# Maximum Transmit Power for UE in an LTE Small Cell Uplink
## 1 Introduction
* \(\Delta_{mcs}\) and \(f(i)\) are the CL/TPC parameters defining the modulation and coding scheme and closed-loop correction, respectively, as defined in the 3 GPP standards. To focus our analysis on the OL/TPC, \(\Delta_{mcs}\) and \(f(i)\) are assumed to be zero. At this point, it is important to specify the role of the pathloss compensation factor \(\alpha\) in terms of the mode of TPC being used. The modes of TPC based on the \(\alpha\) value are:  
* \(\alpha=0\) implies \"no power control\" mode. * \(\alpha>0\) designates the \"fractional power control\" mode. In practice, the values from 0.7 to 0.9 are adopted. * \(\alpha=1\) indicates a \"full compensation' mode for the uplink pathloss. To accomplish the task of network densification and optimize the network performance, it is crucial to investigate the uplink power control mechanism for small cells, particularly the maximum transmit power limit \(P_{\mathrm{max}}\) for the case of the small cell uplink. In general, the 3 GPP standards define a \(P_{\mathrm{max}}\) limit of 23 dBm regardless of cell size. However, in the case of small cells, the distance between the eNodeB and UE is shorter, as compared to the macro cell, resulting in different transmit power levels for UE in small cells. An increase in the transmit power improves the received signal strength, and consequently, the received signal-to-interference ratio (SIR). However, in the case of small cells, transmitting at a higher power might result in the degradation of the received SIR due to the significant increase in the inter-cell interference [6]. Similarly, choosing a lower value of \(P_{\mathrm{max}}\) can decrease the interference, but might affect the SIR performance as the received signal strength might go below the receiver threshold in the case of choosing too low a value for \(P_{\mathrm{max}}\). Also, it is important to consider the deployment strategy to furnish the existing macro cell layer with small cells, as the choice of TPC parameters is highly dependent on the location of small cells. This issue implies a need to carefully reconsider the \(P_{\mathrm{max}}\) for small cell deployment. In general, the fractional power control (FPC) mode is adopted for macro cell deployment, which ensures better service quality for the cell's average users at the cost of a slight degradation in the cell edge performance [7]. In References [8; 9; 10], the impact of \(\alpha\) and \(P_{\mathrm{o}}\) on the transmit power was investigated in detail; however, the consideration of variation in the \(P_{\mathrm{max}}\) limit was not considered. In Reference [11], a resource allocation-based uplink transmission energy reduction scheme was presented; however, it is limited only to a macro cell environment and considers the conventional 23 dBm limit for the \(P_{\mathrm{max}}\). Also, for a small cell deployment, no separate description is available in the literature regarding the TPC mode. In Reference [12], the authors presented a detailed study on the downlink transmit power and bandwidth allocation problem for a small cell eNodeB in HetNet deployment. By considering the downlink scenario, the results indicated that for HetNet deployment, the energy efficiency for small cell users as well as the overall system capacity can be improved by increasing the number of small cells and the number of users per small cell. However, the analysis was limited only for the downlink transmit power of the small cell eNodeB and the inter-cell interference analysis was also left for future consideration. In our previous work [13], we proposed a full compensation mode for small cells in homogenous as well as in heterogeneous network (HetNet) deployment scenarios assuming the standard \(P_{\mathrm{max}}\) limit, i.e., 23 dBm. However, we can expect that, with a lower value of \(P_{\mathrm{max}}\), the situation might become different. To provide better insight regarding the impact of the \(P_{\mathrm{max}}\), it is essential to analyze its impact on small and macro cell performances and the TPC mode by adopting OL/TPC.