Time-Division Multiplexed Optical Covert Communication System Based on Gain-Switched Optical Pulses

Abstract

In optical covert communication systems based on gain-switched distributed feedback semiconductor lasers, the trade-off between the modulation frequency and the spectral imperceptibility limits the bit rate of the secure channel. To improve the system performance in terms of the bit rate and covertness, optical time-division multiplexing is introduced to optical covert communication for the first time. The optical time-division multiplexed covert channel can work under both multiple-user and single-user conditions. The optical time-division multiplexed covert communication system is demonstrated via a system simulation. The results show that the covertness is enhanced by the optical time-division multiplexing in the spectral domain. The receiver sensitivity of the multiple-user condition is lower than the single-user one.

1. Introduction

Photonic-layer secure communication safeguards against adversarial detection in the optical domain by employing a range of security technologies, including optical chaos [1,2,3,4,5], optical code division multiplexing [6,7,8], quantum noise randomized ciphers [9,10,11,12], optical frequency hopping [13,14,15], quantum key distribution [16,17], and optical covert communication (OCC) [18,19,20,21,22,23]. OCC requires a higher level of security than merely protecting the content from unauthorized access through encryption, and the security requirement is imperceptibility for optical covert communication.

To ensure the imperceptibility of a system, the signal output from the transmitter should be noise-like in the temporal and spectral domains. An amplified spontaneous emission (ASE) laser [24,25], a distributed feedback (DFB) semiconductor laser [26,27], an external cavity laser [28,29], or a mode-locked laser [30] can be used as carriers of the stealth signal after optical signal processing.

In addition to imperceptibility, there is a growing demand for increased capacity in optical covert communication systems due to the rising volume of information and data. Coherent lasers, such as DFB lasers and mode-locked lasers, show advantages from a capacity point of view. To further improve the capacity, a simple way is to enhance the modulation frequency. However, in DFB laser-based optical covert communication systems, an increase in the modulation frequency leads to an enhancement of the tone-to-noise ratio and a decrease in the concealment [31]. Additionally, the mode-locked lasers have a comb-shaped spectrum, which is a disadvantage for imperceptibility. Then, as a common method to improve capacity, multiplexing may be an option. A wavelength-division multiplex-based scheme has been demonstrated for OCC based on ASE [32], and it can also be applied in OCC based on a broadband coherent source, such as a super-continuum [27]. However, the wavelength resources that can be used by a stealth user are limited in a public network.

For the covertness or undetectability, in this paper, an optical time-division multiplexing method is proposed for an OCC system. The waveform and spectrum of the optical pulses generated by a DFB laser are analyzed. The optical covert signal undergoes optical time-division multiplexing, optical encoding, and time spreading before being sent to the public channel. With different modulation frequencies at the DFB laser, the modulation parameters are optimized to achieve a proper performance. An optical covert communication system over four wavelength-division multiplexed optical public channels is set up in the system simulation.

2. Optical Time-Division Multiplexing Optical Covert Signal

A schematic diagram of optical time-division multiplexing optical covert signal generation is shown in Figure 1a. The total time slot of the optical time-division multiplexing optical stealth signal is m. The original signal in the covert channel is divided into several subsequence by the time-slot number, and the data subsequences are sent to different slots bit by bit. Thus, the data sequence achieves a serial-to-parallel transformation. A local oscillator activates a DFB laser to perform gain-switching on it. The gain-switched optical pulses have a period of T. Mach–Zehnder modulators with different time delays are modulated by the serial-to-parallel transformed signals. The time-division multiplexed signals are then combined using an optical coupler and forwarded to an all-optical encoder for time spreading to transform them into a noise-like signal. Another structure of optical time-division multiplexing optical covert signal generation is shown in Figure 1b. The gain-switched optical pulses are time-division multiplexed by time-delay lines and combined by an optical coupler. Then, the multiplexed signals are sent to the all-optical encoder. In an all-optical encoder, the gain-switched optical pulse is divided in the frequency domain by a wavelength-division multiplexer into different parts, each with a different time delay. Thus, the gain-switched optical pulses are encoded in both the frequency and time domains. The encoded signal is further spread in the time domain through a dispersive fiber after the optical encoder. Thus, the optical time-division multiplexed signal is processed to be a noise-like signal, and can be stealth-sent under optical noise in an optical network.

