# Uplink Transmit Power Control for Single-Carrier Grouped FDMA with Iterative Multiuser Detection
## 1 Introduction
In typical SC-FDMA systems, multiple users are orthogonally allocated in the frequency domain such that a single user is solely served in each chunk. Thus, studies on user scheduling for SC-FDMA have commonly attempted to select the user having the highest signal-to-interference-plus-noise ratio (SINR) [19; 20], to increase the spectral efficiency in each chunk. More sophisticated resource allocation techniques were commonly considered at subframe or frame level across subcarriers or chunks [11; 13; 16; 21; 22]. In contrast, in SC-GFDMA, multiple users access each chunk simultaneously while different groups of users are allocated in different chunks based on the FDMA criterion (Figure 1). Thus, resource allocation significantly affects the available spectral efficiency in each chunk. The scheduling methods for SC-GFDMA should be designed to achieve high spectral efficiency in each chunk while guaranteeing acceptable quality-of-service (QoS) to all scheduled users. For example,  
Figure 1: Frequency domain description for each time slot in SC-FDMA (**a**) and SC-GFDMA (**b**) with localized subcarrier mapping (\(M=4,U=4\)). the study in [23] proposed a pattern-aware user scheduling algorithm that efficiently exploits the non-orthogonal nature of SC-GFDMA, and thus, it achieved near-optimal spectral efficiency for the given transmit power. Moreover, as there is interference among the received signals of multiple users in each chunk, the use of a higher transmit power for each user does not always correspond to a higher total spectral efficiency in each chunk. Therefore, a sophisticated algorithm should be additionally considered to optimize the transmit powers of users in each chunk. That is, the transmit power of each user should be sufficiently high to ensure reliable detection, but sufficiently low to restrict interference with other users. A previous study on SC-GFDMA demonstrated that the scheduling complexity could be decreased when QoS-satisfied users have unequal powers [7]. A low-complexity scheduling algorithm that exploits these properties was introduced in [7], but it achieved a relatively low spectral efficiency at the cost of low complexity of implementation. Moreover, the unequal transmit powers of users were not designed with a specific power control strategy. Owing to the non-orthogonal characteristic, it is difficult to derive explicit mathematical expressions for the performance achieved using the SC-GFDMA structure. Thus, there is a need for power allocation algorithms that can exploit the essential benefits of SC-GFDMA to enhance the performance in each chunk. Various studies on power control for SC-FDMA-based systems [10; 11; 24; 25] were reported previously. However, to the best of our knowledge, a specific power control method applicable to each chunk of the SC-GFDMA structure has not been considered yet. This specificity of the power control method is the focus of this study. In this paper, a power control algorithm that exploits the fundamental structure of SC-GFDMA is proposed to increase the spectral efficiency available in each chunk. The proposed algorithm optimizes the transmit powers of users allocated in each chunk based on a criterion derived from the SINR analysis of the users. First, a maximization problem of the spectral efficiency is formulated in each chunk and is modified to a simplified form. Subsequently, we present an appropriate solution for the power control problem by analyzing the successive SINRs of the users during the IMD, based on a semi-analytic method called signal-to-noise ratio (SNR)-variance density evolution. Consequently, the uplink transmit power of each user is intentionally restricted to reduce its effect as MAI to the signals of other users. Specifically, we place users in the same chunk in the decreasing order of SINR. Then, we demonstrate that the reliable detection of the \(k\)th user is closely related to the SINR of the \((k+2)\)th user.