## 3 Results
### Experimental Results
The highest GMI appears at the 50 th to the 130 th subcarrier, which approximately indicates the spectrum from 70 MHz to 180 MHz corresponding to the flat response part in Figure 3. When the distance goes larger than 3 m, the higher frequency part of the response decreases dramatically, causing the decrease in the bandwidth from 350 MHz to 250 MHz. Figure 7f shows the actual received PS bitloading constellation. Each constellation includes the data in all the subcarriers. The blue dots in Figure 7a-e show the modulation order that the classical bitloading algorithm can achieve under the same SNR conditions with a 7% FEC limit. Though classical bitloading can fill the uneven frequency response with different orders of modulation, the information entropy of uniform distributed constellations is restricted to the integers according to the modulation order which must be integers. Therefore, the entropy in each subcarrier is much lower than the one with PS bitloading. With the help of the probabilistic distribution, PS bitloading has much higher spectrum efficiency than the classical one. Figure 8 shows the PS distribution and the constellation of classical bitloading in the 80 th, the 125 th, and the 160 th subcarrier at a distance of 3 m, as noted in Figure 7c. The center frequency of the 80 th subcarrier is 112 MHz, and the SNR is 22.3 dB, which supports the QAM order up to 7. All the constellation points of the classical bitloading signal, as shown in Figure 8 iv, are of equal probability. With PS, such SNR can support a GMI up to 7.33 bit/Hz for its unequal probability in the constellation points. The probabilistic distribution in the 80 th subcarrier is illustrated in Figure 8i. Similarly, the SNR in the 125 th subcarrier, of which the frequency is 175 MHz, is 20.0 dB. The QAM order supported in this subcarrier is up to 6, while the supported GMI is up to 6.66 bit/Hz as shown in Figure 8 ii,v. In addition, Figure 8 iii,vi shows the PS distribution and the QAM constellation of the 160 th subcarrier  
Figure 7: GMI, source entropy (SE) and the achievable bitloading order of the 250 subcarriers at the calibration point (**a**) 1 m, (**b**) 2 m, (**c**) 3 m, (**d**) 4 m, (**e**) 5 m; and (**f**) the overall received PS bitloading constellation at a distance from 1 m to 5 m.  
located in the frequency of 224 MHz. The supported QAM order in this subcarrier is up to 5 due to the SNR of 16.7 dB, and the GMI is up to 5.68 bit/Hz. The comparison of the average information entropy in each subcarrier between the PS bitloading and the classical bitloading is shown in Table 3.  
The spectrum efficiency of classical bitloading is discrete in each subcarrier, which causes a gap between the spectrum efficiency of the modulation and the Shannon limit. In comparison, the PS bitloading fulfills the modulation with continuous spectrum efficiency. The GMI of PS bitloading signals approaches the Shannon limit as much as possible. Therefore, the average spectrum efficiency of PS bitloading is higher than the classical bitloading. Table 3 shows that the average GMI of PS bitloading can be 0.917 bit/Hz higher than the classical bitloading in the experiment. The testing results at all the points are shown in Figure 9, where all the points are tested with the NGMI strictly greater than 0.92. The highest AIR in this system is 1.8484 Gb/s at the distance of 2 m, which is the highest rate in LED headlight based VLC system as far as we know. The quality of the imaging of the two headlights at the receiving plane determines the SNR. Due to the close distance, the space between the two lights is slightly bigger than the space between the PDs at the point of 1 m. Therefore, the highest AIR appears at the point of 2 m. Table 4 shows the AIR at each calibration points. Figure 9 also shows the error between the tested AIR and the estimated AIR interpolated from the measured points. Within the range of 1 m to 3 m, the AIR increases and decreases linearly.