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Abstract
In this paper, we propose a high-security three-dimensional optical transmission system utilizing time-frequency-space interleaving chaos, which simultaneously enhances the reliability and security of the system. The four-wing 3D chaos model encrypts the time-frequency space interleaved modulation domain of a orthogonal time-frequency space (OTFS) modulation signal and the modulated phase information simultaneously, improving the system's security. We also experimentally validate the proposed high-security 3D-OTFS method, utilizing the hexadecimal modulation technique. The modulated OTFS signal achieves a transmission rate of 34.1 Gb/s over a 2-km seven-core fiber link, with the OTFS signal exhibiting a maximum of 1.31 dB receiver sensitivity gain compared to orthogonal frequency division multiplexing (OFDM) signals under the forward error correction threshold of the bit error rate. The achieved keyspace is equal to 5 × 1048. The findings demonstrate that the proposed high-security three-dimensional optical transmission mechanism, based on time-frequency-space interleaved disruption, exhibits excellent anti-interference ability and confidentiality performance. Consequently, it holds promising prospects for future applications in optical communications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Due to continuous technological developments in optical communication systems, information technology has penetrated into all aspects of people's daily lives.As the main body of the traditional multiplexing technology has almost reached its limit, the explosive increase in intelligent terminal equipment makes the communication system in demand for channel capacity, which has increased dramatically to time, frequency and space [1]. Under the backbone network technology development is becoming more mature and stable background, for short and medium distance communication access network system ushered in the pressure and challenges, especially short distance communication data center of the amount of information exchanged showed explosive growth. In order to meet the increasing demand for communication capacity, a new multiplexing communication technology is urgently needed. Orthogonal frequency division multiplexing (OFDM) is a highly efficient signaling scheme widely employed in wired and wireless communication systems. One of its essential advantages is its capability to combat inter-symbol interference (ISI) caused by dispersive channels [2,3]. However, the output signal in OFDM is real-valued and unipolar (non-negative), necessitating the application of Hermitian symmetry conditions during the coding process. In passive optical networks (PONs), intensity modulated and direct detection OFDM (IMDD-OFDM) systems are commonly used on top of their simplicity and cost-effectiveness [4–6]. Nonetheless, OFDM systems encounter challenges such as complex signal processing, frequency synchronization issues and notable problems like the large peak-to-average power ratio (PAPR) [7], susceptibility to phase noise, sensitivity to carrier frequency offsets (CFOs), and channel fading [8].
The orthogonal time-frequency space (OTFS) modulation system is an innovative two-dimensional (2D) modulation scheme introduced by Hadani et al. and other researchers [10]. Orthogonal time-frequency modulation technology as one of the potential application techniques in 6 G sense-computing fusion scenarios. OTFS is unique in terms of its exceptional reliability and high-speed data transmission capabilities in time-frequency dual-selective channels. This approach directly modulates data within the delay-doppler (DD) domain, extending its coverage across the entire time-frequency domain [11]. By adopting OTFS technology, the system's channel capacity experiences significant enhancements, offering a novel solution to address the resource scarcity challenges encountered by current communication systems. With its ability to enable data modulation in the time-frequency domain, OTFS presents a new and promising paradigm to meet the coming challenges in communication networks. It improves the channel capacity, providing a new suitable solution to address current communication systems’ resource scarcity issues. Another noteworthy advantage of OTFS [12] is its adaptability to various multicarrier modulation schemes through pre-processing and post-processing transforms. OTFS can be seen as a generalization of time division multiplexing access(TDMA) and OFDM, as emphasized in [10]. Additionally, OTFS can be interpreted as a generalization of other multicarrier modulation schemes. This interpretation is verified in the GFDM system, where the OTFS signal pre-processing scheme is utilized in [13] to accomplish the pre-modulation of the GFDM system and achieve the gain of the signal. Research in [14] has shown that the system architecture of OTFS is equivalent to asymmetric orthogonal frequency division multiplexing (A-OFDM) [15] in static multipath channels, which also offers better transmission performance than OFDM. A-OFDM, based on a novel three-layer FFT structure, connects general-purpose OFDM and single-carrier systems. It exhibits advantages like reduced PAPR, improved sensitivity to carrier frequency offsets (CFOs), frequency diversity compared to OFDM, and lower complexity compared to SC-FDE systems, thus providing significant flexibility in system design and operation [15]. Moreover, the OTFS technique does not impose an explicit threshold limit for the doppler shift. To further enhance the system's channel capacity, multicore fibers (MCFs) have been proposed. MCFs are a promising space division multiplexing (SDM) fiber [16,17] that allows for capacity upgrades by increasing the number of cores within the fiber. While MCFs have been extensively studied for backbone networks [18,19], their applications in access networks using multicore and few-mode fibers are relatively limited.
