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Abstract
In this paper, a secure orthogonal time-frequency space (OTFS) modulation transmission system based on 3D dense constellation mapping (DCM) geometric shaping is proposed, and a selective reduction amplitude algorithm (SRA) for DCM to reduce peak average power ratio (PAPR) is presented. The DCM is based on regular tetrahedron construction to improve its space utilization efficiency. The proposed SRA involves reducing high PAPRs transmitter and restoring them at the receiving end, which only requires an additional 0.57% of the total transmission capacity. The algorithm reduces PAPR while ensuring the bit error rate performance of the system, so it is suitable for systems that need to process large amounts of transmitted data quickly. By verifying the actual transmission performance on a 2 km of 7-core optical fiber transmission system, the optical transmission with a bit rate of 33.93Gb/s is achieved. The experimental results show that when the bit error rate (BER) reaches the 3.8×10−3 threshold, the OTFS system using DCM and SRA could improve the receiver sensitivity by 3.7 dB compared with the OTFS system using concentric cube mapping and SRA, and 2.7 dB compared with the OFDM system using DCM. After adding the SRA, the PAPR of the OTFS system is reduced by more than 2.2 dB. When the received optical power reaches near the bit error rate threshold, the SRA valid data can be fully recovered by optimizing the SRA.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the promotion of real-time 3D high-quality image applications such as virtual reality (VR) and augmented reality (AR), the public's demand for data is increasing daily. Compared with wireless transmission, optical fiber transmission is widely used in long-distance transmission with its excellent anti-interference performance and long-distance high-performance transmission. Optical orthogonal frequency division multiplexing (OFDM) has been widely used in high-speed and large-capacity data transmission for intensity-modulation direct-detection (IM/DD) systems because this technology can exploit the performance diversity over the spectrum to maximize the system capacity [1]. However, OFDM is relatively weak in a high Doppler environment.
In order to improve the transmission quality of a high Doppler environment, Ronny Hadani proposed a two-dimensional (2D) modulation technology driven by a delayed Doppler channel called orthogonal time-frequency space (OTFS) [2]. As one of the possible future 6 G communication technologies, OTFS has received much attention since it was proposed. OFDM uses the addition of cyclic prefixes to overcome high inter-symbol interference (ISI) but suffers orthogonality loss due to Doppler shift. At the same time, OTFS channels can be considered invariant for a short period and can better resist inter-carrier interference (ICI) [3]. The difference is that the symbolic multiplexing and representation of the channel in OTFS is carried out in the delayed Doppler domain, while OFDM is processed in the time-frequency domain [4]. Since all modulation symbols spread uniformly over the time-frequency domain, the peak average power ratio (PAPR) of OTFS signals is lower than OFDM's. In addition, many studies have proved that the key advantage of OTFS is that it can provide better performance than OFDM in transmission scenarios with a high Doppler effect [5–7].
To further improve the performance of the OTFS optical transmission system, we use a 3D dense constellation mapping (DCM). Traditional constellation mapping methods include two-dimensional QPSK, QAM, etc. Compared with 2D constellation mapping, 3D constellation mapping has a larger constellation arrangement space and can obtain better channel conditions in some cases [8], also, it can achieve a more considerable minimum Euclidean distance (MED) under the same average power [9]. Three-dimensional constellation mapping can reduce the average power of the transmission system under the same MED condition. The more common three-dimensional constellation mapping takes reducing the average distance between constellations as the primary goal. It uses geometric shapes that are easy to stack and combine, such as cuboids and regular tetrahedrons, as the basis for building different three-dimensional constellations. After the use of three-dimensional constellation mapping, among these three-dimensional constellation points, the constellation points that are far from the origin in the process of multi-carrier modulation, due to the superposition of multiple subcarrier signals, there will be a situation that a certain instantaneous PAPR is too high, exceeding the saturation area of the high-power amplifier, resulting in difficult to control nonlinear or external radiation on the transmission system. There are many methods to reduce PAPR, such as coding, pulse, probabilistic shaping, etc. Reference [10] proposes a multi-class neural network-assisted SLM algorithm to select the optimal phase vector for each OFDM symbol to reduce the high PAPR and computational complexity of about 3 dB. Reference [11] proposes an OFDM system that optimizes constellation extension (OCE) and reduces PAPR using the SLM algorithm, achieving a PAPR reduction of up to 3.07 dB.
