## 2 Proposed Integrated Mobile VLCP Scheme
### Proposed Scheme for MISO Configuration
\begin{cases}\hat{H}_{T1\_total}^{n}(k)=\hat{H}_{DC,1}^{n}(0)e^{-2\pi k\lambda ft_{1} }+\hat{H}_{DC,2}^{n}(0)e^{-2\pi k\lambda ft_{2}}+\hat{H}_{DC,3}^{n}(0)e^{-2\pi k \lambda ft_{3}}\\ \hat{H}_{T2\_total}^{n}(k)=\hat{H}_{DC,1}^{n}(0)e^{-2\pi k\lambda ft_{1}}+\hat {H}_{DC,2}^{n}(0)e^{-2\pi k\lambda ft_{2}}+\hat{H}_{DC,4}^{n}(0)e^{-2\pi k \lambda ft_{4}}\\ \hat{H}_{T3\_total}^{n}(k)=\hat{H}_{DC,1}^{n}(0)e^{-2\pi k\lambda ft_{1}}+\hat {H}_{DC,3}^{n}(0)e^{-2\pi k\lambda ft_{3}}+\hat{H}_{DC,4}^{n}(0)e^{-2\pi k \lambda ft_{4}}\\ \hat{H}_{T4\_total}^{n}(k)=\hat{H}_{DC,2}^{n}(0)e^{-2\pi k\lambda ft_{2}}+\hat {H}_{DC,3}^{n}(0)e^{-2\pi k\lambda ft_{3}}+\hat{H}_{DC,4}^{n}(0)e^{-2\pi k \lambda ft_{4}}\end{cases} . \tag{5}\]  
Here, \(\hat{H}_{DC,i}^{n}(0)\) is the estimated channel DC gain between the \(i\)th LED and PD1, \(\Delta f\) is the subcarrier frequency interval, and \(t_{i}\) is the propagation time of the signal from the \(i\)th LED to PD1. By squaring both sides simultaneously and setting \(k=1\), we can obtain the estimated channel DC gain from each LED to PD1:  
\[\left\{ \begin{array}{l}\hat{H}_{DC,1}^{n}(0)\approx\frac{1}{3}\big{|}\big{|} \hat{H}_{T1\_total}^{n}(1)\big{|}+\big{|}\hat{H}_{T2\_total}^{n}(1)\big{|}+ \big{|}\hat{H}_{T3\_total}^{n}(1)\big{|}-2\big{|}\hat{H}_{T4\_total}^{n}(1) \big{|}\big{|}\\ \hat{H}_{DC,2}^{n}(0)\approx\frac{1}{3}\big{|}\big{|}\hat{H}_{T1\_total}^{n}(1 )\big{|}+\big{|}\hat{H}_{T2\_total}^{n}(1)\big{|}+\big{|}\hat{H}_{T4\_total}^{n }(1)\big{|}-2\big{|}\hat{H}_{T3\_total}^{n}(1)\big{|}\big{|}\\ \hat{H}_{DC,3}^{n}(0)\approx\frac{1}{3}\big{|}\big{|}\hat{H}_{T1\_total}^{n}(1 )\big{|}+\big{|}\hat{H}_{T3\_total}^{n}(1)\big{|}+\big{|}\hat{H}_{T4\_total}^{n }(1)\big{|}-2\big{|}\hat{H}_{T2\_total}^{n}(1)\big{|}\big{|}\\ \hat{H}_{DC,4}^{n}(0)\approx\frac{1}{3}\big{|}\big{|}\hat{H}_{T2\_total}^{n}(1 )\big{|}+\big{|}\hat{H}_{T3\_total}^{n}(1)\big{|}+\big{|}\hat{H}_{T4\_total}^{n }(1)\big{|}-2\big{|}\hat{H}_{T1\_total}^{n}(1)\big{|}\end{array} \right.. \tag{6}\]  
In our VLCP scheme, without loss of generality, we consider a VLC channel model where LEDs are assumed to follow a Lambertian radiation pattern [31]. Whether phosphor LEDs or RGB LEDs, as long as they follow this radiation pattern, they can be used in our system. Furthermore, for other types of radiation patterns, as long as the radiation pattern is known and the distances between LEDs and PDs can be determined from the estimated channel DC gains, these types of LEDs can also be used. Considering the Lambertian radiation model, the distance between the \(i\)th LED and PD1 can be estimated using the RSS scheme:  
\[\hat{D}_{i}^{n}=\sqrt[n+1]{\frac{(m+1)AT_{s}(\varphi)g(\varphi)h^{m+1}}{2\pi \hat{H}_{DC,i}^{n}(0)}}, \tag{7}\]  
where \(m\) is the Lambertian emission order, \(A\) is the effective area of the PD, \(T_{s}(\varphi)\) is the optical filter gain, \(g(\varphi)\) is the concentrator gain, and \(h\) is the vertical distance between the LEDs and the receiving plane. Based on Equation (7), we can select three from the four estimated distances to estimate the location of the receiver. For example, using \(\hat{D}_{1}^{n}\), \(\hat{D}_{2}^{n}\), and \(\hat{D}_{3}^{n}\), the horizontal coordinate of PD1 (\(\hat{x}_{r1}\), \(\hat{y}_{r1}\)) can be estimated with trilateration by solving the following:  
\[\left\{ \begin{array}{l}\big{(}\hat{D}_{1}^{n}\big{)}^{2}=\big{(}\hat{x}_{r1}- x_{1}\big{)}^{2}+\big{(}\hat{y}_{r1}-y_{1}\big{)}^{2}+h^{2}\\ \big{(}\hat{D}_{2}^{n}\big{)}^{2}=\big{(}\hat{x}_{r1}-x_{2}\big{)}^{2}+\big{(} \hat{y}_{r1}-y_{2}\big{)}^{2}+h^{2}\\ \big{(}\hat{D}_{3}^{n}\big{)}^{2}=\big{(}\hat{x}_{r1}-x_{3}\big{)}^{2}+\big{(} \hat{y}_{r1}-y_{3}\big{)}^{2}+h^{2}\\ \end{array} \right.. \tag{8}\]  
In the MISO scenario, (\(\hat{x}_{r1}\), \(\hat{y}_{r1}\)) can simply be assumed as the receiver's horizontal coordinate (\(\hat{x}_{R}\), \(\hat{y}_{R}\)).