# Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication
## 3 The Proposed Optical Steganography System Setup and Simulation Results
### Interference Cancellation of Stealth and Public Signals  
At the receiver side, a 3-dB optical coupler is used to split the mixed signal comprising the public and stealth signals into two portions. To detect the BPSK signal, the portion in the public receiver is sent to a BPSK demodulator. As shown in Figure 13, the BPSK demodulator comprises a sine generator and a low-pass filter. The photocurrent of the BPSK public signal and the stealth signal during a 1-bit period can be respectively expressed as follows:  
\[S_{n}(t)=\sqrt{\frac{2E_{b}}{T_{b}}}\cos[2\pi f_{c}t+\pi(1-b)],b=0,1, \tag{23}\]  
Figure 11: Waveform of stealth signal in time domain (**a**) before and (**b**) after pulse broadening.  
Figure 12: Waveform of public channel in time domain (**a**) without stealth signal; (**b**) with stealth signal (1600 ps/nm); and (**c**) with stealth signal (no dispersion).  
\[S_{st}(t)=I_{0}rect(t)=\left\{\begin{array}{c}I_{0},0\leq t\leq T_{b}\\ 0,\quad\text{{other}}\end{array}\right., \tag{24}\]  
where \(E_{b}\) is the energy per bit, \(T_{b}\) is the 1-bit duration, \(f_{c}\) is the frequency of the carrier wave, \(b\) is the data, and \(I_{0}\) is the intensity of the photocurrent. Then, the mixed photocurrent is multiplied by \(\cos(2\pi f_{c}t)\), following which the photocurrent of the stealth signal can be written as  
\[S_{st}(t)\cdot\cos(2\pi f_{c}t)=I_{0}\cos(2\pi f_{c}t). \tag{25}\]  
Compared with Equations (13) and (14), the stealth signal contains the term \(\cos(2\pi f_{c}t)\). Because \(f_{c}\) is much higher than the bit rate, the high-frequency terms are filtered out by the low-pass filter. Consequently, the public signal can be recovered successfully and relatively unaffected by the stealth signal.  
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 to the original profile. At the decoder, the public BPSK signal is divided into mutually orthogonal SOPs with identical power by the PBS, which is designed according to the SOP of the CW laser. The power of the public signal from the upper and lower branches of the PBS is equal, as shown in Figure 14. For example, the electric field of the CW laser with linear +45 polarization is written as E(45\({}^{\circ}\)), and the PBS is designed to divide the light into two beams with horizontally linear polarization and vertically linear polarization. The electric fields of the two beams can be expressed as E(45\({}^{\circ}\))cos45\({}^{\circ}\) and E(45\({}^{\circ}\))sin45\({}^{\circ}\). Next, the final subtraction after the photodiodes is given by  
\[\text{E(45}^{\circ})\text{cos45}^{\circ}-\text{E(45}^{\circ})\text{sin45}^{ \circ}=0, \tag{26}\]  
Thus, the public signal is eliminated by the double balance-difference detection. In the next section, we derive the signal-to-noise ratio (SNR) and bit-error rate (BER) to evaluate the system's performance.  
Figure 13: Decoder of SPC stealth signal and demodulator of public signal.