Due to the characteristics of optical fiber, optical transmission has a higher security level than wireless transmission. However, in the downlink transmission of the PON system, information can be easily stolen, and the security performance faces challenges that cannot be ignored. Therefore, transmission security has become the focus of optical communication research in recent years. Reference [12] proposes a new dimension of sparse code scrambling to achieve a joint encryption of the four-dimensional region, and there is no introduction of additional phase noise to the system. Reference [13] improves the key space of the chaotic encryption model and reduces the complexity by using the generated adduction network. Reference [14] proposes a high-security transmission scheme of power division 3-D carrier-less amplitude and phase based on polling-permutation encryption and noise masking key distribution, by implementing the 6D Lorenz digital chaotic system. Reference [15] proposes a physical layer encryption scheme for data cluster disturbance under the chaotic sequence color-seeking mechanism caused by Brownian motion determined by key.
Based on 3D dense geometric shaping, this paper proposes a secure time-frequency domain coding modulation system scheme to reduce PAPR and verify its actual transmission performance on a transmission experiment system. OTFS has a foreseeable application prospect in the field of wireless transmission. In the transmission scheme that uses both optical fiber and wireless transmission, using OTFS modulation could improve transmission performance. It provides a feasible way to meet the demand for large-capacity transmission for future mobile. In this paper, we proposed a selective reduction amplitude algorithm (SRA). In an OTFS transmission system using dense constellation mapping (DCM), the effect of reducing the high PAPR of individual bits is obvious, and only about 0.57% of the total transmission capacity is required. PAPR reduction is effective in systems that require rapid processing of large amounts of transmission data.
2. Principles
The flow chart of the OTFS transmission system is shown in Fig. 1. The randomly generated bit stream signal passes through the DCM we set, and each four-bit number corresponds to a 3D constellation point. Then, OTFS modulates the mapped matrix to obtain the time domain signal, and then the cycle prefix and suffix are added. ISI significantly affects signal quality due to excessive data transmission. Finally, SRA reduces the high PAPR of individual bits generated by intensive constellation mapping and improves the system's performance.
To ensure the quality of the transmission system and the space utilization of the mapping constellation, we use the tetrahedral interstacking model to construct our constellation mapping model. As shown in Fig. 2.
Unlike the standard concentric cube distribution or regular tetrahedral mapping, the constellation points we use are staggered and stacked in a typical tetrahedron way. The MED between adjacent constellation points is 2, and the distance between the two points adjacent to the origin is 1. Such construction mode makes the constellation points adjacent to each constellation point of each constellation denser. There is sufficient noise tolerance between each constellation point. The average power of the transmission system can also be controlled at a lower level, which is beneficial to reducing the signal's average power that needs to be converted into real numbers in the channel. The proposed DCM mapping rules are shown in Table 1. We chose to contrast it with concentric cubes, common in 3D mapping. The calculation method of the three-dimensional constellation figure of merit (CFM) is shown as follows [16]:
