# 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  
BPSK is the simplest form of the phase-shift keying technique and is a digital modulation method that transmits data by changing the phase of the carrier wave. The phase difference of the carrier wave is 180\({}^{\circ}\) when transmitting data bits 1 and 0. Furthermore, the frequency of the carrier wave is typically 10 times the bit rate. We transmit a BPSK signal in the public channel to make the signal always exist irrespective of the data bit transmitted. The stealth signal is not exposed because of the disappearance of the public signal. Figure 6 presents the structure of the public channel. In this structure, NRZ pulses are multiplied by a sinusoidal wave and the BPSK signal is generated. The following equation shows the general form of the BPSK signal:  
\[S_{b}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos[2\pi f_{c}t+\pi(1-b)],\ b=\ 0,\ 1. \tag{10}\]  
From the general form, we can conclude that binary data is conveyed using the following signals:  
\[S_{1}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t),\ \text{for bit 1}, \tag{11}\]  
\[S_{0}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t+\pi)=-\sqrt{\frac{2E_{b}} {T_{b}}}\cos(2\pi f_{c}t+\pi),\ \text{for bit 0}, \tag{12}\]  
where \(E_{b}\) is the energy per bit, \(T_{b}\) is the 1-bit duration, \(f_{c}\) is the frequency of the carrier wave, and \(b\) is the data bit. Then, the BPSK signal drives a Mach-Zehnder modulator (MZM) to modulate a continuous-wave (CW) laser. To demodulate the public BPSK signal, the optical signal is first  
Figure 5: Schematic of optical steganography transmission system. Figure 6: Schematic of BPSK public channel. transformed into an electrical signal by the photodiode, following which the photocurrent is multiplied by \(\cos(2\pi f_{c}t)\):  
\[S_{1}(t)\cos(2\pi f_{c}t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t)\cos(2\pi f _{c}t), \tag{13}\]  
\[S_{0}(t)\cos(2\pi f_{c}t)=-\sqrt{\frac{2E_{b}}{T_{b}}}\cos(2\pi f_{c}t)\cos(2 \pi f_{c}t), \tag{14}\]  
The term \(\cos(4\pi f_{c}t)\) is filtered using a low-pass filter. The data bit is recovered by an appropriate thresholder. The transmitter in the stealth channel is illustrated in Figure 7. On-off keying (OOK) data are generated using a white light source, and the MZM is driven by a pseudorandom binary sequence (PRBS). A polarization controller is placed between the modulator and the PBS to adjust the SOP. The modulated signal is divided into mutually orthogonal SOPs by the PBS and then input into the AWG-based OCDMA encoder. We input two orthogonal SOPs to different AWG input ports. According to the wavelength cyclic-shifted characteristic property of AWG routers detailed in Equation (8), we can obtain the spectrum encoded by the Walsh-Hadamard code \(C_{k}(\mathrm{H})\) and its complementary code \(\overline{C_{k}}(\mathrm{V})\). The encoded stealth signals are combined using a coupler and passed through a CFBG for further pulse broadening to lower the peak power for effectively concealing the stealth channel beneath the public channel. Figure 8 shows the structure of the proposed SPC decoder. To restore the stealth signal, the received signal is first passed through a CFBG, which is the same as that at the transmitter except with opposite dispersion. The stretched stealth signal is then compressed back into the original profile. Thereafter, the mutually orthogonal SOP components from the encoded spectrum are input to the AWG router for OCDMA decoding. The output ports of the AWG couple with the upper and lower couplers depending on the signature code \(C_{k}\) and its complementary code \(\overline{C_{k}}\). With the PBS, the same SOPs of spectra are extracted for balanced detection. Furthermore, the detected electrical signal from the lower branch is subtracted from the corresponding signal from the upper branch. Finally, the stealth signal is obtained using the decoding mechanism. Figure 8: Schematic of stealth channel decoder. Figure 7: Schematic of stealth channel encoder.