# Constant Transmission Efficiency Dimming Control Scheme for VLC Systems
## 2 System Model  
The system model of the proposed ECWCS scheme will be presented in this section. In this paper, the scheme is proposed for the single-input single-output VLC system, which contains a single LED and a single photodetector (PD). The system model is shown as Figure 1. First, the codeword set is constructed according to the dimming factor. After generated by the massage generator, the binary data is encoded by the dimming encoder. Then the coded binary data are modulated by the OOK modulator to the LED. After passing through the optical channel with additive white Gaussian noise (AWGN), the received signals are detected by the PD and then decoded by the dimming decoder. There is a point that should be noted: This scheme can not only be applied to OOK modulation but also pulse amplitude modulation (PAM) and multi-carrier modulation (MCM). Figure 1 is just an example of the ECWCS scheme applied to OOK modulation for the convenience of understanding. When the algorithm is applied to PAM, we should also adjust the average code weight of the codeword set to realize dimming control. Because PAM has a higher modulation order, the codeword set will be further expanded, and the spectral efficiency will be further increased. However, the corresponding error performance will have a certain amount of loss. When the algorithm is applied to MCM, we should ensure the average code weight of the codeword set for every subcarrier is constant and adjust it to realize dimming control. When MCM is utilized in the proposed ECWCS scheme, the throughput will be increased, and the resistance to interference will be enhanced. However, the implementation complexity and cost will also be significantly increased. Modern Discrete Multi-Tone (DMT) modulation is a kind of MCM and can be utilized in the proposed scheme. Paper [15] reported the first visible light link based on WDM and DMT modulation of a single RGB-type white LED, and paper [16] proposed 1-Gb/s VLC systems using a white LED and the DMT signal. Both of the two schemes improved the throughput to a large extent. However, the implementation complexity and the cost of the electronic devices are weaknesses for the DMT modulation. At last, the message will be output to the users. In this system model, there are a few assumptions that should be noted:  
1. The channel state information (CSI) is available both at the receiver and the transmitter. 2. Compared with the direct light, the reflected light is much weaker in the indoor VLC systems [1; 17]. For the convenience of computer analysis, we only consider the LOS path. Therefore, the multipath influence may not be considered in the proposed indoor dimmable VLC system. 3. A static link should be supposed in the proposed scheme because the channel is slow time-varying. From Figure 1 and the assumptions we mentioned before, we can conclude that the received signal can be expressed as  
\[y=\mu hx+n, \tag{1}\]  
where \(y\) represents the received signal, \(x\) denotes the transmitted signal, \(\mu\) is the photoelectric conversion factor which can be normalized as \(\mu=1\), \(h\) is the channel gain we will introduce in this section, and \(n\) is the additive white Gaussian noise of which the mean is 0 and the variance is \(\sigma^{2}\). Figure 1: System model of the proposed dimming control scheme applied to on-off keying (OOK) modulation. From the contents in [1], the channel can be modeled as the Lambertian model, and the channel can be calculated by:  
\[h= \begin{cases}\frac{A(u+1)}{2\pi D^{2}}\cos^{u}(\phi)T_{S}(\psi)g(\psi)\cos\psi, &0\leq\psi\leq\Psi_{C}\\ 0,&\psi>\Psi_{C}\end{cases}  \tag{2}\]  
where \(h\) is the channel gain between the receiver and the transmitter, \(D\) is the distance from the LED to the PD, \(u\) is the order of the Lambertian model, and \(A\) represents the physical area. The other physical quantities are about illumination. \(\psi\) is the incidence angle, and \(\phi\) denotes the irradiance angle.