# Energy Efficient Transceiver Design for NOMA VLC Downlinks with Finite-Alphabet Inputs
## 1 Introduction  
As an adjunct or alternative to radio frequency (RF) communications and as a promising technology for 5G systems, visible light communications (VLC) has become a very important area of research [1; 2; 3; 4; 5; 6; 7; 8] due to its advantage of low cost, ultra-high bandwidth, freedom from spectral licensing issues, etc. Considering the realistic application, the VLC systems are generally expected to support multiple users, and multiple access strategies are essential for VLC systems. Well-known orthogonal multiple access (OMA) methods such as code division multiple access (CDMA), time division multiple access (TDMA) and orthogonal frequency division multiple access (OFDMA) have been widely used to support multiuser communications. However, since different users are allocated orthogonal resources in either the code, time or frequency domain, these methods cannot provide sufficient resource reuse. In contrast to these OMA methods, a novel multiple access strategy called non-orthogonal multiple access (NOMA), which has been proposed as a promising solution for the 5G wireless networks [9; 10; 11; 12], allows multiple users simultaneously to utilize the entire available code, time and frequency resources by multiplexing users in the power domain using superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver. In VLC systems, NOMA has recently drawn great attention as an efficient solution to the limited bandwidth of light emitting diodes (LEDs) [13; 14; 15]. In [13], the performance of the NOMA VLC downlink was investigated in terms of coverage probability and ergodic sum rate, and it was verified that NOMA can achieve higher system capacity than TDMA. In [14], the authors proposed a grain ratio power allocation strategy to ensure efficiency and fairness, and it was shown that the system sum rate can be enhanced by tuning the semi-angle of LEDs and the field of view (FOV) of photodiodes (PDs). An optimal power control algorithm was proposed in [15] by using the dual method to get maximized sum logarithmic user rate. However, the above studies were mainly committed to system capacity, sum rate and user fairness, ignoring the bit error rate (BER),which is an important index to evaluate the reliability of wireless communication systems. In addition, all the above studies utilized SIC at the receiver. As illustrated by Figure 1, the SIC-based receiver first detects one signal from the received composite signal by treating the other signals present in the same composite signal as noise. Then, the detected signal is subtracted from the received composite signal so as to detect the other signals. Since the SIC-based receiver treated the other signals as noise when detecting one signal from the same received composite signal,the SIC receiver may lead to error propagation and degrade system performance. Motivated by the aforementioned considerations, in this paper, we consider the energy-efficient transceiver design for NOMA VLC downlinks from a BER performance perspective. We develop an optimal power allocation strategy with finite-alphabet inputs for the transmitter and propose a joint detection and decoding (JDD) algorithm for the receiver. In addition, since TDMA is commonly used in the multi-user VLC system and it is easy to implement [16; 17; 18; 19], in this paper, we choose TDMA for comparison. Comprehensive computer simulations demonstrate that our proposed NOMA strategy can achieve significant performance gains over the time division multiple access (TDMA) scheme, and our designed JDD algorithm outperforms the conventional SIC algorithm for NOMA. The rest of this paper is organized as follows. Section 2 introduces the indoor NOMA VLC system model. Section 3 presents an optimal power allocation strategy for the transmitter and develops an efficient joint detection and decoding algorithm for the receiver. Section 4 compares the BER performance of our proposed NOMA and TDMA, as well as compares the BER performance of our proposed JDD and conventional SIC.