## 5 Results and Discussion
### Achievable Transmission Rate  
To maximize the capacity of the POP system, the split sub-band number \(L\) must first be evaluated. Both a fixed electrical power of six decibel-milliwatts and a 10-mA biasing current are used for the practical transmission. The CR is maintained at a constant \(\gamma~{}=\) 12 dB. In addition, the Chow bit-loading algorithm [PERSON] (1975) with a BER target of \(P_{e}=1\times 10^{-3}\) is adopted. The number of sub-carriers varies with the fixed spacing \(\Delta f=0.488\) MHz. Note that channel coding is not used in this study.  
For various signal bandwidths between 50 MHz and 500 MHz, the total achievable transmission rates of the C-DMT and the proposed scheme with \(L=1\), \(L=4\), and \(L=8\) are compared in Figure 9a. Both the proposed scheme and the C-DMT can achieve their maximal transmission rates based on the optimal signal bandwidth \(B_{u}\), which varies along with \(L\). In the case of \(L=1\), the optimal bandwidth range \(\psi\) is limited between approximately 150 MHz and 200 MHz due to the achievable transmission rate is sensitive to the signal bandwidth. In addition, the performance is severely degraded when the used bandwidth exceeds the \(\psi\). The \(\psi\) for both \(L=4\) and \(L=8\) are wider than that of \(L=1\). In addition, compared to the C-DMT, the transmission rate of the proposed scheme with  
Figure 8: Power spectral density (PSD) performance comparison.  
Figure 7: CCDF performance comparison: (**a**) \(\mathbb{E}\Big{\{}\left|\rho_{\text{C}}(q)\right|^{2}\Big{\}}\) values for various subcarriers (**b**) probability density functions (PDFs) of aperiodic autocorrelation function (ACF) performance comparison (for 512 subcarrier with 4000 discrete multi-tone (DMT) symbols).  
\(L=4\) improves by at least eight percent, and its highest transmission rate is achieved at approximately 1.204 Gbps for \(B_{u}=228\) MHz. For this case, the corresponding bit and power distributions of each sub-carrier are depicted in Figure 9b. As discussed in the previous section, each subcarrier in the same sub-band obtains the same \(SNR^{l}\) value after both equalization and dispreading have taken place. Therefore, based on the calculations of the Chow algorithm [25], both equal numbers of the modulated bits and equal amounts of power are allocated to each sub-carrier in the same sub-band, even in a frequency selective channel such as the POF. As shown in the figure, there also exists some slight distinction of the bit and power allocations in the last sub-band because the target number of total bits has already nearly been allocated by the previous sub-carriers, leading to fewer bits being assigned to the last sub-carrier (e.g., a single bit could be enough). In addition, the effective SNR distribution among the sub-carriers for the proposed scheme (\(L=4\)) is depicted in Figure 9c. As seen in the figure, the overall SNR gain of the system is achieved obviously by the proposed scheme compared the C-DMT at the same clipping threshold.  
Stated thusly, a moderate \(L\) can guarantee both the validity and the feasibility of the proposed scheme as well as maximize the transmission rate, which is more important for a practical transmission system. Note that the proposed scheme chooses the optimal \(L\) according to the actual signal bandwidth.  
Figure 9: Fifty-metre step index polymer optical fiber (SI-POF) transmission (**a**) Transmission rate (at a bit error rate (BER) of \(10^{-3}\), without channel coding) (**b**) Bit and power distribution of the proposed scheme with \(L=4\) (for transmission rate of 1.204 Gbps) (**c**) The effective SNRs distribution.