## 1 Introduction  
The international telecommunications union-radio communications sector (ITU-R) has published the recommendations and key capabilities of next-generation wireless communication, in which the three-type high densities of users, the number of access points (APs) and the area traffic requirement are important performance indicators in the indoor ultra-dense network (UDN) scenario [1]. For illuminations in architecture, optical sources are ubiquitous and the inter-site distance (ISD) of optical APs is much smaller than in traditional cellular or wireless local area networks. Furthermore, the increase in optical AP density with a smaller area of coverage is an efficient way to improve the system traffic capacity, especially in hotspot scenarios [2]. Therefore, to deal with three-type densities, visible light communication (VLC) is a complementary networking scheme of optical wireless communication (OWC) to split cells and improve the spectrum reuse for dense indoor scenes [3]. For high user density, the corresponding user density in typical indoor scenarios, such as at home and in the office, is 0.25 persons per m\({}^{2}\) under the cover of each grid [1]. For high AP density, the ISD of optical devices in the office or at home may be less than 10 metres. Compared with mm-wavecommunication, the higher frequencies of OWC may reduce the cell sizes, leading to the concept of LiFi attocells [3], which have a smaller area of coverage than the coverage of femtocells or WiFi. For high traffic requirements, indoor users within different VLC channel conditions may share different communication services with others at the same moment. This leads to a very high traffic density requirement which can reach almost 10 Mbps/m\({}^{2}\)[1]. For VLC channels, the system bandwidth of physical optical devices in common markets is limited by the constraint of illuminations, and both illumination and communication functions in indoor VLC networks lead to non-negative signals and strong channel correlations. Therefore, the different quality-of-service (QoS) requirements of VLC users and the efficient spectrum utilization of limited bandwidth should be taken into account in VLC-UDN resource allocation. Compared with orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA) [4; 5; 6] exploits the entire bandwidth for the time-frequency utilization of all degrees of freedom, in order to increase spectral efficiency. In NOMA, the gain ratio power allocation (GRPA) [7] allocates the sorted transmitted power for users with inverse sorted channel gains, which guarantees both fairness and throughput enhancements. In research by [PERSON] et al. [4], analytical solutions for the NOMA-VLC user outage probability in a single cell for guaranteed QoS were derived. In other research by [PERSON] et al. [5], the user was allocated with a higher power allocation coefficient, since the QoS requirements of a user are given by higher priority. With the residual interference from the successive interference cancellation (SIC) of NOMA, user grouping was introduced into the power allocation under the QoS constraints of max-min and max-sum rate criteria for the VLC system throughput enhancement [6]. In a series of studies [7; 8; 9; 10], a GRPA strategy based on a power law strategy (PLS) that considers user channel conditions was presented. In PLS, the power allocation of other user gains depends on the gain of the first user, sorted in ascending order, with the assigned power of exponential decrease. The relationship of PLS ensures fairness, whereby a poor channel user will need much higher power due to the large degree of interference. Based on PLS, [PERSON] et al. [11] determined the power coefficients based on a pre-defined QoS per user. High priority users are guaranteed by the signal power allocation based on a pre-defined QoS, while no QoS limitations are defined for lower priority users.