Furthermore, as society develops rapidly, each industry has increasingly stringent requirements for communication quality and information security. The security of communication and information affects not only the users’ privacy but also the security of businesses and even entire nations. Consequently, enhancing the security performance of communication systems has become imperative. For PON, the security issue cannot be overlooked, especially with the surge in access users. llegal optical network units (ONUs) will be disguised as legitimate ones. When optical line terminals (OLTs) transmit downstream data through broadcasting, these illegal ONUs may steal or tamper with the downstream data signals. Therefore, it is crucial to implement security encryption on PONs at the physical layer to address these concerns. Digital-domain chaotic encryption at the physical layer has garnered significant attention for high-speed multicarrier optical communication systems [20]. Physical layer encryption, widely employed in digital signal processing (DSP), is favored for its cost-effectiveness, high flexibility, and compatibility. By taking advantages of such encryption techniques, PONs can bolster their security measures and ensure the integrity and confidentiality of transmitted data. Physical layer encryption based on chaotic systems offers several valuable characteristics, including traversal, pseudo-random, parameter-sensitive, fundamental, and unpredictable. These attributes make it highly effective in safeguarding transmitted information against brute-force attacks. In the context of orthogonal frequency division multiplexing-passive optical network (OFDM-PON) security enhancement, Liu et al. proposed techniques based on symbol-level and bit-level chaotic scrambling [21–24]. Additionally, Deng et al. experimentally verified that fixed-point digital chaos algorithms [25] and fractional-order Fourier-transform chaotic techniques [26] meet the requirements of OFDM-PON with low implementation complexity and high-security performance. It is promising that the system achieves even higher security and better performance by combining digital chaotic encryption with specific areas [27]. Notably, studies have demonstrated that 3D modulation can attain superior spectral and energy efficiency compared to 2D modulation [28]. Furthermore, the multi-dimensional space in 3D modulation allows more flexible constellation encryption transformations and increases the key space, further enhancing the system's security. Utilizing these advanced encryption techniques in conjunction with multi-dimensional modulation can significantly reinforce the security and reliability of modern communication systems.
In this paper, to the best of our knowledge, a highly secure three-dimensional optical transmission mechanism based on time-frequency-space interleaving disorder is proposed for the first time, The constellations are accomplished from two-dimensional to three-dimensional enhancement in optical communication while the modulation of the signal by OTFS is accomplished.We employ a new four-wing three-dimensional chaotic model to chaotically perturb the time-frequency-space interleaving modulation domain and complete the constellations mask vector encryption for the constellations’ point rotations, which is compared with that in the traditional OFDM three-dimensional chaotic encrypted modulation scheme. This method effectively improves the BER performance and transmission security performance of the system, and adopts hexadecimal modulation at the transmitting end. Experiments on a 2 km seven-core fiber link successfully demonstrate that the high-security 3D optical transmission mechanism based on the time-frequency-space interleaving modulation domain time-frequency extension technique proposed in this paper has a 1.31 dB performance improvement over the traditional OFDM 3D chaotic cryptographic modulation scheme. It verifies that the signal security of optical transmission in the time-frequency-space interleaved modulation domain and verifies the feasibility of this scheme.