In the gain-switching of a DFB laser, the interaction between photons and carriers in the DFB laser can be modeled by the rate equations [33,34,35]. The dynamics of the carrier density $N\left(t\right)$ and complex electric field $E\left(t\right)$ in the DFB laser can be expressed as follows:

$$\begin{array}{c}\frac{dE\left(t\right)}{dt}=\frac{v_{g}a(N\left(t\right)-N_t)\mathrm{\Gamma }E\left(t\right)}{2[1+\epsilon E^2\left(t\right)]}-\frac{E\left(t\right)}{2{\tau }_p}+\frac{\mathrm{\Gamma }\beta B{N}^2\left(t\right)}{2E\left(t\right)}+F_E\hfill \\ \frac{dN\left(t\right)}{dt}=\frac{I\left(t\right)}{eV}-\frac{v_{g}a(N\left(t\right)-N_0)}{1+\epsilon E^2\left(t\right)}{E}^2\left(t\right)-\frac{N\left(t\right)}{{\tau }_n}+F_N\hfill \end{array}$$

(1)

where the names and values of the parameters are listed in

Table 1. Some parameter definitions and values used in the simulations.

Parameter	Value
Confinement factor ($\mathrm{\Gamma }$)	0.3
Linear material gain coefficient (a)	$3.3\times {10}^{-20}$m2
Spontaneous emission rate ($\beta$)	$1\times {10}^{-4}$
Group velocity ($v_g$)	$7.5\times {10}^7$ms−1
Electron charge (e)	$1.6\times {10}^{-19}$ C
Volume of the active region (V)	$1.8\times {10}^{-16}$ m3
Carrier density at transparency ($N_t$)	$1.5\times {10}^{24}$ m−3
Nonlinear gain compact factor ($\epsilon$)	$3\times {10}^{-23}$ m3
Photon lifetime (${\tau }_p$)	$3\times {10}^{-12}$ s
Carrier life time at threshold (${\tau }_n$)	$2.1\times {10}^{-9}$ s
Bimolecular recombination coefficient (B)	$1.0\times {10}^{-16}$ m3s−1

. The signal output from the local oscillator is $I\left(t\right)$, which is a time-varying injection current and contains the bias current $I_b$ and sinusoidally varying current $I_m$. The Langevin noise sources $F_E$ and $F_N$ take into account spontaneous emission and spontaneous carrier recombination.

For a DFB laser gain-switched by a 10 GHz electrical signal, the waveform and spectrum are shown in Figure 2a and Figure 2c, respectively. $I_b$ is 0.2 A and $I_m$ is 0.2 A. The spectra of the gain-switched optical pulses are optical frequency combs. For a DFB laser gain-switched by a 2.5 GHz electrical signal, the waveform and spectrum of the optical time-division multiplexed signal are shown in Figure 2b,d. $I_b$ is 0.08 A and $I_m$ is 0.2 A. The optical time-division multiplexed signals have the same bit rate as 10 Gbps optical pulses, and the spectrum is continuum and wideband.

3. Optical Covert Communication System

A schematic diagram for the proposed time-division multiplexed OCC system based on gain-switched optical pulses is shown in Figure 3. The public channel consists of four signals with center frequencies of 192.81, 193.02, 193.22, and 193.42 THz. The public optical signals are modulated by a non-return to zero (NRZ) signal with bit rate of 10 Gbps. The optical covert signal is sent to the public channel through an optical coupler, which is followed by a 50 km single-mode fiber (SMF) span. The optical covert transmitter has the same structure as that in Figure 1a. In the public receiver, the public signals are directly detected after passing through a dispersion-compensation fiber and a de-multiplexer. For the optical covert channel, the public signals are suppressed by an optical filter and then amplified by an EDFA. The residual dispersion is compensated by a fiber span with a dispersion of −332 ps/nm. The time-compressed signal is then decoded by the decoder and then de-multiplexed in the time domain by an electro-absorption modulator. The signal is restored through P/S conversion before the BER tester.

