## 2 System Model
### Inherent Impairment of an IM/DD Channel  
In VLC system, the channel impairments are mainly introduced by the electrical-to-optical (E/O) conversion of the LED and the multipath propagation of optical link. The LED suffers from strong nonlinearity as it is driven by OFDM with high PAPR. Additionally, due to multiple reflections in the indoor environment, the dispersive channel leads to complicated ISI. In addition, the memory nonlinearity is more significant as the bandwidth of the driving signal is increased. The Wiener model, which consists of a linear filter block and a memoryless nonlinear block, can be employed to model the LED nonlinear behavior. The first block is used to describe the memory effect of LED, which can be expressed by a low-pass finite impulse response (FIR) filter, shown as follows:  
\[h_{LED}(n)=\exp(-2\pi nf_{0}), \tag{4}\]  
where \(f_{0}\) is the 3 dB cut-off frequency of LED. The second nonlinear block is used to model the memoryless or static nonlinearity of LED, which can be represented by a polynomial function, expressed as follows:  
\[f_{LED}(x(n))=\sum_{p=0}^{p}a_{p}x^{p}(n), \tag{5}\]  
where \(a_{p}\) and \(P\) are the coefficient and nonlinear order of \(f_{LED}(x(n))\). It should be noted that \(a_{p}\) and \(P\) can be obtained by fitting with the actual measurement data of a commercially  
Figure 1: Block diagram of the DCO-OFDM system with an IM/DD channel. available LED [39]. For simplicity, \(P=3\) is employed in this paper and \(a_{p}\) can be calculated as follows:  
\[a_{p}=[-0.0003,2.0565,-1.0886,0.2855]. \tag{6}\]  
The multipath propagation effect in the VLC channel can be illustrated by the channel impulse response (CIR), which is usually adopted in the literature [16; 39]. The corresponding CIR of VLC channel can be expressed by the following:  
\[h_{v}(n)=\sum_{i=1}^{N_{r}}P_{i}\delta(n-\tau_{i}), \tag{7}\]  
where \(P_{i}\) and \(\tau_{i}\) are the optical power and propagation time of the \(i\)-_th_ ray, respectively, and \(N_{r}\) is the number of received rays at the PD. The parameters in (7) can be obtained using a ray-tracing-based approach [39]. Note that the time-dispersive properties of the optical link can be evaluated by the corresponding root mean square (RMS) delay spread of \(h_{v}(n)\). Moreover, the PD can be modeled by the Dirac channel due to the linear transformation. Let \(R_{PD}\) denotes the responsivity, and the CIR of PD is given by the following:  
\[h_{PD}(n)=R_{PD}\delta(n). \tag{8}\]  
The dominant ambient noise can be modeled as additive white Gaussian noise (AWGN) and follows \(\mathcal{N}\big{(}0,\sigma_{e}^{2}\big{)}\). Finally, the outputs of IM/DD channel can be calculated as follows:  
\[y(n)=R_{PD}f_{LED}[(\overline{x}(n)+I_{DC})*h_{LED}(n)]*h_{v}(n)+\varepsilon( n). \tag{9}\]  
However, the channel distortion involved in \(y(n)\) affects the demodulation quality. Therefore, the overall channel distortion should be well mitigated so as to recover the original information correctly. It is worth noting that the phase characteristics are not considered because only the real-valued intensity waveform is employed in IM/DD to carry useful information. In order to intuitively illustrate the influence of channel impairment on the received signal in (9), the amplitude-to-amplitude (AM/AM) performance is evaluated and depicted in Figure 2 by comparing the original received and the ideal equalized signal over the IM/DD channel. The details of the two type of signals can be found in the following Section 4. We know that the ideal equalized signal is always expected to be the same as the original transmitted. It can be clearly seen from the figure that the received signal exhibits strong nonlinearity since its amplitude is distorted and divergent severely. Therefore, the overall channel impairment of the cascade of \(h_{LED}(n)\), \(f_{LED}(x)\), and \(h_{v}(n)\) should be simultaneously compensated in order to achieve the high-speed data transmission. Figure 2: The memory effect of the channel impairments involving in the received signal.