## 2 Modeling the VLC Networks: Architecture, System Model and Scenarios
### Multi-Carrier Modulations  
Optical orthogonal frequency division multiplexing (O-OFDM) schemes are the most common multi-carrier modulations for VLC, which are variations of the traditional OFDM that is being widely used by current communication systems, such as 5G, 4G, WiFi and digital television [64, 65]. However, due to the constraint of generating a real and non-negative transmitted signal for VLC, traditional OFDM schemes for RF transmission cannot be straightforwardly applied. The two main O-OFDM schemes are DC-biased optical-orthogonal frequency division multiplexing (DCO-OFDM) [66] and asymmetrically clipping optical-orthogonal frequency division multiplexing (ACO-OFDM) [67]. Besides, alternative O-OFDM schemes can be found in [68]. Since OFDM schemes are directly based on the fast Fourier transform (FFT) and its inverse (IFFT), generating a real-valued signal requires one to employ some of its properties. In this sense, the input to the IFFT on the transmitter side, i.e., the frequency-domain data, is well-known to be organized in two halves. Specifically, the second half of the frequency-domain data must be the symmetric Hermitian version of the first half. Besides, sub-carriers 0 and \(N/2\) must be 0, where \(N\) is the number of sub-carriers. This way, due to the Fourier transform properties, the output of the IFFT is real-valued. At this point, there exists a clear difference between DCO-OFDM and ACO-OFDM. For DCO-OFDM, the frequency-domain data, which is denoted as \(\mathbf{X}_{\text{DCO}}\), can be mathematically expressed as  
\[\mathbf{X}_{\text{DCO}}=[0\quad X_{d}[1]\quad X_{d}[2]\cdots X_{d}[N/2-1]\quad 0 \quad X_{d}[N/2-1]^{*}\cdots X_{d}[2]^{*}\quad X_{d}[1]^{*}], \tag{1}\]  
while for ACO-OFDM, it is given by  
\[\mathbf{X}_{\text{ACO}}=[0\quad X_{d}[1]\quad 0\quad X_{d}[3]\cdots 0\quad X_{d}[N/2-1]\quad 0 \quad X_{d}[N/2-1]^{*}\cdots 0\quad X_{d}[3]^{*}\quad 0\quad X_{d}[1]^{*}], \tag{2}\]  
where \((\cdot)^{*}\) denotes the complex conjugate, and \(X_{d}[n]\) is the frequency-domain data at \(n\)-th sub-carrier, usually selected from a quadrature amplitude modulation (QAM) constellation point. Notice that only half of the bandwidth can convey useful data. Furthermore, it is worth noting that QAM constellations cannot be applied to single-carrier modulations, since they are subject to consider complex values of the transmitted signal. On the other hand, O-OFDM schemes allow us to use complex-valued constellations in VLC. Then, the IFFT is applied to frequency-domain signal \(\mathbf{X}\), where \(\mathbf{X}_{\text{DCO}}\) and \(\mathbf{X}_{\text{ACO}}\) are now generalized as \(\mathbf{X}\) for the sake of simplicity, to obtain the time-domain transmitted signal  
\[\mathbf{x}_{\text{raw}}=\text{IFFT}\{\mathbf{X}\}. \tag{3}\]  
After that, the cyclic prefix is added to obtain  
\[\mathbf{x}=[\mathbf{x}_{\text{raw}}(N-L_{\text{CP}}:N-1)\quad\mathbf{x}_{ \text{raw}}], \tag{4}\]  
where \(L_{\text{CP}}\) is the length of the cyclic prefix. Once it is ensured that the output of the IFFT is real-valued, the transmitted signal must fit in the dynamic range of the optical transmitter. That is, the transmitted signal ought to be given by non-negative and non-above \(P_{\text{max}}\) values (see Figure 5). Beyond this range, the signal is affected by clipping [69]. For DCO-OFDM, an offset is directly added to the resulting signal after IFFT plus cyclic prefix (see Figure 6), resulting  
\[\mathbf{x}_{\text{bx}}=\mathbf{x}+\text{DC}. \tag{5}\]As the DC component does not carry any data, DCO-OFDM may be considered as energy-inefficient. However, this is usually not a problem for VLC systems, because a DC value is indeed required for providing a satisfactory illumination level. Differently, ACO-OFDM makes use of another property of Fourier transform in order to obtain a non-negative signal.