1. Introduction

In recent years, new challenges and limitations over single-mode fiber (SMF)-based optical networks remain exacerbated owing to the incremental requirement of data traffic including 6G, Internet of Things, and virtual reality [1–3]. At present, optical communication has the advantage of a high security level over wireless communication due to the characteristics of optical fiber. However, in the downlink transmission of the PON system, information is vulnerable to illegal theft and faces severe security problems [4]. Therefore, transmission performance and security have become hotspots in optical communication.

As a current popular high-speed multicarrier transmission technology, orthogonal frequency division multiplexing (OFDM) has the advantages of resilience to chromatic dispersion and high spectral efficiencies [5–7]. However, owing to bandwidth-limited devices, OFDM suffers from frequency-selective fading, which limits transmission performance [8]. Similar to OFDM, the newly proposed orthogonal chirp division multiplexing (OCDM) technology introduces traditional chirped spread spectrum technology to multi-carrier modulation (MCM), which applies orthogonal chirp subcarriers for information modulation [9]. It has the ability to effectively alleviate system impairments including interference and frequency-selective fading. Additionally, limiting to the nonlinear effect of single-mode fiber (SMF), it is difficult for the SMF transmission system to approach the Shannon limit. Therefore, spatial division multiplexing (SDM), which enhances the transmission channels and the number of users in PON, has become a potential candidate to improve the transmission capacity [10]. Therefore, SDM-OCDM-PON will become an effective scheme for future optical transmission systems.

In recent security systems, digital chaotic encryption applied in the physical layer is widely used for its characteristics of its high sensitivity to initial value and pseudo randomness [11]. However, traditional chaotic models suffer from low security because chaotic mapping is relatively low-dimensional [12]. And the models have simple structures and very low key-space, which are vulnerable to brute force attack. Also, the traditional integral-order based models are calculated by linear iterative equation calculation, which always requires many computational resources, which could cause much complex burden to communication system. Therefore, to enhance the security and efficiency of the system, low-cost and high security encryption scheme is highly required.

In this work, we report a secure OCDM-PON optical communication system based on generative adversarial networks (GAN). DFnT and IDFnT is adopted for the digital realization of OCDM signals, which is similar to FFT and DFT for OFDM. GAN networks are trained and used to generate constellation masking vectors and frequency masking vectors to encrypt the constellation points and orthogonal chirped subcarriers. We design the architectures of networks and the loss function to improve the performance of adversarial training process. To verify our proposed scheme, a weakly coupled 7 core fiber of 2 km is set up to achieve a 70 Gb/s transmission in the experiment. The results demonstrates that our proposed scheme has a maximum receiver sensitivity gain of about 1.26dB gain than traditional OFDM transmission system, and our encryption scheme has a large key space at about 1 × 10²⁰² against brute force cracking by illegal optical network units (ONU) with only 0.63% running time compared with traditional chaotic scheme. The experimental results demonstrate the security and the efficiency of our proposed scheme.

The framework of the paper is organized as follows: the second part explains the proposed GAN structures and the proposed OCDM encryption scheme. Experimental setup is described in the third section and the results are discussed in the fourth part. Finally, we conclude the paper in the fifth section.

2. Principle

The main framework of a secure OCDM-PON based on proposed encryption scheme is demonstrated in the following Fig. 1. Firstly, the proposed GAN networks is trained by various chaotic sequences. And then Generator of the GAN takes the initial value to generate masking vectors for encryption. Through serial to parallel (S/P) conversion of signals on transmitting end, the constellation modulation by 16QAM mapping is encrypted by the constellation masking vectors through rotating the constellation points. Moreover, the inverse discrete Fresnel transform (IDFnT) matrix is used to realize the OCDM modulation, and the chirped subcarriers are encrypted by frequency masking vectors. Finally, we add the cyclic prefix and the encrypted signals are converted to real signals of single-channel via parallel to serial (P/S) conversion for transmission. At the receiver side, the original signal bitstream could be acquired via decoding and decryption with the inverse steps of the transmitter side. The frameworks of proposed GAN networks and the OCDM encryption is introduced as follows.

 

Fig. 1. The proposed GAN enhanced encryption scheme.

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GAN is one of attractive deep generative models with an adversarial training process, which is composed of a generator and a discriminator. As shown in Fig. 2, the main framework of our proposed networks is activated by the deep convolutional GAN (DCGAN) as proposed in [13], which introduced convolutional layers into GAN. As an adversarial process, the Generator network functions to learn the distribution of source data and generate new data of similar distribution to fool the Discriminator. At the same time, A 1 × 16 noise vector z which follows the distribution p_z(z)∼N(0,I) are input into generator networks to generate fake data. The Discriminator network discriminates the reconstructed fake data by generator and the source data to help raise the reconstruction ability of Generator.