2. Principles
Figure 1 illustrates the schematic framework diagram of the high-security 3D optical transmission mechanism based on time-frequency-space interleaved disruption. It comprises a 3D mapping scheme for the constellations, the OTFS processing module, the constellation scrambling modulation, and the encryption module. At the transmitter terminal, to begin with, we use a pseudo-random binary sequence (PRBS) generated by the DSP as the original input data. The data undergoes serial-to-parallel (S/P) conversion to generate a matrix. After modulation through 3D post hexadecimal modulation, each four bits carry a set of 3D information. Meanwhile, two pairs of chaotic sequences generated by the chaotic model are used to modulate and encode the signals through random time-frequency-space interleaved modulation domain signal scrambling modulation. The scrambled signals then undergo OTFS modulation. Subsequently, the modulated signal undergoes through phase scrambling using chaotic vectors on the time-frequency-space interleaved modulated signal, which accomplishes constellation masking to complete the phase perturbation. After the constellation masking, the signals are subjected to fast Fourier transform, and a cyclic prefix is added. Finally, the encrypted signals are converted through parallel-to-serial (P/S) into single-channel signals for transmission, thus achieving 3D-OTFS modulation. A four-wing 3D chaotic system generates vectors perturbing the time-frequency-space interleaved modulation domain and the constellation angle.
Fig. 1. Schematic diagram of a highly secure 3D optical transmission mechanism based on time-frequency-space interleaving disruption.
2.1 Time-frequency-space interleaved modulation domain based on OTFS
Fundamentally, a signal can be expressed as a quasi-periodic function involving time, frequency, and delay-doppler. These three representations are interconnected through a canonical transformation, as illustrated in Fig. 2. The triangular node representation in this figure illustrates the three methods of representing a signal through this triangular transformation. The conversion between the time and frequency representations is achieved through the Fourier transform. On the other hand, the conversion from the delayed-doppler representation to the time and frequency representations is accomplished using the Zak transforms Zt and Zf, respectively.
In particular, it is possible to obtain any pair of transforms by combining the remaining transforms. Specifically, we can express the fourier transform as combining two Zak transforms [29].
The key characteristic of OTFS modulation that sets it apart from other time-frequency (TF) modulation schemes is the utilization of DD fields to multiplex modulation symbols. These symbols in the delayed doppler domain can be transformed to the time domain through the Zak transform Zt. Using a single Zak transform to convert a delayed doppler-domain signal into a time-domain signal can also be achieved by two steps. Initially, the delayed doppler domain signals are transformed into the time-frequency domain. Then the resulting time-frequency signal is converted to a time-domain signal by a second transform.
The block diagram of the conventional OTFS modulation scheme is shown in Fig. 3. At the transmitter, the information symbols (QAM symbols) represented by x[k, l] residing in the delayed Doppler domain are mapped to the TF signal X[n, m] by the inverse sims finite fourier transform (ISFFT). Subsequently, this TF signal is transformed into a time-domain signal x(t) for transmission by the Heisenberg transform. At the receiver, the received signal y(t) is transformed back to the TF-domain signal Y[n,m] by the wigner transform (Heisenberg inverse transform). The resulting TF signal Y[n,m] is mapped to the delayed doppler-domain signal y[k,l] for demodulation using the sing finite fourier transform (SFFT).
In a static multipath channel state, the relationship between OTFS modulation and A-OFDM [30] suggests that OTFS modulation and A-OFDM schemes share the same transmitter and receiver. The main difference lies in the mapping of input signals, which is significantly distinct between the two schemes. In OTFS modulation, the input signal belongs to the delayed doppler domain. In contrast, in A-OFDM and Q-OFDMA, it is represented as an intermediate domain resulting from the hierarchical FFT. In the context of a fiber optic channel, a new definition is based on the fourier dyadic relationship between the delay-doppler and the reciprocal lattice in the time-frequency plane after the signal passing through the OTFS architecture. The signal now exists in the intermediate domain between the delay-doppler domain and the time-frequency domain. To describe this intermediate domain in the present scheme, the term “time-frequency-space interleaved modulation domain” is used in this paper.
