## 3 Results and Discussion
For instance, in Route 1, the BER with DFCE improves from 4.9 \(\times\) 10\({}^{-2}\) to 5.4 \(\times\) 10\({}^{-4}\) and from 1.1 \(\times\) 10\({}^{-1}\) to 1.3 \(\times\) 10\({}^{-3}\) at velocities of 2 m/s and 4 m/s, respectively. In Route 2, at 1 m/s, the BER with DFCE improves from 2.8 \(\times\) 10\({}^{-2}\) to 1.3 \(\times\) 10\({}^{-2}\). These results highlight the effectiveness of DFCE in accurately estimating the time-varying channel and recovering the transmitted signal, especially at higher velocities. Next, we assess the positioning performance of the mobile VLCP systems. Figure 7 displays the positioning results for the MISO and MIMO systems when the receiver moves along different routes. In both scenarios and routes, when DFCE is not utilized, the positioning results are only obtained at discrete locations near the receiver's moving trajectories. This limitation arises from solely using training symbols for channel estimation, resulting in a constant CSI estimation throughout the entire OFDM packet. Consequently, the positioning results in each packet overlap at the same locations. After employing DFCE, continuous positioning results become apparent, being in much closer alignment with the actual locations. This improvement is attributed to the ability of DFCE to dynamically estimate the channel, thereby yielding more accurate CSI. This accurate CSI, in turn, contributes to enhanced positioning accuracy within the VLCP system. Furthermore, in Figure 7b, due to the receiver's higher SNRs in Route 1, the positioning accuracy appears to be superior compared to Route 2 for the MIMO system. Therefore, the VLCP scheme with DFCE can leverage the advantages of higher SNRs to enhance positioning accuracy. In Figure 8, we compare the cumulative distribution functions (CDFs) of positioning errors calculated from the results in Figure 7, for both the MISO and MIMO systems. For the MISO system in Figure 8a, before using DFCE, 90% of positioning errors are less than 9.5 cm and 9.4 cm when the receiver moves along Route 1 and Route 2, respectively. After using DFCE, these errors decrease to 5.8 cm and 7.5 cm, respectively. Similar trends are observed in the MIMO system in Figure 8b. Along Route 1, before employing DFCE, 90% of positioning errors are less than 8.2 cm. However, this error reduces to 4.0 cm with the adoption of DFCE. The advantage of DFCE becomes more obvious along Route 2. Without DFCE, 90% of positioning errors are less than 22.4 cm. However, this error significantly reduces to 16.5 cm when DFCE is employed. These findings validate the effectiveness of the feedback mechanism in enhancing mobile positioning accuracy. It is worth mentioning that the BERs and positioning errors mentioned above are average values observed while the receiver moves along different routes. For VLC, the BERs are linked to the performance of all subcarrier channels. When channel characteristics degrade, error propagation due to decision feedback, which is a weakness of DFCE, impacts overall BER performance. This issue is particularly pronounced when light intensity is low. However, the CSI used for positioning remains accurate as it only depends on the estimated FDTF of the first subcarrier channel, as shown in Equations (6) and (15). At \(k=1\), subcarrier symbols experience a higher channel response and greater noise robustness compared to others. Therefore, even at overall BER levels higher than \(10^{-3}\) as in Figures 5 and 6, positioning errors are still maintained at the centimeter level. To further explain this, Figure 9 compares the eye diagrams of the real part for the received 4-QAM symbols in different subcarrier channels equalized with DFCE in Route 2. In both MISO and MIMO scenarios, we can clearly see that for \(k=1\), due to higher noise robustness, the eye diagram is clear and open. Conversely, for \(k=100\), due to lower noise robustness and the high possibility of error propagation from decision feedback, the eye diagram is closed, indicating poor performance.