 

Fig. 2. Architecture of GAN

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The training of generator and discriminator are in an adversarial process and the loss function can be represented as follows:

In this condition, the networks aims to seek saddle point of Eq. (1) via calculating optimal value of parameters ${\hat{\theta }_g},{\hat{\theta }_d}$, which represents the parameters of Generator network and Discriminator network, respectively.

In this work, we preprocess the initial training samples via performing unit power normalization, which transform the source data x as follows:

Furthermore, to alleviate the mode collapse of adversarial training, we modify the loss function and design reconstruction error L_y between source data and generated data which follows the HΔH [15] to help define the difference of different data distribution.

In this work, the output of Discriminator network is set randomly from [0.8∼1.2] and [0∼0.2], respectively, rather than strictly 1 and 0 to decide as true source data or reconstructed fake data. And the operation can raise the help raise the noise tolerance. Pointing to the ReLU-like activation functions, Adam optimization algorithm [16] was applied to update the parameters of networks. After training, different masking vectors can be generated by Generator and applied for the following OCDM signals encryption in different dimensions.

OCDM as proposed [9] is evolved from OFDM technology and introduced enhanced traditional chirped spread spectrum (CSS) into MCM technology, which can independently modulate the information to different chirped subcarriers and demodulate them via the orthogonality of chirped signals. Profit from the advantages of CSS, OCDM signals have the ability to relieve the system impairments over the spectrum so as to have an enhanced system performance [9]. Different from OFDM with IDFT, baseband OCDM signals are generated by synthesizing the orthogonal chirps with inverse discrete Fresnel transform (IDFnT), which could be derived as follows:

The main structure of the proposed encryption scheme mainly contains constellation masking and Frequency masking. Note that our proposed encryption scheme also has the ability to encrypt the signals on time domain after IDFnT to further enhance the security of the system. The constellation masking process can be derived as follows:

After 16QAM modulation and constellation encryption, the different chirp subcarriers are encrypted by frequency masking vectors as follows:

In the receiver side, the OCDM signals can be decrypted by reverse operation of the encryption process according to the decryption masking vectors generated the corresponding key as the transmitting side.

3. Experimental Setup

To verify the feasibility of the proposed encryption scheme on the OCDM-PON system, the experimental setup on a 2 km 7 core fiber was performed as in Fig. 3. Firstly, on the optical line terminal (OLT) side, the original signals were modulated and encrypted by the key generated by a well-trained neural network. Then the arbitrary waveform generator (AWG, TekAWG70002A) took the encrypted OCDM signals with the sampling rate of 12.5GSa/s. The light source of 1550nm wavelength was launched from a continuous-wave (CW) laser and the optical power was 14.5 dBm. Then the encrypted OCDM signal was amplified via an electrical amplifier (EA) and input into the Mach-Zehnder modulator (MZM) for intensity modulation. The loss of MZM was about 6.5dB, and the optical power was about 8dBm after MZM modulation and about 15dBm after EDFA amplification. Then, the modulated optical signals were divided by the power splitter into seven paths with different delay lines to simulate different user signals. The seven single-mode fibers and the 2 km weakly coupled 7 core fiber was coupled via a fan-in device. The isolation degree of the 7 cores fiber is shown in Table. 1. On optical network units (ONU) side, we performed legal ONU receiving ends to experimentally measure the performance of the system. The 7 core channels were demultiplexed into seven single-mode fibers via a fan-out device. Then, the optical power was adjusted with an EDFA and a variable optical attenuator. A photodiode was used to convert the detected optical signals into electric signals. After that, a mixed-signal oscilloscope (MSO, TekMSO73304DX) with a 50 GSa/s sampling rate was implemented to receive electrical signals. Finally, the initial signal can be acquired with the key generated by the Generator in ONU.

 

Fig. 3. Experimental Setup (MZM: Mach-Zehnder modulator; AWG: arbitrary waveform generator; EDFA: Erbium-doped fiber amplifier; VOA: Variable optical attenuator; PD: Photodiode; MSO: mixed-signal oscilloscope).

