## 4 Results and Discussion  
To study the performance of the advanced PS bit loading scheme, we first evaluate the characteristic of the system. Figure 3 shows the luminance-voltage-current (L-V-I) characteristics of the LD which were experimentally obtained at 24 \({}^{\circ}\)C. The threshold current of the LD is 25 mA. And a large linear operating area for the LD can be verified from Figure 3.  
Before transmitting the PS bit loading DMT signal, the frequency response was often characterized as a figure of merit to evaluate the allowable direct modulation bandwidth of the whole system. Figure 4 shows the S21 transfer response of the system at different driven currents, which was measured by a network analyzer. The decrease throughout in intensity at the high-frequency region is mainly caused by the bandwidth limitation of the amplifier and the APD. Theoretically, raising the driven current makes the LD up-shift its relaxation oscillation frequency which results in the extension of the modulation bandwidth [11]. However, from Figure 4, we find that the high-frequency response was declined as the driven current increased. Additionally, it was caused by the saturation of the APD. Although an absorptive ND filter was utilized to attenuate the incident light on the APD, the light attenuation was not enough when the output power was relatively large at a high driven current. As a consequence, the modulation bandwidth (-10 dB) of the system is about 1 GHz due to these constraints. Figure 3: The L-V-I characteristics of the LD at 24 \({}^{\circ}\)C.  
To further discuss the transmission performance of the system, we searched for the optimal operating point by sending PS bit loading DMT data at the bandwidth of 1.5 GHz. Firstly, SNR estimation was done at different driven currents, and Figure 5a shows the SNR versus subcarrier index. At this time, signal Vpp was fixed at 200 mV. At low driven current region, the output power of the LD was limited, and the system was constrained by the whole SNR. Increasing the driven current from 37 to 57 mA increased the SNR among all subcarriers. However, the overly driven current of larger than 57 mA further increased light intensity and made the APD saturated, which resulted in the reduction of the SNR. And it should be noted that the enlarged driven current declines the frequency response at the low-frequency region, which may also deteriorate the system performance. The SNR distribution of subcarriers corresponds to the frequency response shown in Figure 4.  
Figure 5b shows the source entropy versus subcarrier index at driven current at 37 mA and 57 mA. In a sense, the distribution of the SNR reflects the source entropy loading of subcarriers, according to the entropy-loading strategy. Table 1 shows the GMI at different driven currents. The highest GMI can be obtained at a driven current of 57 mA. And GMI at 37 mA was lower than that at 57 mA even with a larger modulation bandwidth due to the SNR limitation. Figure 4: The S21 plot at different driven currents. Figure 5: (**a**) SNR versus subcarrier index at different driven currents; (**b**) Source entropy versus subcarrier index at driven current of 37 mA and 57 mA. At the optimal driven current of 57 mA, we measured the SNR of all subcarriers at different signal Vpp, as represented in Figure 6. A similar tendency can be found just as is shown in Figure 5a. Increasing the signal Vpp raised the SNR of the received signal, thus improved the system throughput. This indicates the linear operating area of the LD and the output power varies linearly with the signal Vpp. Table 2 shows the GMI at different signal Vpp. At the signal Vpp of 240 mV, we achieved the highest GMI of 7.03 bits/symbol. When the signal Vpp exceeds 240 mV, nonlinear distortion will be introduced, and it causes performance loss for the system. In the following experiments, the operating point of the system was selected as driven current at 57 mA and signal Vpp at 240 mV.