where $\textrm{d\; }_{\textrm{min}}^\textrm{2}\textrm{(s)}$ is the minimum Euclidean distance between standard constellations, which is set as 2 in this paper, M is the number of constellation points, n is the dimension of the constellation, which is 3 in this paper, and $\sum \textrm{d\; }_{\textrm{ori}}^\textrm{2}\textrm{(s)}$ is the sum of distances from each point to the origin. According to formula (1), the CFM of DCM is 1.2632, and the CFM of the concentric cube map is 0.7089. It can be seen that the proposed DCM improves the CFM index by about 78% compared with concentric cube. After mapping the above constellation, a two-dimensional constellation symbol of M×N is obtained. Unlike OFDM, OTFS modulation will perform an inverse symplectic finite Fourier transform (ISFFT) on the constellation symbol, which is carried out in the delay-Doppler domain, and then use the Heisenberg transform to transform the signal into a continuous time-domain waveform, thus achieving OTFS modulation. ISFFT is divided into two steps. First, the signal in the time-delay Doppler domain is modulated by IFFT to convert the signal in the time-delay domain to the signal in the frequency domain. Then, FFT is applied to Doppler symbols to transform Doppler signals into time-domain signals. The mathematical expression of ISFFT is as follows [7]:
Table 1. Three-dimensional space coordinates and drawing rules of DCM
Because of 3D mapping, OTFS modulation requires 2D-ISFFT to acquire time domain signals. Specifically, the initial binary sequence is first transformed into V low-rate parallel binary sequences by serial-parallel (S/P) conversion, where V is the number of subcarriers. Each low-rate bit sequence is then mapped to a 3D constellation point. Then, the signal on the k subcarrier can be expressed as follows:
The three elements of the matrix represent the vectors of the three-dimensional constellation points on the x, y, and z axes. In this way, we can get a frequency domain signal composed of V carriers, which can be given as:
As mentioned above, ISFFT is composed of IFFT and FFT, so for 2D-ISFFT, 2D-IFFT and 2D-FFT are used. In addition, to make sure the signal applied to the optical access system of IM/DD, adopt Hermitian symmetric three-dimensional frequency domain signal is converted to a real value [17], and the transformed 2D-IFFT can be presented as:
where N represents the number of IFFT points, $\textrm{M}_\textrm{3}^{\; \; \textrm{ - 1}}$ and $\textrm{M}_\textrm{C}^{\; \; \textrm{ - 1}}$ represents the IFFT matrix of 3 × 3 and C × C, and $\textrm{F}_{\textrm{all}}$ contains the original signal $\textrm{F}_{\textrm{3D}} $ and the complex conjugate signal conj($\textrm{F}_{\textrm{3D}} $). After 2D-IFFT, we need 2D-FFT and Heisenberg transform. Then, the series are converted to real signals of single-channel via parallel to serial (P/S). The signal will go through the reverse process at the receiving end, including serial to parallel (S/P), Weiger transform, SFFT, 3D demapping to get the original bit information.To prevent external illegal users from hijacking the information, we use the lantern-type 3D chaotic model to simulate the 3D sign encryption [18], the physical 3D lantern-shaped function definition of the chaotic model is given in Eq. (7) for:
When receiving signals encrypted by these complex, chaotic sequences, decryption will fail without the exact secret key, thus guaranteeing high-security performance. The three chaotic sequences xA, xB, and xC generated around the chaotic model are vectors composed of the chaos model variable A mentioned above. After M iterations of about time t, the length is M, the three chaotic sequences are processed to generate masking factors for the rotation, frequency and symbol masking of constellation points, as shown in formula (8-10):
Traditional PAPR reduction algorithms typically include SLM and PTS, both of which need to process the data to be transmitted into n copies and then select the data with the lowest PAPR for transmission; that is, the PAPR of n copies of data needs to be calculated, which requires a considerable amount of computation. In addition, both algorithms compress the overall data. In the case of low transmission power, the overall bit error rate (BER) performance is affected. The SRA proposed in this paper only needs to calculate the PAPR of the data to be transmitted and set the reduction coefficient dc, recovery coefficient rc and reduction threshold TR according to the peak power and average power, where dc and rc are reciprocal. Then, traverse the entire data, multiply the signals exceeding the threshold by the drop coefficient, record their coordinates, process these coordinates into the data Nhsadd in the frame header format, and finally combine the frame header Nh, coordinate data Nhsadd and the data to be transmitted ST into a frame structure in order, as shown in Fig. 4.
