# AI-Enabled Intelligent Visible Light Communications: Challenges, Progress, and Future
## 2 Status and Challenges of VLC
### Visible Light Communication E2E Channel  
The VLC end-to-end channel \(\mathcal{H}(x)\) includes a digital-to-analog converter (DAC, in arbitrary waveform generator), electronic amplifier (EA), bias tee, LED, transmission channel, receiver, and analog-to-digital converter (ADC, in oscilloscope), as shown in Figure 1. The entire transmission link contains electrical voltage signals, current signals, and optical signals, as well as the conversion between them. However, due to the complexity of the visible light channel, research now focuses on the LED emitter and the transmission channel, which are (d), (e), and (f) of Figure 1.  
From the communication point of view, the most primitive LED transmission model is the frequency domain model, which is given as [19]:  
\[H(\omega)=e^{-\frac{\omega_{c}}{\omega_{c}}} \tag{1}\]  
where \(\omega_{c}\) is a fitted coefficient. This model mainly represents not only the frequency-selective fading phenomenon of the visible light channel, but also the inter-symbol interference (ISI) and linear memory effects. The high-frequency fading of the exp (exponential) fits well with the limited bandwidth of visible light communication. Therefore, when only linear channels are considered, the expression form of exp is also applicable to the underwater visible light channel [20]. However, a linear model alone cannot describe a channel that is as complex as visible light communication. The first consideration is the V-I transfer model of VLC [21], which extends from the solid state power amplifier (SSPA) model [22]. Similarly, there are equivalent circuit models [23] to equate the V-I transfer curve and frequency response of VLC. Such a model implies that the nonlinear term is only amplitude-dependent, independent of frequency and time, and independent of adjacent symbols. Figure 1: Overview of VLC end-to-end channel; (**a**) DAC, (**b**) EA, (**c**) bias tee, (**d**) V-I, (**e**) I-P, (**f**) transmission channel, (**g**) P-I, (**h**) transimpedance amplifier (TIA), (**i**) EA and (**j**) ADC. If we want to take all the above factors into account, a simple way is to equate the overall linearity and nonlinearity to the Volterra series [24; 25], as a black-box model. A second-order Volterra expansion can be expressed as [25]:  
\[y(m)=\sum_{i=0}^{N-1}h(i)x(m-i)+\sum_{i=0}^{L-1}\sum_{j=k}^{L-1}w(ij)x(m-i)(m-j) \tag{2}\]  
where \(h\) and \(w\) are the linear and nonlinear weights, and \(N\) and \(L\) are the tap numbers of linearity and nonlinearity. When the signal bandwidth is small (14 MHz bandwidth) and the signal amplitude is small (40 mA DC bias), the second-order Volterra is proven to have better similarity [24]. High-speed visible light communication, however, often requires a higher signal-to-noise ratio (SNR) and modulation bandwidth to meet the 6G transmission rate requirements. Higher-order Volterra series may be expected to fit well, but would introduce an exponential increase in computational complexity. None of the above-mentioned channel models from the communication dimension actually take the substance of photoelectric and electro-optical conversion into account in computation. They simply treat it as a black box. Since LED is a GaN wide-bandgap semiconductor material based on a multi-quantum wells (QWs) structure, the carrier rate equation can be modeled for LED from semiconductor material considerations [26; 27; 28; 29]. The model is named as the ABC model, where A, B, and C represent Shockley-Read-Hall (SRH, nonradiative) recombination, radiative recombination, and Auger recombination (nonradiative), respectively. Considering both recombination and leakage of carriers, the recombination rate \(R\) can be expressed as follows [28]:  
\[R=An+Bn^{2}+Cn^{3}+f(n) \tag{3}\]  
\[f(n)\approx an+bn^{2}+cn^{3}+dn^{4}\ldots \tag{4}\]  
where \(A\), \(B\), and \(C\) represent the SRH, radiative, and Auger recombination coefficient. \(n\) is the minority carrier concentration. \(f(n)\) is the carrier leakage term, which has been expanded into the Taylor series.