## 3 Result Analysis and Discussion
### Peak-to-Average-Power Ratio (PAPR)  
The PAPR is a crucial parameter in optical OFDM systems, significantly influencing the power efficiency of optical transmission. A large PAPR indicates a substantial disparity between the average and maximum power levels, which can lead to enlarged nonlinearity and the introduction of undesirable distortions. Conversely, a low PAPR indicates a more regular energy distribution [49; 50]. In the Flip-F-OFDM technique, the dipolar signal is split into two unipolar values: the positive and negative halves, which include all negative values that are inverted and transmitted as positive. These components are conveyed in separated time slots, and the receiver subsequently recombines them to reconstruct the original F-OFDM signal. The maximum power for Flip-F-OFDM will occur in either the positive side \({}^{+}x(n)\) or the flipped negative side \({}^{-}x(n)\), Thus, the peak power for Flip-F-OFDM is specified by:  
Figure 10: Flip\(-\)F\(-\)OFDM addition complexity. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Schemes** & **Additions** & **Multiplications** \\ \hline Proposed Flip-F-OFDM & 388 & 16,452 \\ Conventional Flip-F-OFDM & 964 & 32,964 \\ JM-DCO-F-OFDM [38] & 964 & 32,964 \\ HSF Flip-OFDM [44] & 964 & 196 \\ Flip-OFDM [19; 43] & 2308 & 516 \\ ACO-OFDM [19; 37; 43] & 2308 & 516 \\ DCO-OFDM [14; 19; 43] & 2308 & 516 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational complexity assessment among the proposed Flip-F-OFDM, conventional Flip-F-OFDM, JM-DCO-F-OFDM, HSF Flip-OFDM, Flip-OFDM, ACO-OFDM, and DCO-OFDM. \[\max\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2}\biggr{\}}=\max\Bigl{\{}\max \bigl{|}x^{+}(n)\bigr{|}^{2},\;\max\bigl{|}x^{-}(n)\bigr{|}^{2}\biggr{\}} \tag{34}\]  
But since both halves are derived from the same signal \(x(n)\), then (34) can be rewritten as:  
\[\max\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2}\biggr{\}}=\max\Bigl{\{}|x(n) |^{2}\biggr{\}} \tag{35}\]  
Furthermore, the overall average power in Flip-F-OFDM is the cumulative total of the average powers of the two components (the flipped negative and the positive values) that are transmitted independently. Each segment utilizes an entire time slot; thus, the total average power of the Flip-OFDM signal is articulated as follows:  
\[E\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2}\biggr{\}}=E\Bigl{\{}\big{|}x^{ +}(n)\big{|}^{2}\biggr{\}}+E\Bigl{\{}\big{|}x^{-}(n)\big{|}^{2}\biggr{\}} \tag{36}\]  
Since \(x^{+}(n)\) and \(x^{-}(n)\) are derived from the same signal, the average power is split evenly between the two halves as follows:  
\[E\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2}\biggr{\}}=2\times\frac{1}{2}E \Bigl{\{}\big{|}x(n)\big{|}^{2}\biggr{\}}=E\Bigl{\{}\big{|}x(n)\big{|}^{2}\biggr{\}} \tag{37}\]  
Using (35) and (37) for peak power and average power, the PAPR for Flip-OFDM is given as:  
\[\text{PAPR}_{\text{Flip-F-OFDM}}=\frac{\max\biggl{\{}\Big{|}x_{\text{Flip}}(n) \Big{|}^{2}\biggr{\}}}{E\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2}\biggr{\}}} \tag{38}\]  
For the purported Flip-F-OFDM scheme, the peak power stays congruous with that of the conventional Flip-F-OFDM, as the elimination of Hermitian symmetry impacts the spectral structure without altering the peak amplitude of the time domain signal. In addition, since the real and imaginary parts contribute to the overall signal power, the average power is maintained at the same level as in conventional Flip-F-OFDM. Consequently, the PAPR of the proposed Flip-F-OFDM is articulated as follows:  
\[\text{PAPR}_{\text{NHS Flip-F-OFDM}}=\frac{\max\biggl{\{}\Big{|}x_{\text{Flip}}(n )\Big{|}^{2}\biggr{\}}}{E\biggl{\{}\Big{|}x_{\text{Flip}}(n)\Big{|}^{2} \biggr{\}}}=\text{PAPR}_{\text{Flip-F-OFDM}} \tag{39}\]  
The mathematical analysis indicates that the NHS-Flip-F-OFDM method effectively prevents any rise in the PAPR [43]. As a result, the NHS-F-OFDM approach facilitates the generation of unipolar F-OFDM signals that maintain the same PAPR levels as those produced by conventional unipolar Flip-F-OFDM techniques.