Nhsadd contains the coordinate information of SRA taking effect, which is set to 900 bits. This length can be modified according to the effect of SRA on actual data. High PAPR points are SRA processing objects. Fortunately, the proportion of occurrence is low. Too much reduction of the overall PAPR of the system will lead to deterioration of the transmission through the optical fiber, so we can control the reduction of the threshold TR according to the calculation of the average power in PAPR, which can ensure that the number of data effective by SRA is less than 45, usually about 20. The coordinates of these data are converted to hexadecimal numbers, and then these hexadecimal numbers are converted to the coordinate information of the bit-binary bit stream, which is processed as the 1/-1 data stream of the class frame header, and the remaining positions are supplemented with zeros. In order to facilitate decoding at the receiving end, ten zeros are inserted before Nhsadd. After the frame header is removed at the receiving end, Nhsadd is restored as the coordinate information, and the corresponding position information in the signal is multiplied by rc according to the obtained coordinates. The simulation results show that we can obtain a time-domain signal with relatively average transmitting power by combining the designed DCM and SRA, and the requirement of extra capacity is Nhsadd size + zeros size / [dimension × symbol number (/carrier) × (IFFT size + CP size) + CS size + Nhead size + Nhsadd size + zeros size] = 900 + 10 / [3 × 80 × (512 + 128) + 20 + 3900 + 900 + 10] = 0.57%. In the extreme case that Nhsadd cannot be solved entirely, we optimize the algorithm of the receiving end. If the received Nhsadd does not meet some data characteristics of the sending end, SRA will choose not to process the received data. In this case, SRA achieves an effect similar to amplitude-limiting filtering, and the amount of changed data is minimal. It does not affect the BER performance of the receiving end by orders of magnitude and has strong robustness.
3. Experiment setup and results
The transmission experiment of the secure time-frequency domain transmission system based on three-dimensional dense constellation shaping to reduce PAPR through SRA is shown in the Fig. 5. In the experiment, data will be allocated to 240 subcarriers, each subcarrier containing 80 symbols, the protection interval will be set to 1/4, and the size of the Fourier transform sampling point will be set to 512. An offline digital signal processing (DSP) generates the encrypted time-frequency spatial signal at the optical line terminal (OLT). Then, the signal is loaded into an arbitrary waveform generator (AWG, TekAWG70002A) for digital-to-analog conversion (DAC) with a sampling rate of 10 GSa/s. After linear amplification by an electrical amplifier (EA) which gain is 22 dB, the analog signal drives a Mach-Zehnder modulator (MZM) with 40 Ghz bandwidth. MZM is biased at the intersection. A laser with a linewidth of less than 100kHz produces a 1550 nm optical carrier for optical signal modulation. After the modulated optical signal is amplified by an erbium-doped fiber amplifier (EDFA), it is divided into seven beams by an optical coupler (OC) and transmitted by a fan-in device to 2 km of 7-core fiber.
Fig. 5. The experimental setup of the proposed scheme. (AWG: arbitrary waveform generator; EA: Electronic amplifier; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; MCF: multicore fiber; OC: optical coupler; VOA: variable optical attenuator; PD: photodiode; MSO: mixed-signal oscilloscope)
At the receiving end, the 7-core channel is demultiplexed into a single-mode fiber through a fan-out device, resulting in a net bit rate of 33.93Gb/s, the total bit rate is the subcarrier number × symbol number (/carrier) × 4(bits/symbol) × number of cores × AWG sampling rate / [dimension × symbol number per carrier × (IFFT size + CP size) + CS size + Nhead size + Nhsadd size + zeros size] = 240 × 80 × 4 × 7 × 10 / [ 3 × 80 × (512 + 128) + 20 + 3900 + 900 + 10] = 33.93 Gb/s. And a variable optical attenuator (VOA) is installed to adjust the received optical power. Photodiodes (PD) are used for signal detection. After an analog-to-digital conversion (ADC) via a mixed signal oscilloscope (MSO, TekMSO73304DX) with a sampling rate of 50 GSa/s, the offline DSP extracts the key and recovers the original data.
