## 3 Chaos Oscillator Synchronization Noise Immunity
### Result Analyses
This imbalance can negatively impact data transmission since one signal may be more likely to be detected correctly, leading to an increased error rate for specific bits. For example, an imbalance in synchronization levels may result in a scenario where more '0' s are incorrectly detected compared to '1' s. It is a point to improve the chaos-based communication system so that each bit is detected with equal probability to ensure a balanced transmission process. The next part of this study examines the cross-correlation of response chaos oscillator signals as a function of the synchronization channel SNR. This analysis extends the findings from the previous part by evaluating how the relationship between \(X^{\prime}\) and \(Y^{\prime}\) signals evolves across different configurations. The cross-correlation value between these signals is crucial for maintaining balance in a data transmission system, as imbalances can lead to an increased number of errors. Figure 6: Vilnius chaos oscillator synchronization noise immunity. Figure 7 presents the study results for the Colpitts chaos oscillator, illustrating the cross-correlation coefficients under different synchronization configurations. The results indicate that when \(v_{RL}\) is used as the synchronization signal, the cross-correlation coefficient remains close to one, meaning the response chaos oscillator signals exhibit similar dynamics. However, in this configuration, the Colpitts chaos oscillator correlation coefficient of data-carrying signals was of nearly zero level in the drive-response system, leading the response oscillator to enter a periodic mode instead of remaining chaotic. For the other two synchronization signals, \(v_{\text{C1}}\) and \(v_{\text{C2}}\), the cross-correlation between response oscillator signals decreases as the noise level decreases. Additionally, it can be observed that when \(v_{\text{C1}}\) is used as the synchronization signal, the absolute value of the cross-correlation coefficient is lower compared to the \(v_{\text{C2}}\) configuration. Figure 8 illustrates the cross-correlation coefficients as a function of the SNR in the Vilnius chaos oscillator for different synchronization signals. In Figure 8, the cross-correlation coefficient between \(X^{\prime}\) and \(Y^{\prime}\) decreases as the noise level decreases in configurations where \(v_{\text{C1}}\) and \(v_{R1}\) are used as synchronization signals. A more significant variation in the cross-correlation coefficient is observed when \(v_{R1}\) is used,  
Figure 8: Results of the Vilnius chaos oscillator, showing the signal cross-correlation coefficients for different synchronization signals. Figure 7: Results of the Colpitts chaos oscillator, showing the signal cross-correlation coefficients under different synchronization configurations. suggesting that synchronization in this configuration is more affected by noise. Conversely, when \(v_{\text{C2}}\) is used as the synchronization signal, the cross-correlation coefficient remains nearly constant, indicating a strong and noise-resistant synchronization. Comparing Figures 7 and 8 with previous results (Figures 5 and 6), it is evident that the Vilnius chaos oscillator demonstrates the most robust synchronization when \(v_{\text{C2}}\) is employed as the synchronization signal. In this case, the correlation between \(X\) and \(X^{\prime}\) and between \(Y\) and \(Y^{\prime}\) is balanced, while the cross-correlation between \(X^{\prime}\) and \(Y^{\prime}\) remains stable, regardless of the noise level. However, a high cross-correlation level between data-carrying signals complicates signal discrimination in the receiver in this configuration. On the other hand, in the Colpitts chaos oscillator, \(v_{\text{C1}}\) appears to be the most suitable synchronization signal for communication system applications. In this configuration, the absolute value of the cross-correlation coefficient is the lowest of the observed, and its dependence on the noise level is minimal.