Open Access
Add to BibSonomy
Abstract
In this Letter, we propose a novel, to the best of our knowledge, way to reduce the peak to average power ratio (PAPR) based on the selective mapping–partial transmit sequence (SLM-PTS) method, which uses chaotic sequences to give rise to random phases and random split positions. For the first time, the public and private keys are both used for encryption in the sparse code multiple access–orthogonal frequency division multiplexing (SCMA-OFDM) system. The public keys are used for improvement of the PAPR while the private keys show great promises in the protection of the privacy for different users. Meanwhile, the accurate phases and split positions at the receiver can be easily obtained by transmitting the initial values and parameters of the 3D Lorenz chaotic system simplifying the transmission of the sideband information significantly with the key space of nearly 101337. In addition, the transmission of 42-Gb/s encrypted SCMA-OFDM signals have been experimentally demonstrated over a 2-km seven-core fiber, showing that the proposed scheme could improve the receiver sensitivity by 1.0 dB compared with the traditional SCMA-OFDM signals due to the great reduction in the PAPR. The bit error rate of the illegal optical network unit remains near 0.5, verifying the high security of the transmitted message.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
With the development of optical networks, the data rate requirements for users and enterprises are rising exponentially [1,2]. The traditional orthogonal multiple access (OMA) is required to maintain orthogonality in the time, frequency, and coding domains with limited access users. Comparatively, non-orthogonal multiple access (NOMA) offers a scheme to superimpose the data of multiple users to realize the connection of one time-frequency resource, which could further avoid the scheduling transmission, simplify the signaling process, and reduce the data delay. Among the current multitudinous NOMA technologies, sparse code multiple access (SCMA) [3] is the only one that has achieved multi-user multiplexing at the transmitter based on multi-dimensional modulation and sparse spread spectrum processing.
In the field of high-speed access technology, optical orthogonal frequency division multiplexing (OFDM) [4], which has shown great promise in spectrum utilization and anti-dispersion ability, has emerged as a dominant research and development area. For the massive user accesses, the application of SCMA-OFDM is particularly necessary. Therefore, this Letter focuses on the application of SCMA-OFDM in a passive optical network (PON). However, an instantaneous high peak to average power ratio (PAPR) may occur during the OFDM signal transmission even though the amplitudes of those superimposed multiple subcarrier signals are the same. The OFDM signals with high PAPRs suffer from either severe nonlinear distortions or out-of-band radiations once the saturation region of the high-power amplifiers is reached/exceeded. This Letter adopts the method of suppressing the PAPR by probabilistic class: selective mapping (SLM) and partial transmit sequence (PTS). Meanwhile, since the PON owns point-to-multipoint broadcast characteristics, the private and sensitive data could be easily attacked by trespassers. Multiple users share a resource at the same time, which also brings the risk of data leakage. Overall, the combination of the security issue and PAPR reduction needs to be resolved in the SCMA-OFDM PON.
To guarantee the confidentiality and authenticity in the communication network, increasingly more researchers have paid attention to physical layer encryption in recent years. The channel quality indicator-mapped spatially modulated SCMA is introduced, and a scheme that secures the confidential information exchange in the multi-hop aeronautical ad hoc networking is proposed [5]. To achieve the improvement in receiver sensitivity and security performance in OFDM-PON, probabilistic shaping by means of chaotic constant composition distribution matching is demonstrated in Ref. [6]. Most studies only focus on SCMA and OFDM, with a few on the security of SCMA-OFDM.
In this Letter, we propose a novel NOMA access method with a reduced PAPR and enhanced security enhancement at the physical layer in an SCMA-OFDM system based on the chaotic-SLM-PTS method. For the first time, we adopt public and private keys for the encryption in the SCMA-OFDM system and public keys to reduce the PAPR. The chaotic sequences generated by the sixth-order cellular neural network (CNN) chaotic system are used as the private key while the three-dimensional (3D) chaotic sequences generated by a Lorenz map are used as the public key.
