# Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication
## 4 System Performance Analysis with Stealth Signal
The index \(P_{sr}\) is the effective power from a single source at the receiver, \(R\) is the responsibility of PD, \(B\) is the noise-equivalent electrical bandwidth of the receiver, \(\tau_{c}\) is the coherence time of the source, \(e\) is the electron charge, \(K_{b}\) is Boltzmann's constant, \(T_{n}\) is the absolute receiver noise temperature, and \(R_{L}\) is the receiver load resistor. Using Equations (40) and (41), the SNR of the stealth signal can be represented as  
\[SNR=\frac{\left(I_{b_{k}=1}-I_{b_{k}=0}\right)^{2}}{\left\langle I_{PINI}^{2} \right\rangle+\left\langle I_{shot}^{2}\right\rangle+\left\langle I_{thermal }^{2}\right\rangle+\left(\alpha I_{pn}\right)^{2}}=\frac{\left(\frac{RP_{sr}}{ \sqrt{2}}\right)^{2}}{2e\left(\frac{RP_{sr}}{\sqrt{2}}\right)B+\frac{BR^{2}P_{ sr}^{2}}{\Delta v}+\frac{4K_{b}T_{n}B}{R_{L}}+\left(\alpha I_{pn}\right)^{2}}. \tag{42}\]Based on an approximation to the Gaussian distribution, the BER of the SPC-OCDMA system can be expressed as  
\[\text{BER}=\frac{1}{2}erfc\left[\left(\frac{SNR}{8}\right)^{\frac{1}{2}}\right], \tag{43}\]  
where _erfc_ is the complementary error function, which can be expressed as  
\[erfc=\frac{2}{\sqrt{\pi}}\int_{x}^{\infty}\exp(-t^{2})dt. \tag{44}\]  
Thus, we can draw BER-related curves using the aforementioned equations. When the public noise power is \(-3\) dBm, the correlation between the BER and received stealth signal is as shown in Figure 15.  
The BER decreases with increasing power of the received stealth signal. A BER of \(10^{-9}\) is achieved when the received power is \(-9\) dBm. Figure 16 shows the relationship between the received power of public noise and BER when the received power of the stealth SPC signal is \(-5\), \(-10\), \(-15\), and \(-20\) dBm. Figure 16: BER versus received power of public noise. Figure 15: BER versus received stealth signal. In Figure 16, we observe that the BER decreases when the received public noise power increases. The BER remains constant once the received public noise power has decreased to below a certain value. This is because the received public noise is neglected compared with the shot noise, thermal noise, or PINN. The larger the power of the public noise, the more confidential the stealth signal. With larger public noise, the stealth signal can be hidden more efficiently, but this causes a higher BER. By contrast, smaller noise power results in superior BERs. The relative parameters used in the analysis are shown in Table 1.  
Next, power attenuation due to the free space optical link is calculated. The performance of the FSO system is affected most strongly by atmospheric turbulence. Although the influence of outer limits is unavoidable, we can control the internal parameters of the FSO system, such as the transmission power of the optical source, laser beam divergence, and receiver aperture area. Opti-System 7.0 is used to calculate the power attenuation. The system parameters are displayed in Table 2.  
The power attenuation is observed to be \(-25\) and \(-30\) dB under weather conditions of clear sky and heavy rain, respectively. We discuss the correlation between the BER and transmission distance under the weather conditions of a clear sky and rainy day as shown in Figure 17. The transmission power is set to 20 dBm, which is the maximum value that ensures eye and skin safety. \begin{table}
\begin{tabular}{c c} \hline \hline \(B\): noise-equivalent electrical bandwidth of the receiver. & 0.5 GHz \\ \(K_{b}\): [PERSON]’s constant & \(1.38\times 10^{-23}\) J/K \\ \(T_{n}\): absolute receiver noise temperature & 300 K \\ \(R_{L}\): receiver load resistor. & 1030 \\ \(\Delta v\):optical source bandwidth & 1 THz \\ \(R\):responsibility of the PD & 0.8 A/W \\ \(\alpha\):public noise-suppression factor & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Relative parameters used in BER analysis.