## 2 System Model
### The Proposed Flip-Filtered OFDM  
#### 2.2.1 Transmitter  
To address the Hermitian symmetry (HS) constraints in real signal generation, we introduce a novel scheme, non-Hermitian symmetry (NHS), that reduces system hardware complexity by eliminating the necessity for frequency symbols to adhere to HS constraints. The schema of the suggested Flip-F-OFDM is illustrated in Figure 2. Indeed, the proposed Flip-F-OFDM technique eliminates the need for HS constraints by directly applying the IFFT to the frequency symbols. This method enables the creation of a nonreal F-OFDM signal at the output of IFFT. Because quadrature amplitude modulation (QAM) can lower noise interference and enhance system performance, thereby enabling high-speed data transmission, it is used in this research [15; 37]. The nonreal signal from the IFFT output is rehabilitated into a noncomplex signal via a signal processing method known as the juxtaposition process.  
The input data stream of the transmitter is depicted in Figure 2, which is converted into QAM symbols and then directly fed into the \(N\)-point IFFT. Since there is no HS constraint applied, the output stream of the IFFT will be complex and is stated as follows [37]:  
\[x(n)=\sum_{\kappa=0}^{N-1}[X_{\Re}(\kappa)+jX_{\Im}(\kappa)]exp^{\frac{2\pi j \kappa n}{N}} \tag{9}\]  
Here, \(X_{\Re}(\kappa)\) and \(X_{\Im}(\kappa)\) are denoted as the two components of \(X(\kappa)\). Then, the output IFFT signal is processed using a window function and a carefully constructed sub-band filter to create the F-OFDM signal [38; 39]. To produce a double \(N\)-index noncomplex F-OFDM signal, \(x_{2N}(n)\), the portions of the nonreal F-OFDM signal, real and imaginary as indicated in Figure 3, are combined in the time domain, resulting in the below juxtaposition:  
\[x_{2N}(n)=\begin{cases}x_{\Re}(n),&\implies\quad n=0,1,\ldots,N-1\\ x_{\Im}(n-N),&\implies\quad n=N,\ldots,2N-1\end{cases} \tag{10}\]  
The subsequent \(2N\)-point bipolar signal is then forwarded to a polarity separator. This separator treats the bipolar signal as a combination of a positive value, \({}^{+}x_{2N}(n)\), and a negative value, \({}^{-}x_{2N}(n)\), which is stated as follows:  
\[{}^{+}x_{2N}(n)=\begin{cases}x_{2N}(n),&\implies\quad x(n)\geq 0\\ 0,&\implies\quad x(n)<0\end{cases} \tag{11}\]  
\[{}^{-}x_{2N}(n)=\begin{cases}x_{2N}(n),&\implies\quad x(n)<0\\ 0,&\implies\quad x(n)\geq 0\end{cases} \tag{12}\]  
The generated unipolar signal is then represented as:  
\[x_{4N}(n)=\begin{cases}{}^{+}x_{2N}(n),&n=0,1,\ldots,2N-1\\ {}^{--}x_{2N}(n-N),&n=2N,\ldots,4N-1\end{cases} \tag{13}\]  
For the Flip-Filtered OFDM, the first part of the signal, \({}^{+}x_{2N}(n)\), is sent out in the first subframe, whilst the subsequent subframe is dedicated to the transmission of the flipped signal, \({}^{--}x_{2N}(n)\), as depicted in Figure 4. Given that the communication takes place over a dispersing optical channel, cyclic prefixes are inserted for each Filtered OFDM subframe, delaying the second subframe by \((N+CP)\), where \(N\) and \(CP\) represent the IFFT size and cyclic prefix, respectively [29]. The generated unipolar signal facilitates intensity modulation and is suitable for transmitting through the optical channel.  
Figure 2: The transmitter of the suggested Flip\(-\)Filter\(-\)OFDM.