTE-A equipped devices, with each device having some data \(d_{k}\) to upload in a TTI. Let \(C\) be the number of available CQI levels and let \(c_{k}\in\{1,2,\ldots,C\}\) be the CQI reported by device \(k\in\mathcal{K}\) in the uplink. Each CQI level is associated to a given supported MCS. For a given MCS value \(m\), the bits per RB that can be sent depend on the spectral efficiency for the given MCS, \(b_{m}\) expressed in bit/s/Hz as reported in Table 1. Moreover, let \(\mathcal{R}\) be the set of \(R\) radio resources (the RBs) that can be allocated to the UEs in \(\mathcal{K}\).  
We assume the eNodeB implements a simple Round Robin allocation, whereby the whole set of radio resources is equally shared by all _cellular mode_ UEs. Moreover, we assume that the transmission power for a device is equally distributed over the available RBs. Hence, the maximum uplink resources allocated to each UE will be \(r_{k}=\lceil R/K\rceil\), \(\forall k\in\mathcal{K}\). The maximum data rate for UE \(k\) is proportional to the number of allocated resources \(r_{k}\) and the CQI level \(c_{k}\). However, the IoT data is of small size (a few bytes) and typically, one RB per single TTI is enough to upload all the data and, as also pointed out in [14], leads to a low usage of the RB. In particular, the minimum IoT data size to be transmitted over an LTE network is 1 byte, to which the overhead from different headers (IP/UDP/TCP/RTP protocols) has to be added, in the range of 20-60 bytes. However, header compression solutions exist, such as the Routing and cOde-waveform CHannelization (ROCH) protocol, which drastically reduce the header size [47]. Therefore, for a single transmission we have to consider the following terms: (i) IoT application data 1 byte; (ii) a ROCH header, which can be either 1 (IPv4/UDP and IPv4/UDP/RTP cases), 3 (IPv6/UDP and IPv4/UDP/RTP cases) or 4 bytes long (IPv4/TCP and IPv6/TCP cases); (iii) a PDCP header that can be either 1 or 2 bytes long; (iv) an RLC header that can be either 1 or 2 bytes long; (v) a MAC header that can be either 2 or 3 bytes long. As a result the minimum amount of data to be transmitted is 6 bytes, whereas for IoT data also a minimum of a few additional metadata bytes should be considered.  
The low efficient use of the radio resources has, at the same time, an impact on energy efficiency. In particular, with the classic _cellular mode_ IoT data uploading, the energy consumption is intrinsically determined by the amount of data to upload and the efficiency \(b_{m}\) for the MCS of each device. In general, we can define the energy efficiency as the ratio between the amount of data to upload expressed in bits, \(D\), and the energy consumption, \(E\), \(\eta=D/E\). The energy consumption for user \(k\) over the LTE-A link can be computed as the product of the transmit power \(P_{k}\) per single RB, the number of allocated RBs \(r_{k}\) and the transmission time, _i.e._, the TTI: \(E_{k}=P_{k}\cdot r_{k}\cdot TTI\). Thus, the overall energy efficiency for the IoT data uploading from all \(K\) LTE-A equipped devices in _cellular mode_ can be computed as:  
\[\eta=\sum_{k\in\mathcal{K}}\frac{d_{k}}{P_{k}\cdot r_{k}\cdot TTI} \tag{1}\]