# Maximum Transmit Power for UE in an LTE Small Cell Uplink
## 1 Introduction  
Mobile broadband traffic has exponentially increased with the advent of modern smart phones, tablets, and communication devices, resulting in an ever-increasing data rate demand by end users. This requires an increase in network capacity and available data rates, power efficient connectivity, and decreased latency in the network. To increase capacity, network densification is necessary for radio access networks [1]. By deploying additional network nodes per unit area, the distance between the eNodeB and the user equipment (UE) can be minimized, which allows accommodating more UE per unit area, resulting in a link-budget improvement [2]. While addressing the capacity demands in areas with a high density of UE, such as urban and metropolitan areas (often referred to as hotspots), it is vital to choose the appropriate deployment option as well as the right configuration regarding the network's parameters to ensure acceptable data rates, minimum interference generation, and improved service quality for users. To configure network settings with newly furnished small cells, it is necessary to analyze the impact of different parameters such as cell size, distance between UE and the serving eNodeB, inter-site distance among neighboring cells, and the power control parameters particularly in the uplink direction [3]. To ensure power efficient connectivity, mitigate interference, and improve service quality, the 3 rd generation partnership project (3 GPP) standards introduced transmit power control (TPC) which enables power control for both the downlink and uplink directions in long term evolution (LTE) [4]. A precise control mechanism for the UE uplink transmission power is emphasized to mitigate theadverse impact of the interference on the network performance. There are two methods for TPC in the LTE uplink: open loop (OL) and closed loop (CL). The OP/TPC is the capability of the UE to set its uplink transmit power to a specified value suitable for the receiver. The UE can set its output power level by estimating the pathloss between the UE and the serving eNodeB based on the reference symbol received power (RSRP) and the OL/TPC parameters specified in Equation (1). The CL/TPC is the capability of the UE to adjust the uplink transmit power in accordance with the closed-loop correction value, also known as TPC commands. The eNodeB transmits the TPC commands towards the UE, based on the closed-loop signal-to-interference and noise ratio (SINR) target and measured received SINR. In CL/TPC, the uplink receiver at the eNodeB estimates the SINR of the received signal and compares it with the desired SINR target value. When the received SINR is below the SINR target, a TPC command is transmitted to the UE to request an increase in the transmitter power. Otherwise, the TPC command will request a decrease in transmitter power. The closed-loop power control operates around an open-loop point of operation. The initial transmit power for the UE is set using the open-loop power control. The initial power is further adjusted using a closed-loop correction value via downlink signaling of TPC commands to the UE. In summary, OL/TPC determines the initial power settings of the network while CL/TPC aims to correct errors in OL/TPC configurations. The 3 GPP specification defines the UE transmit power \(P_{\mathrm{Tx}}\) (dBm) for the LTE uplink as [5]:  
\[P_{\mathrm{Tx}}=\min\Bigl{\{}P_{\mathrm{max}},10\log_{10}\mathrm{M}+P_{\mathrm{ o}}+\alpha.\mathrm{PL}+\Delta_{mcs}+f(i)\Bigr{\}} \tag{1}\]  
* \(P_{\mathrm{max}}\) is the maximum allowable transmit power for the UE. * M is the number of physical resource blocks (PRBs). For simplicity, M is set to 1 in this paper. * \(P_{\mathrm{o}}\) is the cell/UE specific parameter. \(P_{\mathrm{o}}\) is assumed to be UE specific in this paper. * \(\alpha\) is the pathloss compensation factor. * PL is the pathloss between the UE and serving eNodeB.