# A Review-Unguided Optical Communications: Developments, Technology Evolution, and Challenges
## 5 Advancements in Optical Wireless Communications
### Visible Light Communication (VLC)
The DC attenuation \(dh_{r}[u,a]\) of the channel is given on the first reflection when the angle of incidence \(\psi_{r}\) is lower than the FoV, according to [280], which is stated in Equation (35),  
\[dh_{r}[u,a]=\frac{(w+1)A_{pd}}{2\pi^{2}l_{1}^{2}l_{2}^{2}}\cdot p\cdot dD_{wall }\cdot cos^{w}(\phi_{r})Xcos(\beta_{1})\cdot cos(\beta_{2})\cdot T_{s}(\psi_{ r})g(\psi_{r})cos(\psi_{r}) \tag{35}\]  
where \(l_{1}\) and \(l_{2}\) represent the distance between the \(Tx\) and the reflective point, as well as the distance between the reflective point and the receiver, respectively. The reflectance element and the reflective area are denoted by \(\rho\) and \(dD_{wall}\), respectively. In addition, \(\beta_{1}\) and \(\beta_{2}\) show the angles of irradiance to the reflecting point and receiver, respectively. Then, the VLC channels can be given with a basic model as  
\[y(t)=x(t)\otimes h(t)+n(t), \tag{36}\]  
where the transmitted signal is \(x(t)\), the optical received signal is \(y(t)\), \(h(t)\) represents the channel's impulse response, \(n(t)\) shows the total noise, and \(\otimes\) is the convolution operator. Mainly, reflections exploit the propagation of multipath that causes the received signal to spread out. The power delay profile (PDP) is used to assess the impact of transceiver multipath dispersion. One of the most extensively utilized VLC networks was suggested by Lee et al. [283; 284], in which the multipath PDP is defined as  
\[h(t)=\sum_{n=1}^{N_{LED}}\sum_{k=0}^{\infty}h^{(k)}(t;p_{n}) \tag{37}\]  
In Equation (35), NLED is the total number of LEDs considered to be the same, and each LED is assumed to transmit the same amount of power. In addition, \(p_{n}\) is the Nth LED's power spectral distribution (PSD). The response to the nth LED source following the kth reflection is [283]\[h^{(k)}(t;p_{n})=\int_{S}\bigg{[}L_{1}\cdot L_{2}\cdot\cdot\cdot L_{k+1}\cdot \Gamma_{n}^{(k)}\cdot rect\bigg{(}\frac{\theta_{k+1}}{\psi_{F}}\bigg{)}\times \delta\bigg{(}t-\frac{d_{1}+d_{2}+\ldots+d_{k+1}}{c}\bigg{)}\bigg{]}d_{A_{ref}},k\geq 1 \tag{38}\]  
where \(Lk\) indicates the \(kth\) path's path-loss as stated below:  
\[L_{1}=\frac{A_{ref}\cdot(w+1)\cdot cos^{w}(\phi_{1}).cos(\psi_{1})}{2\pi d_{1} ^{2}},L_{2}=\frac{A_{ref}\cdot(w+1)\cdot cos(\phi_{2})\cdot cos(\psi_{2})}{\pi d _{2}^{2}},\ldots,L_{k+1}=\frac{A_{PD}\cdot cos(\phi_{k})\cdot cos(\psi_{k+1})}{ \pi d_{k+1}^{2}}. \tag{39}\]  
The reflecting area is \(A_{ref}\) in Equation (39), the integration carried out in Equation (38) concerns the S surface of all the reflectors, and \(d_{k}\) denotes the kth path length. The rectangular function can be defined as follows:  
\[rect(x)=\bigg{\{} \begin{aligned} & 1,|x|\leq 1\\ & 0,Otherwise\end{aligned}  \tag{40}\]  
The reflected power \(\Gamma_{n}^{(k)}\) is then defined as  
\[\Gamma_{n}^{(k)}=\int_{\lambda}P_{n}(\lambda)\cdot\rho_{1}(\lambda)\cdot \rho_{2}(\lambda)\cdot\cdot\cdot\rho_{k}(\lambda)d\lambda \tag{41}\]  
where, \(\rho_{k}(\lambda)\) is the spectral reflectance. The PDP of the \(LOS\) path is defined as [283]  
\[h^{(k)}(t;p_{n})=L_{0}\cdot p_{n}\cdot rect\bigg{(}\frac{\theta_{0}}{\psi_{F} }\bigg{)}\cdot\delta\bigg{(}t-\frac{d_{0}}{c}\bigg{)}, \tag{42}\]  
where  
\[L_{0}=\frac{A_{pd}\cdot(w+1)\cdot cos^{w}(\phi_{0})\cdot cos(\psi_{0})}{2\pi d _{0}^{2}},P_{n}=\int_{\lambda}P_{n}(\lambda).\]  
The indoor VLC link includes three major sources of noise, which are (i) signal and ambient light-induced shot noise in the PD; (ii) noise from doors, windows, incandescent/fluorescent lamps and solar radiation; and (iii) electrical noise in the PD's preamplifier (known as thermal noise). Artificial/ambient lights cause DC interference which biases the received voltage. To accurately account for such noises, extensive indoor noise review/measurements are needed.