## 4 Precoding Schemes
### Introduction to Precoding Schemes
#### 4.1.2 Requirements for VLC Precoding Schemes  
In the following, the requirements for deploying VLC precoding schemes are presented:  
_Uplink and CSI:_ VLC systems naturally consider a frequency division duplex (FDD) operation mode. Although downlink typically occurs in the visible optical domain, infrared  
Figure 17: Schematic diagram for precoding schemes in a MU-MIMO VLC system.  
(IR) communications [142; 143] or umbrella RF networks such as WiFi or femtocells [144; 145] are considered for implementing the uplink transmission. Notice that time division duplex (TDD) requires one to transmit both downlink and uplink through the visible optical domain, which may be annoying for practical implementations. Thus, the first issue that must be solved for implementing precoding techniques is to provide CSI in order to determine the precoding matrix \(\mathbf{W}\). In [146; 147], the cost of providing CSI in MIMO networks is analyzed. First, \(P\) orthogonal estimation pilots are transmitted comprising \(P\) dedicated time/frequency slots. The downlink channel estimated by each of the \(K\) users is then fed back through the uplink to the optical APs. To conclude, once the precoding vectors are calculated, pilots considering the precoding vectors are transmitted in an orthogonal fashion for coherence detection. Let us denote the fraction of downlink transmission resources, either time or frequency, allocated for estimation pilots and coherence detection as \(\theta_{\text{ep}}\) and \(\theta_{\text{cd}}\), respectively. Similarly, the fraction of uplink transmission resources for channel feedback is denoted as \(\theta_{\text{fb}}\). Therefore, the efficiency of the user-rate for precoding schemes is penalized by a factor \(\eta_{p}=1-\left(P(\theta_{\text{ep}}+\theta_{\text{cd}})+K\theta_{\text{fb}}\right)\). It is worth remarking that this penalty must be taken into consideration when comparing precoding schemes with blind transmission schemes such as orthogonal resource allocation [109] or blind interference alignment [29].  
_Backhaul_: Data sharing among optical APs is required for implementing precoding schemes. As can be seen in (20), each optical AP knows the symbols intended to the \(K\) users and generate a transmitted signal given by a linear combination of the precoding vectors and these symbols. Notice that this fact makes the network system based on precoding schemes more resilient to the blockage of one or several links between any pair optical AP user, as discussed below. As described in the previous section, multiple approaches can be considered for providing backhauling in VLC, such as PLC [83; 84], Ethernet [86], optical fiber [87] and wireless, either optical or RF communications [45; 90; 91; 92]. Thus, precoding schemes require one to implement a central unit (CU) to generate the symbols intended to the users, manage the pilot transmission, obtain the CSI knowledge and calculate the precoding vectors, as can be seen in Figure 10.  
_Transmission within the LED dynamic range:_ As described in Section 2, the transmitted signal in the optical domain for IM/DD must correspond to a real and non-negative value. However, canceling or simply managing the interference by using linear precoding implicitly generates negative values. Hence, once the precoded signal is generated, a DC bias current is added at each optical AP to ensure the non-negativity of the signal. However, this condition may lead to clipping noise when the resulting signal does not fit in the dynamic range of the LED transmitters (see Figure 5). The scheme for implementing a precoding scheme in VLC is shown in Figure 17.