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Table 1. Seven core fiber isolation degree

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4. Results and discussion

The loss of Generator and Discriminator for the training of GAN is demonstrated as Fig. 4. It can be seen that at first the loss of Discriminator is very high but decrease rapidly to a very small value, and after many iterations of training it finally converges to a small value. The loss of the Generator is very small at first but increases very fast, and it requires a long journey to converge to a small value. Different from the loss of normal networks, which always starts from a high value and decreases to converge at a small value. This can be explained with the mechanism of adversarial training. In adversarial progress, at first, the Generator takes noise vector as original input and it has little knowledge about the training samples, the task tends to be very easy to generate some noise vector; however, as the Discriminator learns to discriminate the generated samples and the training samples, the Generator begins to learn the original chaotic sequences and the task becomes complex, which results in a relatively high loss. After a period of training, the Generator can generate high-quality samples to confuse the discriminator, and the loss of the Generator decreases to a small value. As the adversarial training of Generator and Discriminator networks, they finally converge to a Nash equilibrium and the loss fluctuates around a small value, which means that the training of networks is completed.

 

Fig. 4. The loss of Generator and Discriminator during the training of GAN

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The running time of the traditional iteration equations-based model and the GAN-based model in the condition of the same hardware and software is recorded as shown in Table. 2. The codes of both models are run with NVIDA GeForce RTX 2060 Graphics Cards. As presented in Table. 2, the running time of the Iteration equations-based model increases with the data size on the GPU. Due to the parallel computing and the well-designed Cuda Core of NVIDA for deep learning tasks, the running time of GAN keeps constant at about 1.9 ms, which is significantly shorter than the iteration equations-based method. When the data size of keys is 800, the running time of GAN based model is 1.99 ms, which is 0.63% of that of 315 ms of Iteration equations-based model. To assure the security of communication system, large amounts of keys are needed in practice, where the proposed scheme saves many computing sources and ensure both the security and efficiency of the communication system.

Table 2. Comparison between Iteration equations and GAN

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To further verify the performance of the proposed scheme for a communication system, bit error rate with different received optical power is computed. Since isolation of each fiber works very well as shown in Table. 1, the crosstalk of different cores can be ignored and signals transmitted through each core are almost independent which is the same as single-mode fiber transmission. In Fig. 5 it can be seen from the results that, while received optical power is about −13 dBm, the BER is smaller than 10⁻³ and the signals are successfully decrypted and recovered. The experimental results demonstrate that our proposed scheme has few side effects on the quality of signals in the transmission system.

To verify the performance of our proposed scheme, the comparison of signal quality between the OFDM signals and OCDM signals is performed in the same core fiber. As shown in Fig. 6, when the received optical power is very low and only linear effects such as chromatic effect work, OCDM and OFDM technologies have similar performance. However, with the increase of the received optical power, to achieve the BER to 1 × 10⁻³, the OCDM signals require about −12.73dBm and the OFDM requires −11.48dBm, which means the receiver sensitivity of OCDM signals has 1.26dB gain compared with OFDM signals. The results reveal that our scheme has better transmission performance than the traditional scheme.

 

Fig. 5. BER curves at different optical power in different cores.

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Fig. 6. BER curves of encrypted OCDM and OFDM signals at different optical power transmitted in the same core.

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Additionally, to measure the security performance of the proposed scheme, we perform the calculation of the keyspace. As presented in above Fig. 7, the key is composed of initial values as original vector z for networks, and control parameters including learning rate, and batch size. Also, with the modified loss function, the sensitivity of each parameter is enhanced to some extent. Therefore, keyspace is performed as (1 × 10¹²)¹⁶×(1 × 10⁶)×(1 × 10⁴) = 1 × 10²⁰². In addition to the parameters of networks, the number of training samples, the training epochs, and the number of network layers are also adjustable and can increase the complexity of the proposed security scheme. Compared to the traditional Iteration equations-based model such as the Chens model, which has the initial sensitivity of 1 × 10¹⁶ for each key, the total keyspace is improved by a large number of parameters of networks. In the condition, the proposed scheme is robust to brute force attack and thus ensures the security of the communication system.

 

Fig. 7. BER curves with. tiny changes of the initial value.

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5. Conclusion

In this work, we report a high-security and low-complexity OCDM transmission scheme based on GAN enhanced chaotic encryption. To improve the security of the transmission system, the proposed GAN networks are adopted to generate masking keys for the encryption of the OCDM constellation points and frequency signals. Moreover, we adopt the basic model of DCGAN and design our networks with new network architectures and loss functions to improve the adversarial training performance of the network. To verify the feasibility of our proposed scheme, a weakly coupled 7 core fiber of 2 km was set up to experimentally achieve a 70 Gb/s transmission. The experimental results show that our proposed scheme has about 1.26 dB receiver sensitivity gain than traditional OFDM transmission system, and our encryption scheme has a large keyspace at about 1 × 10²⁰² against brute force cracking by illegal ONU with only 0.63% running time compared with the traditional chaotic scheme. The fact proves that the proposed encryption scheme is a promising candidate for next-generation PONs.