# Enhanced Gain Difference Power Allocation for NOMA-Based Visible Light Communications
## 1 Introduction  
Wireless data traffic has grown exponentially with the increase in mobile applications and emerging services [1]. However, the limited spectrum of existing radio frequency (RF) is progressively becoming congested, and the available RF resources cannot fully satisfy the specific communication requirements for high spectral and energy efficiency scenarios [2]. Recently, visible light communication (VLC) has been regarded as a potential supplementary technology to traditional RF wireless networks [3] due to its many advantages, such as an abundant and unlicensed spectrum, low cost, low power consumption, and enhanced security characteristics [4]. One of the main disadvantages of VLC is the limited modulation bandwidth of the employed light-emitting diodes (LEDs) [5], where the 3 dB bandwidth has only 5\(\sim\)10 MHz. To improve the achievable data rate, extensive studies on methods such as advanced optical modulation [6; 7], channel equalization [8], multiple access schemes [9], and multiple-input multiple-output (MIMO) [10] have been carried out based on intensity modulation and direct detection (IM/DD) architecture. Non-orthogonal multiple access (NOMA) is one of the key- enabler technologies in 5G networks and has attracted increasing attention from the academic and industrial communities owing to its high spectrum efficiency, user fairness, strong reliability, and massive connectivity [11]. Unlike orthogonal multiple access (OMA) techniques, multiple users can be simultaneously served with the same time-frequency resources by using NOMA, which is more suitable for massive connectivity. Briefly, the power domain resources are used at the transmitter to distinguish and superimpose transmission for different users, while successive interference cancellation (SIC) is performed at the receiver to detect the signals for each user. NOMA can be integrated with VLC since it performs well at a high signal-to-noise ratio (SNR), which is a typical feature guaranteed by VLC systems [12]. By pairingusers and employing appropriate LEDs, the performance of NOMA over traditional OMA can be enhanced accordingly [13]. Closed-form expressions for the bit error rate (BER) of NOMA-VLC systems with on-off keying (OOK) and L-ary pulse position modulation have been derived, considering perfect and imperfect channel state information [14]. The results of [15] demonstrated that the performance metrics (BER, sum rate, and outage probability) in a multi-user NOMA-VLC system can be affected by the number of users, signal type, and shadowing under different half-angles of LEDs and signal reflection path conditions. Due to the intercluster interference in the SIC procedure, users who have poor channel conditions should employ higher power to decode their useful information. How to reasonably allocate the limited power to each user plays a significant role in NOMA [16]. Several studies on efficient power allocation including fixed allocation, fractional transmit allocation, strategy design [17; 18; 19; 20], heuristics [21; 22], and indirect methods based on mathematical theory [23; 24] have been proposed in NOMA-VLC systems. In [17], a gain ratio power allocation (GRPA) strategy was proposed, which was reliant on the user's gain in comparison to that of the first sorted user based on the decoding order. The corresponding BER performance of this strategy was found to outperform the fixed power allocation method. For MIMO-VLC networks, a normalized gain difference power allocation (NGDPA) method that relies on the channel gain difference to determine the power allocation coefficients was proposed to increase the total rate in [18]. In addition, multiple LEDs were utilized to enhance the performance of the communication system and improve the data transfer rate, capacity, and robustness. An improved fractional strategy (IFS) revising the power factors within GRPA was proposed in [19], where the constraints of the proposed strategy were rigorously explained through the proposed asymptotic and compact throughput bound.