## 2 Proposed Integrated Mobile VLCP Scheme
### Proposed Scheme for MIMO Configuration  
Next, we consider the MIMO scenario. Figure 3 illustrates the block diagram of the proposed indoor integrated mobile VLCP scheme for MIMO. At the transmitter, serial source bits are converted into multiple parallel data streams, mapped into QAM symbols, and encoded by STBC. Here, STBC is introduced to ensure the feasibility of DFCE in the MIMO scenario, with the encoding matrix depending on the number of transmitting antennas \(N_{T}\). In this work, we focus on a \(4\times 2\) MIMO system, where the receiver has two PDs (PD1 and PD2). Thus, similar to the MISO case, in this MIMO configuration, there are also four slots in a VLCP data block. For the \(n\)th VLCP data block, the STBC encoding matrix is expressed as [32]:  
\[\mathbf{X}^{n}(k)= \begin{bmatrix}X_{1}^{n,1}(k)&X_{2}^{n,2}(k)&X_{3}^{n,3}(k)& 0\\ -X_{1}^{n,2*}(k)&X_{2}^{n,1*}(k)&0&X_{4}^{n,3}(k)\\ X_{1}^{n,3*}(k)&0&-X_{3}^{n,1*}(k)&X_{4}^{n,2}(k)\\ 0&X_{2}^{n,3*}(k)&-X_{3}^{n,2*}(k)&-X_{4}^{n,1}(k)\end{bmatrix} , \tag{10}\]  
where \(\star\) is the conjugate operation and \(X_{i}^{n,l}(k)\) (\(i=1,\,2,\,3,\,4\) and \(l=1,\,2,\,3,\,4\)) is the \(k\)th transmitted subcarrier symbol of the \(l\)th OFDM symbol at the \(i\)th LED. Each row of the matrix corresponds to signals transmitted during the same slot. These STBC symbols are modulated into DCO-OFDM symbols and transmitted by each LED. Upon traversing the MIMO channel, the VLC signal arrives at the mobile receiver. Following light-to-current inversion, DC filtering, and OFDM demodulation, the signal received at the \(j\)th (\(j=1,\,2\)) PD in the \(n\)th STBC block is represented in the frequency domain as follows:  
\[\mathbf{Y}_{j}^{n}(k)=\mathbf{X}^{n}(k)\mathbf{H}_{j}^{n}(k)+\mathbf{N}_{j}^{ n}(k). \tag{11}\]  
Here, \(\mathbf{Y}_{j}^{n}(t)=[Y_{j}^{n,1}(k),\,Y_{j}^{n,2}(k),\,Y_{j}^{n,3}(k),\,Y_{j} ^{n,A}(k)]^{\text{T}}\), where \(Y_{j}^{n,l}(k)\) is the kth received subcarrier symbol of the lth OFDM symbol at the jth PD, \(\mathbf{H}_{j}^{n}(k)=[H_{j1}^{n}(k),\,H_{j2}^{n}(k),\,H_{j3}^{n}(k),\,H_{j4} ^{n}(k)]^{\text{T}}\), where \(H_{\bar{n}}^{n}(k)\) is the FDTF of the channel between the ith LED and the jth PD, and \(\mathbf{N}_{j}^{n}(k)\) is the noise matrix. The parallel OFDM data are then decoded by STBC, demapped, and finally converted into serial sink bits. Following STBC decoding, the kth OFDM subcarrier symbol in the nth STBC matrix is decoded by [32]:  
\[\mathbf{\hat{S}}^{n}(k)=\frac{ \begin{bmatrix}\hat{H}_{\bar{n}}^{n*}(k)Y_{j}^{ n,1}(k)+\hat{H}_{\bar{n}}^{n}(k)Y_{j}^{n,2*}(k)-\hat{H}_{\bar{n}}^{n*}(k)Y_{j}^{ n,3*}(k)-\hat{H}_{\bar{n}}^{n*}(k)Y_{j}^{n,4}(k)\\ \hat{H}_{\bar{n}}^{n*}(k)Y_{j}^{n,1}(k)-\hat{H}_{j1}^{n}(k)Y_{j}^{n,2*}(k)+\hat {H}_{\bar{n}}^{n*}(k)Y_{j}^{n,3}(k)-\hat{H}_{\bar{n}}^{n}(k)Y_{j}^{n,4*}(k)\\ \hat{H}_{\bar{\beta}}^{n*}(k)Y_{j}^{n,1}(k)+\hat{H}_{\bar{\beta}}^{n}(k)Y_{j}^{ n,2}(k)+\hat{H}_{\bar{\beta}}^{n}(k)Y_{j}^{n,3*}(k)+\hat{H}_{\bar{\beta}}^{n}(k)Y_{j}^{ n,4*}(k)\\ \sum_{i=1}^{4}\Big{|}\hat{H}_{\bar{\beta}}^{n}(k)\Big{|}^{2}\end{bmatrix} . \tag{12}\]  
Based on Equation (12), prior to STBC decoding, the receiver requires a priori knowledge of CSI. To track time-varying channels, we employ DFCE to obtain the CSI, similar to the MISO scenario. The training sequence is used to acquire the initial CSI, resulting in \(\mathbf{\hat{S}}^{n}(k)\). Then, based on \(\mathbf{\hat{S}}^{n}(k)\), the receiver derives the decision value \(\mathbf{\hat{E}}^{n}(k)\), which is encoded by STBC to reconstruct the estimated transmitted signal matrix \(\mathbf{\hat{X}}^{n}(k)\). Finally, \(\mathbf{\hat{H}}_{j}^{n+1}(k)\) is updated for subsequent calculations of \(\hat{\mathbf{S}}^{n+1}(k)\).