## 3 Result Analysis and Discussion
### System Complexity  
This metric provides an estimate of the computational resources required for the system. The impact of increasing FFT/IFFT sizes on computational complexity is detailed in [45]. According to [45], increasing the FFT/IFFT size leads to a rise in the subcarriers' number, which in turn expands the dynamical breadth of the OFDM signal. This expansion involves greater accuracy in arithmetic processes. The findings presented in [45] clearly illustrate the influence of various FFT/IFFT scopes on the error vector magnitude (EVM), with sizes ranging from 32 to 1024. The analysis indicates that reducing the FFT/IFFT sizes leads to a noticeable decrease in EVM for a fixed FFT/IFFT bit accuracy. Additionally, the study shows that both power usage and chip area utilization increase as the FFT/IFFT sizes grow. In particular, this increase is significantly more noticeable for larger transform sizes, particularly when \(N\geqslant 512\). According to the comparison outlined in [45], reducing the FFT size from \(N=1024\) to \(N=512\) led to a decrease of nearly 40% in chip area and 38% in power consumption. The foremost goal of the proposed Flip-F-OFDM procedure is to simplify the transmission and reception components. This is achieved by producing a noncomplex F-OFDM signal using \(N\)-length IFFT/FFT and creating a \(4N\)-length unipolar F-OFDM signal. According to [45], this approach effectively reduces the computational complication of the system while retaining the desired functionality. In the suggested Flip-F-OFDM technique, computational complexity is greater than that of HSF Flip-OFDM in the time domain because of the additional system complexity imposed by the filter at the transmitter side. The computational complication of F-OFDM is determined by increasing the OFDM computational complexity by the size of the filter. Consequently, the addition processes are similar for both F-OFDM and OFDM systems, while the multiplication processes increase according to the filter length for F-OFDM [46]. Compared to the standard Flip-F-OFDM method, the proposed Flip F-OFDM technique provides significant reductions in hardware complexity, achieving an improvement of \(\approx\)50%. Utilizing the radix-2 algorithm of FFT, the required number of additions and  
Figure 8: Evaluation of BER between the proposed Flip\(-\)F\(-\)OFDM and conventional Flip\(-\)F\(-\)OFDM for 4 QAM, 16 QAM, 64 QAM, and 256 QAM. multiplications for computing an \(N/2\)-point real Flip F-OFDM signal using HS can be extracted as follows [47; 48]:  
\[\mathbb{O}_{\text{Add FFT}}=\frac{3N}{2}\log_{2}\!\left(\frac{N}{2}\right)-\frac {3N}{2}+4 \tag{30}\]  
\[\mathbb{O}_{\text{Multip. FFT}}=\frac{N}{2}\log_{2}\!\left(\frac{N}{2}\right)- \frac{3N}{2}+4+\frac{N}{2}(L-1) \tag{31}\]  
Here, \(N\) represents the FFT length, and \(L\) signifies filter size. Alternatively, the number of the operations (additions and multiplications) demanded for computing the FFT transformation in the proposed Flip F-OFDM receiver using \(N/4\)-point IFFT is provided by [47; 48]:  
\[\mathbb{O}_{\text{Add FFT}}=\frac{3N}{4}\log_{2}\!\left(\frac{N}{4}\right)- \frac{3N}{4}+4 \tag{32}\]  
\[\mathbb{O}_{\text{Multip. FFT}}=\frac{N}{4}\log_{2}\!\left(\frac{N}{4}\right)- \frac{3N}{4}+4+\frac{N}{4}(L-1) \tag{33}\]  
Through mathematical analysis, Figures 9 and 10 offer a comparison of computational complexity in terms of multiplications and additions between the proposed Flip F-OFDM and traditional Flip F-OFDM methods for generating real signals. As noted in [45], these figures illustrate that with an increase in the size of the FFT/IFFT, both the occupied chip area and power consumption also increased. Through the utilization of an optimized IFFT algorithm [46; 47], the proposed Flip F-OFDM can achieve further reductions in the computational intricacy of the transmitter. This is a crucial aspect to consider in practical applications. Conversely, the conventional Flip F-OFDM method offers no complexity improvements on the transmitter side.