Based on this two-step conversion, this scheme is to achieve time-frequency spatial interleaving modulation in a fiber optic linear time-invariant channel in the signal. Using the pre-processing and post-processing steps of OTFS, the specific implementation of OTFS modulation in this paper is as follows. Firstly, the symbol X is mapped to the sample X[n,m] on the time-frequency grid using ISFFT,which is follows:
The signal is then converted into a continuous time waveform using the Heisenberg transform x(t):
To achieve OTFS modulation, ISSFT and Heisenberg transforms are combined. Similarly, they are used reverse at the signal-receiving end to achieve OTFS demodulation. This particular scheme involves 3D-OTFS signal modulation. Initially, the original data 1 represents the binary information sequence. This sequence of binary bits is transformed into C low-rate parallel binary sequences through series-parallel transformation. Each low-rate bit sequence is then mapped to a 3D constellation point. If there are N subcarriers, then the signal on the L subcarriers is represented as:
After 3D mapping, the frequency domain signals are converted into time domain signals by 2D IFFT [28]:
Included among these 0 ≤ n1 ≤ 2 and 0 ≤ n2 ≤ C-1, where n1 and n2 are the indices for columns and rows of the 2-D time domain matrix s1, respectively. It can be seen from Eq. (7) that the 2D IFFT can be achieved by two steps IFFT. Then the three-dimensional signal is shown as:
where $M_3^{ - 1}$ with $M_C^{ - 1}$ denotes the 3 × 3 and C × C IFFT matrices, respectively. Since the signal after the above change is still in the complex domain not suitable for optical access systems with direct monitoring of intensity modulation. Therefore we adopt the erdnase symmetry in conventional OFDM to transform the 3D-OTFS signal of the signal into real numbers, i.e., Eq. (8) can be expressed as:N is the number of IFFT points, which is a three-row N-column frequency domain signal matrix containing the original as well as the complex conjugate signal. The signal can be represented after 2D IFFT processing as:
The resulting time-domain signal is then prefixed with a cyclic prefix and suffix, and then subjected to a series-parallel transform. The signal is transformed into
The signal will be obtained at the receiver side after the opposite processing. Then S/P, conversion 2D FFT are employed to get the frequency domain signal, and 3D demapping is used to get the original bit information.
2.2 Chaotic perturbation mechanism based on time-frequency-space interleaved modulation domains
To achieve chaotic scrambling encryption in the time-frequency-space interleaved modulation domain, a quadruple-wing 3D chaotic model is employed. This model scrambles the time-frequency inverse easy grid and the constellation angle in the time-frequency-space interleaved modulation domain. The equations of the four-wing 3D chaotic model are as follows:
When the encrypted signal uses these complex, chaotic trajectories is received, decryption can only be achieved if the exact initial value (private key) is known, ensuring high security. Only with an accurate initial value (private key) can decryption be completed. Around the three chaotic sequences X, Y, Z (as shown in Fig. 4, where X, Y, Z are vectors consisting of the 3D windmill chaotic model variables x, y, and z of length M after M iterations at approximately time t), the three chaotic sequences are processed in a specific order to generate masking factors A, B, and C. These masking factors encrypt the bit-stream anomalies, the constellation point rotations, and the time chaotic scrambling modulation in the frequency-space interleaving modulation domain. The specific rules for this process are as follows:
Fig. 4. Four-winged three-dimensional chaos model (a) projection in x-y-z; (b) projection in x-y; (c) x-z projection; (d) y-z projection.
This paper presents a signal processing system based on the OTFS architecture, which establishes a fourier duality relationship between a grid on the delayed doppler plane and an inverse reciprocal grid on the time-frequency plane. The time-frequency reciprocal lattice comprises frequency points spaced at N intervals and time points spaced at M intervals. OTFS can be understood as a block OFDM with cyclic prefixes and time interleaving, making it easier to grasp. The modulated signal undergoes chaotic perturbation modulation in the time-frequency-space interleaved modulation domain. This process involves randomly generating matrices that disrupt the two-dimensional time-frequency reciprocal grid. The resulting performance effect demonstrates that this random placement will likely perform better than conventional “lattice” placements, such as equally spaced subcarriers combs commonly used in wireless standards [9]. This modulation scheme transforms the time-frequency selective channel into an invariant, separable, and orthogonal interaction. As a result, all received time-frequency conditioned signals experience the same localized impairments, and all time-frequency null-interleaved modulation domain signals are coherently combined. This approach enhances signal transmission and reception robustness and efficiency in challenging channel conditions.
