## 4 Results and Discussion
As mentioned before, the modulation bandwidth severely decreases at a high-frequency region due to the bandwidth limitation of the system devices. Under the optimal operating point, we compared the system performance at different signal modulation bandwidths. Figure 7a shows the SNR in every DMT subcarrier. Increasing the signal bandwidth enlarges the attenuation at a high-frequency region. And the whole SNR will be decreased due to power allocation under the total power budget. Figure 7b-f shows the electrical spectra of the transmitted signal (Tx) and received signal (Rx) at different bandwidths, from which we can understand the system frequency response. The electrical spectra begin to attenuate with a greater negative slope when the signal bandwidth is larger than 1 GHz, which represents the limited system bandwidth. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Current (mA)** & **37** & **47** & **57** & **67** & **77** \\ \hline GMI (bits/symbol) & 5.2513 & 6.0569 & 6.8646 & 6.3487 & 5.8441 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The GMI at different driven currents. Figure 6: SNR versus subcarrier index at different signal Vpp. Under the optimal operating point of the system, source entropy and GMI versus subcarrier index at different signal bandwidths are illustrated in Figure 8a-e. SNR represents the channel capacity to a certain extent and the source entropy obviously follows the trend of channel capacity according to Equation (3). As the gray region shown in the figure, the gap between the source entropy and the GMI is narrow, which means that PS bit loading scheme brings great shaping gain for the system and helps to raise the spectral efficiency. And source entropy adjustment method can be utilized to further improve the system performance. We also give the QAM order that the bit and power loading can achieve in the same SNR limitation. The QAM order was calculated under the 7% FEC threshold. Figure 7: (a) SNR versus subcarrier at different signal bandwidths; (b–f) The electrical spectra of transmitted signal (Tx) and received signal (Rx) at different signal bandwidths. Compared to PS bit loading, the QAM order of bit and power loading can only be an integer, and the entropy in each subcarrier is much lower than with PS bit loading. Therefore, the spectral efficiency of PS bit loading is higher than that of bit and power loading. With PS bit loading, the capacity of the system can approach the Shannon limit, providing higher data rates under the same power budget. Besides, the source entropy of the subcarriers can be adjusted for flexible rate adaption according to different channel conditions, making the transmission link more stable and reliable. Figure 8f shows the NGMI versus subcarrier index under the optimal operating point at the signal bandwidth of 1.5 GHz. The minimum NGMI is 0.932, located in the 31 th subcarrier. And NGMI in all subcarriers are strictly above 0.92, revealing that with 8.7% FEC overhead, error-free post-FEC results  
Figure 8: (**a–e**) Source entropy, GMI, and achievable bit loading QAM order versus subcarrier index at signal bandwidth from 1.3 GHz to 1.7 GHz; (**f**) NGMI versus subcarrier index at signal bandwidth of 1.5 GHz. can be produced [25]. It should be noted that there is still a gap between the tested NGMI and the NGMI threshold of 0.92, so there exist margins in the system. Figure 9 illustrates the constellation diagrams of the received signal at the signal bandwidth of 1.5 GHz with different entropy from 9 to 4 bits/symbol. The AIR versus different signal modulation bandwidths was measured, as shown in Table 3. When the bandwidth was smaller than 1.5 GHz, the AIR increased as the bandwidth enlarged. At this time, the system was bandwidth-constrained so the bandwidth extension improved the system performance. However, the AIR decreased when the bandwidth enlarged overly (larger than 1.5 GHz). Because the system was SNR constrained and the high-frequency response was severely attenuated.