# A Throughput and Energy Efficiency Scheme for Unlicensed Massive Machine Type Communications +
## 2 System Model  
In order to do the throughput and energy efficiency analysis in this paper, we use a dynamic spectrum access network model, shown in Figure 1. The two types of nodes in this model, which are licensed and unlicensed nodes. These nodes share the same frequency band which is used by the licensed nodes in the uplink channel. This sharing is done in a way that the unlicensed users do not cause any interference on the licensed nodes. In this model, the licensed link is the one between the mobile users and the cellular base stations while the unlicensed link is what is used by the sensors to communicate with their corresponding aggregators. The unlicensed users are considered to be static, which would make use of directional antennas with restricted radiation pattern; hence, the orientation errors could be avoided. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Expression** \\ \hline \(\Gamma\left[\cdot\right]\) & Gamma function \\ \hline \(r_{i}\) & Distance from the reference receiver and the ith interfering node \\ \hline \(g_{i}\) & Channel gain \\ \hline \(P_{\text{p}}\) & Licensed users’ transmit power \\ \hline \(P_{\text{s}}\) & Unlicensed users’ transmit power \\ \hline SIR & Signal to interference ratio \\ \hline \(\beta\) & SIR threshold \\ \hline \(\beta^{*}\) & Optimal SIR threshold \\ \hline \(\hat{\Phi}\) & Poisson point process \\ \hline \(P_{\text{out}}\) & Outage probability \\ \hline \(P_{\text{suc}}\) & Probability of a successful transmission \\ \hline \(\lambda\) & Network density (nodes/m\({}^{2}\)) \\ \hline \(T\) & Link throughput \\ \hline \(T^{*}\) & Optimal throughput \\ \hline \(\epsilon\) & Outage threshold \\ \hline EE & Energy efficiency \\ \hline \(\alpha\) & Path loss exponent \\ \hline \(\text{P}_{T}\) & Total energy consumption per bit \\ \hline \(P_{PA}\) & Power amplifier consumed energy \\ \hline \(P_{T_{x}}\) & Transmission power \\ \hline \(P_{R_{x}}\) & Reception power \\ \hline \(m\) & Number of retransmission attempts \\ \hline \(1+\bar{m}\) & Average number of retransmission attempts \\ \hline \(1+\bar{m}_{e}\) & Average number of retransmission attempts in the extreme cases \\ \hline \(m^{*}\) & Maximum allowed number of retransmission attempts \\ \hline \(\delta\) & Drain efficiency \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the functions and symbols. We assume here the ideal case, where the beam can be modeled as a straight line. Although this is a strong assumption, it can be seen as the theoretical limit of this scheme. A more realistic beam with orientation errors has been studied, for example, in [41] where [PERSON] et al. study different trade offs regarding the network throughput and transmission capacity with changes in the antenna beamwidth. In that paper, the authors study an ad hoc network implemented using bipolar Poisson point process and use stochastic geometry in order to analyze the optimal beamwidths that maximize different throughput-based metrics, including the orientation errors. They have shown that in case of having a fixed transmit power, decreasing the beamwidth will increase the antennas main beam gain, which in its turn will result in lower interference from the interfering nodes on the receiver. In such situation, aligning the transmitter and receiver appropriately would be more challenging; however, when they are aligned, it will result in an increase in the desired signal strength. In this paper, we do not consider how the link between sensor and aggregator is formed since the unlicensed network has a fixed topology. In this model, only the typical link in the unlicensed network suffers from the interference caused by the uplink licensed network. The licensed network, on the other hand, is highly mobile in the sense that the topology of active transmitters change at every transmission attempt of the unlicensed network.