Firstly, we conducted a comparison experiment with the OTFS system using concentric cube mapping and the OFDM using DCM to verify the effect of the proposed DCM OTFS system. The results are shown in Fig. 6. The proposed OTFS transmission adopts DCM and adds SRA (line OTFS_DCM) and only changes the constellation mapping to a concentric cube and adds SRA to compare the effect of DCM (line OFDM_Cube). Compared with OFDM transmission using DCM without SRA (line OTFS_DCM), the receiver sensitivity of OTFS under DCM is compared with that of OFDM. Experimental results show that in the proposed OTFS transmission system, DCM improve the receiver sensitivity by 3.7 dB compared with concentric cube mapping and 2.7 dB with OFDM under the same BER threshold. Also, we test legal and illegal ONUs, as depicted in Fig. 6. Illegal users cannot obtain adequate information from the encrypted signal due to the lack of the secret key, and the BER remains around 0.5 under different optical power.
Secondly, in the above 7-core optical fiber experimental environment, we tested the BER performance of the designed time-frequency domain coded modulation transmission system, as shown in Fig. 7, when approaching the BER threshold, the performance between different cores was not more than 0.8 dB. In calculating CFM, we figured that the distance between the farthest constellation point in the three-dimensional constellation and the mapping centre point is 2.6458, and there are six such constellation points in the 16 constellation mappings. In the simulation part, we observed that the mapping would produce extremely high peak waveforms of individual bits. In the experiment, we found that too-high peak waveforms would affect the subsequent received waveforms, degrading system performance. In order to evaluate the PAPR performance of SRA in OTFS system, complementary cumulative distribution function (CCDF) curves before and after SRA are given, as shown in Fig. 8. After combining the SRA, only the excessive peak value is reduced, the overall reduction is about 2.2 dB, and the resulting waveform is more average and does not over-compress the performance.
The experimental results show that the primary data of addition in SRA is correct after channel transmission, but there will be a small amount of error caused by channel loss, noise, etc. Most of the added information can be solved after the algorithm optimization of the receiving end. The data test of the proposed transmission structure through seven-core fiber shows complete solution performance when the BER reaches the threshold value or exceeds the threshold value by order of magnitude. The average decoding rate can get over 89% in all experimental data in seven-core fibre. The decoding rate reaches 100% in the experiment of different mapping and modulation modes.
4. Conclusion
This paper proposes an OTFS multi-core optical fiber transmission system with high-security DCM. Based on the lower PAPR compared with OFDM, the proposed SRA is used to reduce the excessive PAPR further and improve the system's BER performance under low received optical power. Experiments show that the scheme can achieve 33.93Gb/s data transmission in 2 km seven-core fiber, which is significantly improved compared with traditional OFDM or concentric cube geometric shaping. In addition, experiments have verified the universality of SRA for different three-dimensional maps in OTFS modulation; the PAPR reduction effect for individual bits is noticeable, and the complexity is lower than SLM. However, the algorithm makes it difficult to use SRA for modulation methods with high and few peaks; therefore, SLM or PTS is more appropriate.
Funding
National Key Research and Development Program of China (2023YFB2905503); National Natural Science Foundation of China (62275127, U22B2009, 62205151, 62225503, 62035018); Jiangsu Provincial Key Research and Development Program (BE2022079, BE2022055-2); Natural Science Research of Jiangsu Higher Education Institutions of China (22KJB510031); Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology (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.
References
1. W. Zhang, Z. Q. Fan, and J. Zhao, “Reliability-aware subcarrier mapping strategy of QC-LDPC encoded symbols in bandwidth-limited IM/DD OFDM systems,” Opt. Express 29(22), 35400–35413 (2021). [CrossRef]
2. R. Hadani, S. Rakib, M. Tsatsanis, et al., “Orthogonal time frequency space modulation,” 2017 IEEE Wireless Communications and Networking Conference (WCNC), San Francisco, CA, USA, 1–6 (2017).
