## 2 System Model
### VLC Channel Model  
The indoor VLC channel model consists of both line-of-sight (LOS) and non-line-of-sight (NLOS) links. Although NLOS can provide complementary communication through reflected signals, its received power is typically more than 7 dB lower than the worst  
Figure 1: Indoor VLC/Wi-Fi heterogeneous network model.  
line-of-sight link [19]. The path loss of NLOS signals in typical indoor environments (e.g., an office or a factory) with wall reflectivity of about 0.7 can be expressed as follows:  
\[P_{\text{NLOS}}=P_{l}\cdot H_{\text{LOS}}\cdot\frac{\rho A_{\text{eff}}}{\left(d _{1}+d_{2}\right)^{2}}\cos^{m}(\phi)\cos(\theta) \tag{1}\]  
where \(\rho\) is the reflectivity, \(P_{l}\) is the transmit power, \(H_{\text{LOS}}\) is the channel gain of the LOS link, \(A_{\text{eff}}\) is the effective receiving area of the receiver, \(\phi\) is the LED transmitting angle, \(\psi\) is the PD receiving angle, and \(m=-\ln 2/\ln(\cos\phi_{1/2})\) is the Lambertian radiation coefficient; \(d_{1}\) and \(d_{2}\) are the distances from the transmitting end to the reflecting surface and from the reflecting surface to the receiving end, respectively. [PERSON] et al. experimentally determined that the reflected light's contribution to the total received power of the receiver contribution is very low [20]. As shown in Figure 2, direct light occupies the vast majority of the received light, as high as 95.16%, and the proportion of primary and secondary reflected light is relatively low due to the secondary path loss and reflection efficiency limitations and the NLOS is significantly affected by multipath interference and dynamic masking. Therefore, this paper uses LOS as the primary channel model for indoor visible light communication to study the network handover problem under this link.  
The optical channel gain from VLC AP to the user is expressed as  
\[H_{i,j}^{\text{VLC}}(0)=\begin{cases}\frac{(m+1)A_{\text{eff}}}{2\pi D_{i,j}^{ 2}}\cos^{m}\phi T_{s}(\psi)g(\psi)\cos(\psi),&0\leqslant\psi\leqslant\psi_{c} \\ 0,&\psi>\psi_{c}\end{cases} \tag{2}\]  
where \(m=-\ln 2/\ln(\cos\phi_{1/2})\) is the Lambertian radiation coefficient; \(A_{\text{eff}}\) is the effective receiving area of the receiver; \(D_{i,j}\) is the linear distance between the transmitter and receiver; \(\phi\) is the light-emitting diode emission angle; \(\psi\) is the photoelectric detector receiving angle; \(T_{s}(\psi)\) is the optical filter gain; \(g(\psi)\) is the optical concentrator gain; and \(\psi_{c}\) is the receiver half field angle, which determines whether the user can receive the optical signal from the line-of-sight link. The optical concentrator gain is given by [21]  
\[g(\psi)=\begin{cases}\frac{m^{2}}{\sin^{2}\psi_{c}},0\leq\psi\leq\psi_{c}\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad 0,\psi\geq\psi_{c} \end{cases} \tag{3}\]  
Figure 2: Normalized impulse response percentage of direct and reflected light [20].  
where \(n\) is the refractive index of the optical receiver. The signal-to-interference-plus-noise ratio (SINR) of user \(j\) served by VLC AP \(i\) is expressed as  
\[\xi_{i,j}^{\rm VLC}=\frac{\left[\gamma P_{\rm t}^{\rm VLC}H_{i,j}^{\rm VLC}(0) \right]^{2}}{\sum\limits_{k\in K}\left[\gamma P_{\rm t}^{\rm VLC}H_{k,j}^{\rm VLC }(0)\right]^{2}+N_{\rm VLC}B_{\rm VLC}} \tag{4}\]  
where \(\gamma\) is the photoelectric conversion coefficient of the receiver; \(P_{\rm t}^{\rm VLC}\) is the transmitting power; \(K\) is the interference set of VLC APs; \(H_{k,j}^{\rm VLC}(0)\) is the interference channel gain of AP to user \(j\); \(N_{\rm VLC}\) is the noise power spectral density (approximately \(1\times 10^{-21}\) in an indoor environment), and \(B_{\rm VLC}\) is the bandwidth of the visible light communication system.