Figure 5 shows that after the signal undergoes perturbation, the 3D-OTFS signal shows significantly enhanced signal quality compared to other known modulation schemes. Even with the same signal power and channel conditions, the 3D-OTFS signal exhibits improved signal detection capability. In the case of OTFS modulation, the rotating constellation points are encrypted using the constellation mask vector. Exploring the internal cause reveals that chaotic perturbation modulation does not alter its Euclidean distance but enhances its power. This process effectively improves the system's anti-jamming ability, addresses dynamic crosstalk during transmission, and enhances signal security through encryption. Overall, this approach not only enhances the performance of the signal in challenging channel conditions but also ensures improved security through encryption, which makes the system more robust and reliable.
Fig. 5. Raw data modulated signal at the transmitter side:(1)3D-OTFS after chaotic scrambled modulation; (2) 3D-OFDM after chaotic perturbation modulation;(3)3D-OTFS without chaotic perturbation modulation.
3. Experiment setup and results
The practical effect of the time-frequency-space interleaved disruption-based high-security 3D optical transmission system is shown in Fig. 6, which is experimentally verified based on a direct modulation and direct detection (IM/DD) system over a 2-km weakly coupled seven-core fiber. The system uses 240 subcarriers for OFDM, 80 symbols, 512 Fourier points FFT, and a guard interval of 1/4 of the signal length. The encrypted OTFS signals are subjected to digital-to-analog conversion (DAC) using an AWG (AWG, TekAWG70002A) with a sampling rate of 10 GSa/s. The light source is a continuous-wave (CW) laser with a wavelength of 1550 nm and an input power of 8 dBm. The electrical signal is amplified and injected into a mach-zehnder modulator (MZM) to complete the intensity modulation and electro-optical conversion. The EDFA further amplifies the laser before coupling the optical signal to the seven-core fiber through a 1:8 beamsplitter and fan-in device. In the case of a legal ONU, the received optical power is adjusted using a variable optical attenuator (VOA). The received optical signal is then converted to an electrical signal via a photodetector (PD). The obtained electrical signal is passed through a mixed-signal oscilloscope (MSO, TexMSO73304DX) with a sampling rate of 50 GSa/s. After analog-to-digital conversion, the received data is decrypted using the same key as the transmitter. Illegal access users will not be able to retrieve the correct data without the encryption key generated by the offline DSP. This ensures high-security protection for the transmitted data, making it virtually impossible for unauthorized users to access and decipher the information.
Fig. 6. Highly secure three-dimensional optical transmission system based on time-frequency-space interleaving disruption.
Figure 7 presents the BER of 3D-OTFS signals after 2 km of transmission in a seven-core fiber. The results indicate that the BER curves of the seven cores almost overlap, demonstrating the high stability of the seven-core fiber transmission system over the 2 km range. When the system BER is 3.8 × 10−3, the difference in received optical power between the best and worst fiber cores is less than 0.65 dB, confirming the excellent uniformity of the seven-core fiber transmission system over the 2 km range. Furthermore, it can be observed that when the received optical power exceeds -17 dBm, the BER performance of all seven fiber cores remains within the forward error correction (FEC) threshold. As the optical power continuously increases, the BER of each fiber core gradually decreases. This finding indicates that the proposed 3D-OTFS transmission scheme demonstrates excellent performance within the seven-core fiber transmission system. Overall, the experimental results validate the effectiveness of the adopted encryption scheme on 3D-OTFS signals and confirm the stability and uniformity of the seven-core fiber transmission system, providing confidence in the reliability and performance of the proposed 3D-OTFS transmission scheme over the specified range.
To investigate the impact of multicore multiplexing on OTFS signals based on different modulation formats and verify the superiority of the proposed 3D-OTFS scheme, we compared the proposed 3D-OTFS transmission scheme based on different receiver demodulation algorithms. In Fig. 7, it has been proven that the adopted 2 km 7-core fiber optic transmission system has good uniformity and stability. Therefore, when we analyze the performance of the receiver demodulation algorithm, only the performance in the same fiber core was analyzed. The experimental results are shown in Fig. 8. We compared the BER performance of the proposed 3D-OTFS encryption system and the 3D-OFDM encryption system, which can be seen under the FEC$3.8 \times {10^{ - 3}}$ threshold of BER. The 3D-OTFS encryption system has a 1.31 dB performance improvement compared to the 3D-OFDM encryption system.