3. S. E. Zegrar and H. Arslan, “A novel cyclic prefix configuration for enhanced reliability and spectral efficiency in OTFS systems,” IEEE Communications Letters 12(5), 888–892 (2023). [CrossRef]
4. S. S. Das and R. Prasad, “OTFS: orthogonal time frequency space modulation a waveform for 6 G,” in OTFS: Orthogonal Time Frequency Space Modulation A Waveform for 6 G, River Publishers, pp. i-xxvi (2021).
5. S. Buzzi, G. Caire, G. Colavolpe, et al., “LEO satellite diversity in 6 G non-terrestrial networks: OFDM vs. OTFS,” IEEE Commun. Lett. 27(11), 3013–3017 (2023). [CrossRef]
6. D. Zheng, H. M. Zhang, and J. Song, “DCO-OTFS-based full-duplex relay-assisted visible light communications,” Opt. Express 29(25), 41323–41332 (2021). [CrossRef]
7. P. Singh, A. Gupta, H. B. Mishra, et al., “Low-complexity ZF/MMSE MIMO-OTFS receivers for high-speed vehicular communication,” IEEE Open J. Commun. Soc. 3, 209–227 (2022). [CrossRef]
8. P. Shi, H. Huan, and R. Tao, “Waveform design for higher-level 3D constellation mappings and its construction based on regular tetrahedron cells,” Sci. China Inf. Sci. 58(8), 1–12 (2015). [CrossRef]
9. S. G. Kang, Z. Chen, J. Y. Kim, et al., “Construction of higher-level 3-D signal constellations and their accurate symbol error probabilities in AWGN,” IEEE Trans. Signal Process. 59(12), 6267–6272 (2011). [CrossRef]
10. L. Chen, T. Xu, W. Jiang, et al., “Integrating SLM algorithm into neural network for reducing the PAPR of OFDM System,” in Asia Communications and Photonics Conference 2021, Technical Digest Series (Optica Publishing Group, 2021), paper T4A.99 (2022).
11. J. Wang, Q. Zhang, R. Gao, et al., “A PAPR reduction scheme for OOFDM system with optimized constellation extension,” 2022 20th International Conference on Optical Communications and Networks (ICOCN), Shenzhen, China, pp. 1–3 (2022).
12. Y. C. Han, J. X. Ren, B. Liu, et al., “Highly secure non-orthogonal multiple access based on key accompanying transmission in training sequence,” Opt. Express 32(2), 1979–1997 (2024). [CrossRef]
13. D. L. Zhao, X. R. Zhu, B. Liu, et al., “High-security and low-complexity OCDM transmission scheme based on GAN enhanced chaotic encryption,” Opt. Express 30(19), 34898–34907 (2022). [CrossRef]
14. W. C. Xia, B. Liu, J. X. Ren, et al., “High-security transmission scheme of secure key generation and distribution based on polling-permutation encryption,” J. Lightwave Technol. 42(1), 149–157 (2024). [CrossRef]
15. L. Liu, X. F. Tang, F. Li, et al., “Enhanced physical layer security and PAPR performance based on disturbance of data cluster under chaotic sequence color seeking mechanism in CO- OFDM system,” J. Lightwave Technol. 41(20), 6507–6513 (2023). [CrossRef]
16. J. X. Ren, B. Liu, X. Xu, et al., “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019). [CrossRef]
17. S. D. Chen, J. X. Ren, B. Liu, et al., “Performance improvement of non-orthogonal multiple access with a 3D constellation and a 2D IFFT modulator,” Opt. Express 31(5), 7425–7439 (2023). [CrossRef]
18. S. J. Cang, L. Wang, Y. P. Zhang, et al., “Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator,” Chaos Solitons & Fractals 158, 0960–0779 (2022). [CrossRef]
19. S. Y. Zhu, B. Liu, J. X. Ren, et al., “Secure OCDM mode division multiplexed short-reach optical communication based on time-frequency joint perturbation,” J. Lightwave Technol. 40(14), 4599–4606 (2022). [CrossRef]
