## 5 Performance Analysis and Results
### Visual Quality Metrics
Figure 7: PSNR of FFT, FrFT, MPFrFT OFDM over Salt and Pepper noise attack, \(d=0.02\). Table 8 presents both \(BER\) and \(PSNR\) metrics performance for the proposed \(FFT\), \(FrFT\) and \(MPFrFT\) coded OFDM systems at different values of \(E_{b}N_{0}(0\text{dBt016 dB})\) under Speckle noise attack. Speckle noise is represented as a multiplicative noise to the brain medical test image, using uniformly distributed random noise with zero mean, \(\mu=0\) and variance, \(\delta^{2}=0.02\). The results in Table 8 are plotted in Figures 8 and 9 in order to clarify the Speckle noise attack effect on the proposed authenticated secure medical image transmission schemes. BER calculations were obtained for the introduced FFT, FrFT and MP - FrFT coded OFDM systems at \(E_{b}N_{0}=8\)dB; the BER values are \(3.70\times 10^{-8}\), \(0\), and \(3.11\times 10^{-4}\) respectively. At the same \(\text{E}_{b}N_{0}=8\)dB, the PSNR performance values are \(75.1229\text{dB}\), InfdB, and \(54.1514\text{dB}\) respectively. Then, at \(\text{E}_{b}N_{0}\geq 8.50\text{dB}\), the proposed systems provide the highest BER and PSNR performance (0 BERandInfPSNR). Speckle noise is represented as a multiplicative noise to the brain medical test image, using uniformly distributed random noise with zero mean, \(\mu=0\) and variance, \(\delta^{2}=0.02\). In addition, Table 9 shows the \(BER\) and \(PSNR\) performance for FFT, FrFT, and MPFrFT coded OFDM over Speckle noise attack at \(\delta^{2}=0.02\) at \(E_{b}N_{0}=2,8.50\text{dB}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{\(E_{b}N_{0}\) (dB)} & \multicolumn{2}{c}{\(BER\)} & \multicolumn{2}{c}{\(PSNR\) (dB)} \\ \cline{2-5}
**(dB)** & **FFT** & **FrFT** & **MPFrFT** & **FFT** & **FrFT** & **MPFrFT** \\ \hline
0 & 0.1026 & 0.0920 & 0.1444 & 9.8868 & 10.3628 & 8.4049 \\ \hline
2 & 0.0213 & 0.0178 & 0.0340 & 16.7095 & 17.5063 & 14.6790 \\ \hline
4 & 0.0028 & 0.0020 & 0.0050 & 25.4816 & 27.0542 & 22.9900 \\ \hline
6 & \(1.39\times 10^{-4}\) & \(8.58\times 10^{-5}\) & 0.0022 & 38.5823 & 40.6662 & 35.0743 \\ \hline
8 & \(3.07\times 10^{-8}\) & 0 & \(3.11\times 10^{-4}\) & 75.1229 & \(Inf\) & 54.1514 \\ \hline
10 & 0 & 0 & \(3.84\times 10^{-6}\) & \(Inf\) & \(Inf\) & \(Inf\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(BER\) and \(PSNR\) performances of the proposed \(FFT\), \(FrFT\) and \(MPFrFT\) coded OFDM under Speckle noise attack; noise variance \(\delta^{2}=0.02\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{\(E_{b}N_{0}\) (dB)} & \multicolumn{2}{c}{\(BER\)} & \multicolumn{2}{c}{\(PSNR\) (dB)} \\ \cline{2-5}
**(dB)** & **FFT** & **FrFT** & **MPFrFT** & **FFT** & **FrFT** & **MPFrFT** \\ \hline
0 & 0.1026 & 0.0920 & 0.1444 & 9.8868 & 10.3628 & 8.4049 \\ \hline
2 & 0.0213 & 0.0178 & 0.0340 & 16.7095 & 17.5063 & 14.6790 \\ \hline
4 & 0.0028 & 0.0020 & 0.0050 & 25.4816 & 27.0542 & 22.9900 \\ \hline
6 & \(1.39\times 10^{-4}\) & \(8.58\times 10^{-5}\) & 0.0022 & 38.5823 & 40.6662 & 35.0743 \\ \hline
8 & \(3.07\times 10^{-8}\) & 0 & \(3.11\times 10^{-4}\) & 75.1229 & \(Inf\) & 54.1514 \\ \hline
10 & 0 & 0 & \(3.84\times 10^{-6}\) & \(Inf\) & \(Inf\) & \(Inf\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: \(BER\) and \(PSNR\) performances of the proposed \(FFT\), \(FrFT\) and \(MPFrFT\) coded OFDM under Speckle noise attack; noise variance \(\delta^{2}=0.02\). Figure 8: \(BER\) performance, FFT, FrFT, and MPFrFT OFDM over Speckle noise attack, \(\delta^{2}=0.02\). Figure 9: PSNR performance, FFT, FrFT, and MPFrFT OFDM over Speckle noise attack, \(\delta^{2}=0.02\).