Fig. 8. Comparison of BER curves and constellation diagrams for 3D-OTFS chaotic scrambling modulation and 3D-OFDM chaotic scrambling modulation.
The BER performance of 3D-OTFS signals with 3D-OFDM was tested in a scenario involving eavesdropping or brute-force decryption attempts by illegal ONUs at the receiving end without the correct private key. A comparison was made between the 3D-OTFS crypto-modulated signal in a back-to-back (BTB) situation and the encrypted signal in a seven-core fiber system. As shown in Fig. 8, the experimental results indicate that the adopted encryption scheme minimally affects the BER performance of 3D-OTFS signals when the received optical power is more significant than -15 dBm. Additionally,the difference in BER, within the FEC error correction threshold, between the transmission system using a 2 km seven-core optical fiber and the BTB transmission is small and acceptable. These results demonstrate the feasibility of the proposed high-security 3D optical transmission system based on the time-frequency-space interleaved modulation domain and time-frequency expansion technique.
Moreover, at the illegal ONU end, the BER value received through forced decryption is about 0.50 dB, confirming the security of the proposed encryption scheme. The experimental results indicate that the proposed encryption scheme protects the 3D-OTFS signals from unauthorized access and decryption attempts. The system is a reliable and robust solution for secure optical communication systems, providing high-security transmission.
We also compared the performance of OTFS signals with different dimensions when testing different modulation formats,as shown in Fig. 9. From the Figure, it can be seen that the 3D-OTFS signal has a significant improvement compared to the 2D-OTFS signal. After being compared, it is found that the 3D-OTFS signal also has a 0.62 dB improvement compared to the 2D-OTFS signal.
In addition, as depicted in Fig. 10, the proposed encryption scheme's key space is computed rigorously. With sensitivity testing experiments, the critical space can be rigorously calculated by adding 1 × 10-N to a single initial value or initial parameter, and then experiments can be performed to test whether the correct data can be fully demodulated successfully. The magnitude of N is adjusted until a high BER node that is an order of magnitude away from full demodulation is the critical space.The key comprises the initial values of the four-wing 3D chaotic system, the control parameters, and the step size, denoted as {x, y, a}. Considering a step size of [1, 2 × 10−3], the key space can be calculated experimentally as 5 × 102 × 1016 × 1015 × 1015 = 5 × 1048. This results in an enormous key space. The proposed encryption scheme's immense key space enhances the security level of the system, making it highly resistant to attacks and unauthorized intrusions. Besides, the encryption reaffirms its effectiveness in providing high-security data transmission and communication.
4. Conclusion
To enhance the security of the physical layer and improve the system performance simultaneously, we propose a high-security three-dimensional optical transmission mechanism based on the time-frequency extension technique in the time-frequency-space interleaving modulation domain. The four-wing 3D chaotic model is utilized for constellation masking of time-frequency inverse easy grid and constellation angle rotation in time-frequency-space interleaved modulation domain, which provides a key space of 5 × 1048 to resist brute force decryption to improve the security of the system. To verify the scheme's feasibility and compare its quality with traditional encrypted 3D-OFDM, a 2 km MCF was established. And a transmission experiment of 34.10Gb/s was achieved.The experimental results show that our proposed encryption scheme has a relatively small impact on the bit error rate performance within the FEC threshold of 3.8 × 10−3compared to traditional OFDM signals, and has a 1.31 dB improvement compared to traditional 3D-OFDM schemes, verifying that our proposed scheme has extremely reliable security performance.
Funding
National Key Research and Development Program of China (2021YFB2800903); National Natural Science Foundation of China (U22B2010, 62275127, 62205151, 62225503, 61935005); Jiangsu Provincial Key Research and Development Program (BE2022079, BE2022055-2); The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (22KJB510031); The Startup Foundation for Introducing Talent of NUIST.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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