4. Simulation Results and Discussion

4.1. Multiple Users

To quantitatively analyze the influence of optical time-division multiplexing on the system performance, the BER performance of the optical covert channel was studied and shown in Figure 4. The covert signals were modulated by a 2.5 GHz electrical signal and then multiplexed in 4-fold by time delay lines and an optical coupler. As can be seen, the covert signal can be transmitted error-free over a 50 km public transmission link, in which the bias current is 0.08 A and the modulation current is 0.2 A. Due to the different performance of the electro-absorption modulators in the time domain, the receiver sensitivity varies from one time slot to another.

The BER curves versus the different received powers of the public channels are shown in Figure 5. As can be seen, the public channels have different receiver sensitivities. When comparing the BER curves with the ASE noise and with the covert signal, the power penalty is smaller than 0.3 dB. Therefore, the optical time-division multiplexed covert signals have a minimal impact on the public channel.

The eye diagrams of the optical covert channel are shown in Figure 6. As can be seen, the bit rate is 10 Gbps after optical time-division multiplexing. Then, the optical pulses are mixed in with each other after optical encoding; however, the envelope is clear. After time spreading, the optical pulses are noise-like in the time domain, as can be seen in Figure 6c. Then, the noise-like signal can be transmitted under the ASE noise in the optical network.

Combined with the optical covert signal, the spectra of the public channel are shown in Figure 7. Comparing the spectrum of the public channel with the ASE noise and with the optical covert signal, there is little difference. With the ASE noise introduced by the optical amplifier, the covert signal can be hidden with a lower optical signal-to-noise ratio.

Eye diagrams of the public channel with the ASE noise and with optical covert signal are shown in Figure 8. The center frequency of the public signal is 193.02 THz. The two eye diagrams show no difference in the time domain. Therefore, the optical covert channel is hidden in the public channel and has no impact on the public signal.

4.2. Single User

After being optical time-division multiplexed, the covert signal was modulated by a 10 Gbps signal for a single user. The BER curve of the 10 Gbps optical covert signal is shown in Figure 9. The optical covert channel can be transmitted error-free. In addition, the receiver sensitivity of the single-user covert channel is larger than that of the multiple-user covert channel.

The BER curves versus the different received powers of the public channels are shown in Figure 10. Compared with Figure 5, the public channels have similar receiver sensitivities. Furthermore, when comparing the BER curves with the ASE and with the covert signal, it is observed that there is a minor power penalty for the public channel when a single-user optical covert channel is present. Hence, the architecture employed for optical time-division multiplexing has a negligible effect on the performance of the public channel.

5. Discussions and Conclusions

The optical time-division multiplexed covert channel for multiple users has a low receiver sensitivity; however, an electro-absorption modulator or another de-multiplexing device is necessary in the receiver. Thus, for point-to-point communication, optical time-division multiplexed covert channels are suitable for modulating a single message so that the receiver does not have to be de-multiplexed and the concealment performance is similarly improved.

Considering the multiplexing approach, the available bandwidth is limited for signal transmission through optical network equipment. Optical time-division multiplexing is a good choice for increasing the number of users and capacity.

In summary, in order to improve the system performance of optical covert communication, optical time-division multiplexing is introduced in this paper. System simulations have validated the effectiveness of the optical time-division multiplexing in optical covert communication systems. The simulation results show that the covert channel can be transmitted error-free after being optical time-division multiplexed. The structure of the optical time-division multiplexer has no influence on the public channel, but has an impact on the covert channel. Hence, this work provides a novel solution to enhance the bit rate and covertness of optical covert communication.