# Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication
## 3 The Proposed Optical Steganography System Setup and Simulation Results
### Structure of Public and Stealth Channels
The following equations detail the math analyses of the SPC decoding process. When transmitting data bit 1, the received signal is given by  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]0  
The spectrum from the upper and lower couplers can be expressed as in Equations (16) and (17), respectively:  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]1  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]2  
According to the proposed structure, the spectra of \(C_{k}(\mathrm{H})\) and \(\overline{C_{k}}(\mathrm{V})\) are sent to the topmost and lowest photodiode, respectively. Consequently, the final photocurrent received is described by  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]3  
where \(N\) denotes the length of the codeword; here, we assume that each chip of the spectrum produces one unit current. If another user transmits a signal with Walsh-Hadamard code \(C_{l}\), the received signal is given by  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]4  
Then, the spectrum from the upper and lower couplers can be expressed as  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]5  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]6  
Based on the decoder structure, the spectra of \(C_{l}(\mathrm{H})\cdot C_{k}\), \(C_{l}(\mathrm{H})\cdot\overline{C_{k}}\), \(\overline{C_{l}}(\mathrm{V})\cdot C_{k}\), and \(\overline{C_{l}}(\mathrm{V})\cdot\overline{C_{k}}\) are sent to the first to fourth photodiodes, respectively. Consequently, the final photocurrent received can be written as  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]7  
From the calculations, we observe that the photocurrent is zero at the first balance detection. Thus, only the user with the corresponding code can transmit the signal, with multiuser access interference from other users rejected. The parameters of the simulation are as follows. To generate the public BPSK signal, an MZM is used to modulate a CW laser at 3 Gbps with a 2\({}^{\prime}\)-1 PRBS. The center wavelength of the CW laser is 1549.2 nm. In the stealth channel, 1-Gbps OOK data are generated using a white light source followed by an MZM driven by a 2\({}^{\prime}\)-1 PRBS. The modulated signal is encoded using an AWG according to a Walsh-Hadamard code with the length of the codeword being 8. We set the codeword to be (1, 1, 0, 0, 1, 1, 0, 0) for the vertical SOP and (0, 0, 1, 1, 0, 0, 1, 1) for the horizontal SOP. The wavelengths utilized are 1547.6, 1548.4, 1549.2, 1550, 1550.8, 1551.6, 1552.4, and 1553.2 nm, respectively. As discussed in the Introduction, most previous studies on optical steganography have described stealth signals encoded by spread-spectrum OCDMA or phase-encoded OCDMA techniques and transmitted on existing public networks. Therefore, to help fill a gap in knowledge, we investigate the probability of applying other types of OCDMA techniques. The SAC is a promising OCDMA technique that provides high transmission rates with low system complexity and using a low-cost optical source. However, it is not easy using conventional technique to realize physical layer security of multi-wavelength OCDMA system. We compare the proposed SPC with SAC and demonstrate that the proposed SPC-OCDMA system can enhance the security of SAC-OCDMA. The spectrum of the encoded signal is presented in \[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]8 Figure 9a shows the proposed SPC code pattern and Figure 9b displays the traditional SAC code. V and H represent vertical and horizontal linear SOP, respectively. Figure 10 presents the spectrum of the public channel with and without the stealth signal. In Figure 10a, the peak of the spectrum is the public signal and the other peaks are system noise.