# Uplink Transmit Power Control for Single-Carrier Grouped FDMA with Iterative Multiuser Detection
## 2 System Model  
In this study, we consider an SC-GFDMA system based on SC-FDMA with localized subcarrier mapping. In this system, different users occupy different frequency chunks, and each chunk is occupied by a single user [4] (Figure 1a); here, a chunk is defined as a set of \(K\) consecutive subcarriers in the frequency domain during each time slot (Time slot refers to the length of time used to transmit all subcarriers simultaneously, as defined in LTE/LTE-A standards [26]. In [4], the same measure was denoted as a \"block\".). In contrast, SC-GFDMA allows the sharing of a chunk by multiple users (Figure 1b), and thus, it has a non-orthogonal characteristic among user signals. The scheduler determines the allocation of users in each chunk, and the number of users sharing each chunk can be different. Power control and user scheduling are performed chunk-by-chunk by regarding each chunk as the minimum unit of resource allocation. By using channel-dependent power control and scheduling, the spectral efficiency can be significantly increased in each chunk, which is the primary objective of this study.  
In summary, we consider an uplink SC-GFDMA system based on localized subcarrier mapping, in which a BS communicates with \(U\) users. Based on the GFDMA criterion, \(U_{m}\) users access the same chunk \(m\), for \(m=1,\cdots,M\), where \(M\) is the total number of chunks in the frequency domain during each time slot. The scheduler is allowed to map one user to multiple chunks (Figure 1). Thus, we have \(U\leq\sum_{m=1}^{M}U_{m}\). As each chunk consists of \(K\) consecutive subcarriers, the total frequency bandwidth is divided into \(MK\) subcarriers. Before transmitting uplink data, the BS adjusts the transmit powers of the users in each chunk, depending on the estimated uplink channels, and then schedules appropriate users in each chunk from the total user set \(\mathcal{U}=\{1,\cdots,U\}\). Subsequently, the BS sends the information of both adjusted powers and scheduling results to the associated users through a control plane. The detailed procedures for power control and scheduling will be further discussed in Section 2.3. The data streams of each user are sent on the associated chunk through a data plane, based on the control plane information.  
\begin{table}
\begin{tabular}{c c} \hline \(M\) & Total number of chunks in frequency domain \\ \(N\) & Total number of subcarriers in frequency domain \\ \(K\) & Number of subcarriers in each chunk \\ \(\mathcal{U}\) & Set of all users \\ \(U\) & Total number of users: \(U=|\mathcal{U}|\) \\ \(\mathcal{U}_{m}\) & Set of users allocated to chunk \(m\) \\ \(U_{m}\) & Number of users in chunk \(m\): \(U_{m}=|\mathcal{U}_{m}|\) \\ \(L_{u}\) & Pathloss from BS to user \(u\) \\ \(P_{u,m}\) & Transmit power of user \(u\) at chunk \(m\) \\ \(\Lambda_{u,m}\) & Channel frequency response of user \(u\) at chunk \(m\) \\ \(v_{u,m}\) & Estimated variance of the signal of user \(u\) at chunk \(m\) \\ \(\mu_{u,m}\) & Estimated mean of the signal of user \(u\) at chunk \(m\) \\ \(\Gamma_{u,m}\) & Estimated SINR of user \(u\) at chunk \(m\) \\ \(\Gamma_{th}\) & Threshold of SINR for QoS constraint \\ \(\eta_{m}\) & Spectral efficiency at chunk \(m\) \\ \(\tau_{m}\) & Single-user data rate of user \(u\) at chunk \(m\) \\ \(\zeta_{u,m}\) & \(\zeta_{u,m}\triangleq L_{u}P_{u,m}\cdot\mathrm{am}[|\Lambda_{u,m}|^{2}]\) \\ \hline \end{tabular}
\end{table}
Table 1: List of primary symbols.