## 2 Proposed Integrated Mobile VLCP Scheme
### Proposed Scheme for MISO Configuration  
We first consider the MISO scenario. Figure 2 depicts the block diagram of the proposed integrated mobile VLCP scheme for MISO. At the transmitter, serial source bits are converted into quadrature amplitude modulation (QAM) symbols \(X(k)\), where \(k\) represents the subcarrier channel index (\(k\) = 1, 2, 3, \(\ldots\)). These QAM symbols are then modulated into the DC-biased optical OFDM (DCO-OFDM) signal \(x(t)\). Next, \(x(t)\) enters  
Figure 1: Schematic diagram of an integrated mobile VLCP system model. the LED selection stage, where the selector determines the groups of LEDs transmitting the identical \(x(t)\) simultaneously. In our VLCP system, the total number of LEDs is four, which is commonly used to provide adequate and uniform light distribution in the receiving plane. From a communication perspective, adopting more LEDs can enhance SNRs for better link performance. Based on this, a simple way is to adopt all LEDs to send the same signal. However, from a positioning perspective, to enable trilateration, at least three LEDs are required, and the distances between each LED and the PD need to be estimated separately. Using a single-LED setup is inadequate to support trilateration as it does not provide enough distance measurements. For our four-LED setup, using all four LEDs to transmit signals simultaneously does not allow for the establishment of sufficient equations to calculate the distances between LEDs and the PD. To optimize both communication and positioning, different groups of LEDs can be used to transmit signals and calculate the CSI from multipath channels for VLP. For each group, a subset of \(N_{used}\) LEDs out of four LEDs is selected to transmit the same signal. In the case where \(N_{used}=1\), each of the four LEDs transmits the signal in one slot, but this configuration may not optimize the SNR, leading to reduced DFCE accuracy. The same issue arises for \(N_{used}=2\). Since involving more LEDs can enhance the SNR, we focus on \(N_{used}=3\), dividing the four LEDs into four groups: Group 1 (LED1, LED2, LED3), Group 2 (LED1, LED2, LED4), Group 3 (LED1, LED3, LED4), and Group 4 (LED2, LED3, LED4). This division is the optimized solution that ensures both signal recovery and optimized link performance at the receiver. The number of groups equals the total slots per cycle. After each cycle, the CSI can be estimated for VLCP and fed back for the next cycle. The four slots form a VLCP data block, and for the \(n\)th VLCP data block, the LED selection is determined by the LED selection matrix:  
\[\mathbf{X}^{n}(t)= \begin{bmatrix}x_{1}^{n,1}(t)&x_{2}^{n,1}(t)&x_{3}^{n,1}(t)&0 \\ x_{1}^{n,2}(t)&x_{2}^{n,2}(t)&0&x_{4}^{n,2}(t)\\ x_{1}^{n,3}(t)&0&x_{3}^{n,3}(t)&x_{4}^{n,3}(t)\\ 0&x_{2}^{n,4}(t)&x_{3}^{n,4}(t)&x_{4}^{n,4}(t)\end{bmatrix} . \tag{1}\]  
Here, \(x_{i}^{n,w}(t)\) represents the \(w\)th OFDM symbol emitted by the \(i\)th LED in the \(n\)th VLCP data block, where \(i=1\), 2, 3, 4 and \(w=1\), 2, 3, 4. With the same \(w\), \(x_{i}^{n,w}(t)\) in each row of the matrix represents the same signals transmitted during the same slot, and different \(i\) values represent different expressions of the same signals emitted by different LEDs. After passing through multipath channels, the VLC signal arrives at the mobile receiver equipped with a single PD, denoted as PD1. Following light-to-current inversion, DC filtering, and time-to-frequency transformation, the electrical signal of the \(n\)th VLCP data block received by PD1 in the frequency domain can be expressed as follows:  
\[\mathbf{Y}^{n}(k)=\mathbf{X}^{n}(k)\mathbf{H}^{n}(k)+\mathbf{N}^{n}(k). \tag{2}\]  
Here, \(\mathbf{X}^{n}(k)\) is the frequency representation of \(\mathbf{x}^{n}(t)\), implying that each element \(X_{i}^{n,l}(k)\) (\(l=1\), 2, 3, 4) in \(\mathbf{X}^{n}(k)\) is the frequency representation of \(x_{i}^{n,w}(t)\) in \(\mathbf{x}^{n}(t)\) after Fourier transform.