# Analysis of Low Probability of Detection Capability for Chaotic Standard Map-Based FH-OFDMA System
## 4 Simulation Results
Figure 4: Detection probability versus SNR compared to SBS, cat map, and CSM-based FH-OFDMA systems. Figure 3: Bit error rate (BER) performances versus signal-to-noise ratio (SNR) compared to SBS, cat map, and CSM-based FH-OFDMA systems. Figure 6 shows the required false alarm probability for detection probabilities for the SBS, cat map, and CSM-based systems. We choose common parameters as SNR \(=-20\) dB, redundant number of FH-OFDMA frames, \(N_{\text{R}}=100\), number of clusters, \(N_{\text{L}}=11\), and number of transmitting users, \(K=11\). In Figure 6, we observe that the detection probability at the detector decreases as the required false alarm probability increases. As shown in Figure 6, the CSM always has a lower detection probability than the cat map and SBS for all values of the false alarm probabilities. Figure 7 shows the detection probabilities of the SBS, cat map, and CSM-based FH-OFDMA systems for logarithmic scales as the user load increases from 0.1 to 1.0. The user load is defined as the ratio of the number of transmitting users \(K\) to the number of clusters \(N_{\text{L}}\). We set the parameters as false alarm probability, \(P_{fa}=0.05\), redundant number of FH-OFDMA frames, \(N_{\text{R}}=100\), number of clusters, \(N_{\text{L}}=11\), and SNR \(=-20\) dB. When \(K=1\), the detection probabilities of the cat map and CSM-based systems have the same value and lower than that of the SBS-based system. When \(K\) increases  
Figure 5: Detection probability versus redundant number of FH-OFDMA frames for detection compared to SBS, cat map, and CSM-based FH-OFDMA systems. Figure 6: Required false alarm probability versus detection probability compared to SBS, cat map, and CSM-based FH-OFDMA systems. probability of the CSM becomes smaller than that of the cat map. As shown in Figure 7, we can also observe that when user load approaches 1, the detection probabilities are decreased. This means that an increase in user load enhances the LPD capability of the FH-OFDMA system. From Figures 4-7, we conclude that the CSM-based FH-OFDMA system has the greatest LPD capability. Figure 8 shows the effect of the required false alarm probability, \(P_{fa}\) of the CSM-based FH-OFDMA system. We chose three values of \(P_{fa}\) as 0.05, 0.1, and 0.2, while setting redundant number of FH-OFDMA frames, \(N_{\text{R}}\) = 100, number of clusters, \(N_{\text{L}}\) = 11, and number of transmitting users, \(K\) = 11. For the results, we varied the SNR from \(-\)35 to \(-\)10 dB. As the SNR increases from \(-\)35 to \(-\)15 dB, detection probabilities of the CSM sharply increase for all values of \(P_{fa}\). Above SNR = \(-\)15 dB, the detection probabilities are stable. As seen in Figure 8, as the required false alarm probability increases, the detection probability decreases because the threshold to detect the FH-OFDMA signal increases. Figure 8: SNR versus detection probability compared to required false alarm probabilities of 0.05, 0.1, and 0.2 for CSM-based FH-OFDMA system. Figure 7: Detection probability versus user load compared to SBS, cat map, and CSM-based FH patterns.