# Secure Image Signal Transmission Scheme Using Poly-Polarization Filtering and Orthogonal Matrix
## 6 Numerical Result  
In this section, a sampling of simulation results by MATLAB are provided and analyzed to show the validity and security performance of the proposed method. In the simulations, the XPD of the environment and the dual-polarized antennas were both set at 15 dB, and the information sequence was divided into two parts. Each part was translated into \(10^{6}\) AM symbols. In addition, 90% of the signal power was transmitted through the line-of-sight channel while 10% was transmitted through the non-line-of-sight channel. The CSI was updated every 200 symbol periods: \(u=200\) and \(l=10\); \(M=10\). In this simulation, the validity of the proposed scheme was evaluated through BER performance. At first, two image information sequences were modulated into symbols using the pulse-amplified-modulation (PAM) technique, and the BER curves were plotted in Figure 4. Furthermore, 4 PAM and 8 PAM were used for the signal modulation of the two information sequences. We found the BER performances of both the 8 PAM and 4 PAM signals approached the theoretical value, which was calculated according to the ideal Gaussian channel (the CSI matrix was a unit matrix). This was because based on the PPF-OM scheme, the PDL was naturally eliminated, and there was no mutual interference between orthogonal polarizations. In addition, the noise power was not amplified. Thus, the two signals could be separately demodulated. Next, 4 PAM and 8 PAM were replaced by 4 PSK and 8 PSK, respectively, and the BER curves are shown in Figure 5. We found that the BER curves approached the theoretical ones, which had the same results as the PAM technique. Furthermore, we utilized 4 QAM and 16 QAM to modulate the two information sequences, and the BER curves are shown in Figure 6. The two BER curves approached the theoretical ones. Overall, regardless of the modulation techniques used in the PPF-OM scheme, the two signals could be demodulated without interference and approach theoretical values. The simulations demonstrated the validity of the proposed scheme for eliminating the PDL, which was consistent with the theoretical derivations. Figure 4: BER performance of PPF-OM (PAM). Figure 5: BER performance of PPF-OM (PSK). In this simulation, the security performance of the PPF-OM scheme was evaluated in terms of the BER performance when there were errors in the orthogonal matrix. Here, we assumed [PERSON] could correctly reshape the matrix into the \(\frac{l}{2}\times\frac{2u}{l}\ =\ 5\times 40\) matrix and knew \(M=10\) as well as the PSs that had been used to process the two image signal vectors. However, [PERSON] did not know the correct orthogonal matrix. Both 4 PSK and 8 PSK were utilized to modulate two information sequences, which yielded the \(10^{6}\) 4 PSK and \(10^{6}\) 8 PSK symbols, respectively. Figure 7 shows the plots of the BER curves when there were errors in the orthogonal matrix. In the simulation, we add the error to all the elements in the orthogonal matrix. We found that when the error was 0.1, the BER performance deteriorated significantly, and when the error grew larger, almost no information could be correctly recovered. In addition, with the PPF-OM scheme, it was difficult for Eve to decipher the orthogonal matrix for the signal matrices, as after being processed by the OM, they were composite matrices, which made it difficult to determine the correct OM. Thus, the information security was enhanced. In this simulation, the security performance of the PPF-OM scheme was evaluated in terms of the BER performance when there were errors in the PSs. Both 4 PSK and 8 PSK were utilized to modulate the two information sequences, which yielded the \(10^{6}\) 4 PSK and \(10^{6}\) 8 PSK symbols, respectively. Here, the errors were added to the polarization parameter \(\gamma\) while th other parameters were distortionless. The BER curves of 4 PSK and 8 PSK with \(\Delta\gamma\)=\(3^{\circ},5^{\circ},10^{\circ},15^{\circ},20^{\circ}\) are shown in Figure 8. We found that a larger error in \(\gamma\) would led to a worse BER.