# Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication

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## Abstract

**:**

## 1. Introduction

## 2. The Theories and Principles Background of the Proposed Stealth Communication Approach

#### 2.1. Chromatic Dispersion

_{g}. The group velocity ν

_{g}is given by

_{g}= dω/dβ,

^{2})β″LΔλ = DLΔλ,

^{2})Δλ, where β” is the second derivative with respect to λ and D is the dispersion parameter with units ps/(nm·km). A negative dispersion parameter indicates that lightwave with longer wavelength travels faster than lightwave with shorter wavelength.

#### 2.2. Spectral-Polarization Coding Using Walsh–Hadamard Codes

_{N}

_{/2}. It is clear that the autocorrelation value is N/2 and the cross-correlation value between different rows is N/4. Let us introduce the Walsh–Hadamard code correlation properties as follows:

_{k}is the code sequence in the kth row of the Walsh–Hadamard matrix. According to the property ${R}_{CC}\left(k,l\right)$ = ${R}_{C\overline{C}}\left(k,l\right)$ for k ≠ l, a receiver is designed to perform correlation subtraction expressed as ${R}_{CC}\left(k,l\right)$ − ${R}_{C\overline{C}}\left(k,l\right)$:

_{k}(H) and $\overline{{C}_{k}}\left(\mathrm{V}\right)$, where H and V denote the vertical and horizontal polarization, respectively.

_{1H}, λ

_{2H}, 0, 0, λ

_{5H}, λ

_{6H}, 0, 0) and (0, 0, λ

_{3V}, λ

_{4V}, 0, 0, λ

_{7V}, λ

_{8V}), respectively. Therefore, the wavelength-coding patterns of the SPC code are (λ

_{1H}, λ

_{2H,}λ

_{3V}, λ

_{4V}, λ

_{5H}, λ

_{6H,}λ

_{7V}, λ

_{8V}) when a data bit 1 is transmitted and (0, 0, 0, 0, 0, 0, 0, 0) when a data bit 0 is transmitted. The subscripts of λ

_{ij}denote the ith wavelength encoded and the SOP:

#### 2.3. Chirped Fiber Bragg Gratings

_{B}, which is given by

_{eff}is the effective refractive index of the core and Λ is the grating period. The chirping of a fiber Bragg grating indicates changes in the period of the grating with distance.

#### 2.4. Free Space Optical Communication (FSO)

## 3. The Proposed Optical Steganography System Setup and Simulation Results

#### 3.1. Structure of Public and Stealth Channels

_{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 transformed into an electrical signal by the photodiode, following which the photocurrent is multiplied by cos(2πf

_{c}t):

_{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.

_{k}(H) and its complementary code $\overline{{C}_{k}}\left(\mathrm{V}\right)$. 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.

_{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.

_{k}(H) and $\overline{{C}_{k}}\left(\mathrm{V}\right)$ are sent to the topmost and lowest photodiode, respectively. Consequently, the final photocurrent received is described by

_{l}, the received signal is given by

^{7}-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

^{7}-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.

#### 3.2. Interference Cancellation of Stealth and Public Signals

_{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(2πf

_{c}t), following which the photocurrent of the stealth signal can be written as

_{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.

^{°})cos45° − E(45°)sin45° = 0,

## 4. System Performance Analysis with Stealth Signal

_{0}− Δv/2, v

_{0}+ Δv/2], where v

_{0}is the central optical frequency and Δv is the optical source bandwidth. From the aforementioned assumptions, we can easily calculate the proposed system performance using Gaussian approximation and u(v), the unit step function, which is expressed as

_{k}(i) be the ith element of the kth low of the Walsh–Hadamard matrix. The power spectral density (PSD) of the received optical signal can be written as

_{sr}is the effective power from a single source at the receiver, b

_{k}is the data bit of the stealth signal, and N is the length of the codeword. The rect(i) function in Equation (28) is given by

_{1}, PD

_{2}, PD

_{3}, and PD

_{4}of the stealth receiver during the 1-bit period can be written as follows:

_{1}–PD

_{4}can be written as I

_{1}, I

_{2}, I

_{3}, and I

_{4}, respectively:

_{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, τ

_{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.

^{−9}is achieved when the received power is −9 dBm.

^{−9}when the transmission distance is 320 m on a rainy day. When the sky is clear, a BER of 1.62 × 10

^{−9}is achieved at a transmission distance of 380 m.

## 5. Conclusions

^{−9}under a clear sky and 320 m at a BER of 2.4 × 10

^{−9}on a rainy day. Since the system configuration is done in the study, the proposed stealth communication system can furthermore be used to investigate the hiding capacity, distortion measurement and impact on network performance in the future work.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Spectrum of public channel: (

**a**) without stealth signal; (

**b**) with SPC signal; and (

**c**) with SAC signal.

**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).

B: noise-equivalent electrical bandwidth of the receiver. | 0.5 GHz |

K_{b}: Boltzmann’s constant | 1.38 × 10^{−23} J/K |

T_{n}: absolute receiver noise temperature | 300 K |

R_{L}: receiver load resistor. | 1030 |

Δv:optical source bandwidth | 1 THz |

R:responsibility of the PD | 0.8 A/W |

α:public noise-suppression factor | 0.01 |

L: range | 1 km |

Ω: attenuation | 3 dB/km (clear sky); 8 dB/km (heavy rain) [29] |

Dt: transmitter aperture diameter | 4 cm |

Dr: receiver aperture diameter | 8 cm |

θ: beam divergence | 1 mrad |

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**MDPI and ACS Style**

Yen, C.-T.; Huang, J.-F.; Zhang, W.-Z.
Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication. *Appl. Sci.* **2018**, *8*, 1731.
https://doi.org/10.3390/app8101731

**AMA Style**

Yen C-T, Huang J-F, Zhang W-Z.
Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication. *Applied Sciences*. 2018; 8(10):1731.
https://doi.org/10.3390/app8101731

**Chicago/Turabian Style**

Yen, Chih-Ta, Jen-Fa Huang, and Wen-Zong Zhang.
2018. "Hiding Stealth Optical CDMA Signals in Public BPSK Channels for Optical Wireless Communication" *Applied Sciences* 8, no. 10: 1731.
https://doi.org/10.3390/app8101731