Figure 1 shows the principle of the proposed SCMA-OFDM system with a reduced PAPR using chaotic-SLM-PTS algorithms. The original SCMA-OFDM signal is multiplied by U phase sequences to generate U candidate SCMA-OFDM signals X. At the transmitter, a pseudo-random binary sequence (PRBS) is used as the input data. After the serial-to-parallel (S/P) converter, the input data are classified into six signals for six users. Then, the six signals are encrypted with six chaotic sequences, respectively. The dynamic model of hyper chaotic system of sixth-order CNN is depicted as follows [7]:
We set the initial values as ${x_1} = 0.1,\textrm{ }{x_2} = 0.01,\textrm{ }{x_3} = 0.015,\textrm{ }{x_4} = 0.001,\textrm{ }{x_5} = 0.02,\textrm{ }{x_6} = 0.2$. The Runge–Kutta method is specified as $h = 0.001$, $\{ {\dot{x}_1},\textrm{ }{\dot{x}_2},\textrm{ }{\dot{x}_3},\textrm{ }{\dot{x}_4},\textrm{ }{\dot{x}_5},\textrm{ }{\dot{x}_6}\}$ are digitalized by Eq. (4), $\bmod ({\cdot} )$ stands for modulo operation, and $floor({\cdot} )$ returns the nearest integer rounded to zero. We extract the 15th digit of the six chaotic sequences. If the value is replaced by another one, the encryption performance is similar. Then we take the remainder of 2, and finally round the remainder in the direction of zero to obtain six masking vectors consisting of 0 and 1. The six masking vectors ${D_{{x_1}}},\textrm{ }{D_{{x_2}}},\textrm{ }{D_{{x_3}}},\textrm{ }{D_{{x_4}}},\textrm{ }{D_{{x_5}}}\textrm{ and }{D_{{x_6}}}$ are to encrypt the original bits of the six users.
As shown in Fig. 2, ${D_{{x_1},i \times 2 + 1}},{D_{{x_1},i \times 2 + 2}}(i = 0,1,2 \cdots )$ represents two adjacent bits in the scrambled sequence. Here, ${O_{{x_1},i \times 2 + 1}},{O_{{x_1},i \times 2 + 2}}$ represents the original bits without digitization, while ${T_{{x_1},i \times 2 + 1}},{T_{{x_1},i \times 2 + 2}}$ represents the encrypted bits. Figure 3 illustrates the bit operation. For example, when ${D_{{x_1},i \times 2 + 1}},{D_{{x_1},i \times 2 + 2}} = \{ 1, 0\}$, ${O_{{x_1},i \times 2 + 1}},{O_{{x_1},i \times 2 + 2}} = \{ 0, 1\}$, the rule 3 is adopted with the encrypted bits are $\{{0,0} \}$. The operation process can be expressed as follows: $0 \oplus \tilde{1} = 0 \oplus 0 = 0, \textrm{ }1 \oplus \tilde{0} = 1 \oplus 1 = 0$.
After the private key encryption, SCMA encoding is performed. The bits are mapped into multi-dimensional codewords in the complex domain. Then, the codewords of different users are superimposed on the same resource. A codebook with six data layers is shown in Fig. 4, where there are four multidimensional complex codewords in the codebook. As shown in the figure, the constellation of four subcarriers is a non-uniform hexagon, with dense inner constellation points and greater distance between outer constellation points. As depicted in Fig. 5, the symbols from layer 1, layer 3, and layer 5 are superimposed on OFDM subcarrier 1. Six users share four resources, resulting in an overloading factor of 150%.
The PAPR of each OFDM symbol can be defined as
The CCDFs of the OFDM-SCMA signals with different values of U are shown in Fig. 6(a). The signals with the smallest PAPR are selected for transmission, and the phase is controlled by ${S_x} \in \{ 1,2,3,4\}$ for encryption. To lower the computational complexity, the phase factor is $\theta \in [{1, - 1,j, - j} ]$. The numbers in ${S_x}$ correspond to the phase factor $\theta$ in turn. For example, “3” corresponds to “$j$”. Figure 6(b) illustrates the CCDF curves with different numbers of sub-blocks V in the case of chaotic PTS. The position of the random split can be controlled by ${S_y} \in \{ 1,2,3,4,5,6,7,8\}$ while the phase factor ${S_z} \in \{ 1,2\}$ corresponds to $\varphi \in [{1, - 1} ]$. It would be suitable to set U = 32 and V = 8 for the simulation.
Fig. 6. CCDF curves of the OFDM-SCMA signals (a) with and without chaotic SLM and (b) with and without the chaotic PTS.
The CCDF of the proposed chaotic-SLM-PTS scheme has been shown in Fig. 7. The application of the chaotic-SLM-PTS enables nearly 1 dB improvement in the PAPR compared with only the chaotic SLM as well as the chaotic PTS.
The experimental setup of the encrypted SCMA-OFDM signals transmission is shown in Fig. 8, where the regular optical network unit (ONU) and the illegal ONU are discussed. In such a PON, the PAPR can be limited greatly. Thirty-two SCMA blocks are used in the optical line terminal (OLT), and each of them corresponds to four OFDM subcarriers for six users. The size of the (inverse fast Fourier transform) IFFT is 512. A cyclic prefix (CP) of 1/4 length IFFT size is added onto each OFDM symbol. After the private key encryption and the parallel-to-serial (P/S) converter, the electrical signals are first processed by an arbitrary waveform generator (AWG, TekAWG70002A) with 10 GSa/s for digital-to-analog conversion (DAC). Then the amplified signals are loaded onto the 1550-nm light wave by Mach–Zehnder modulator (MZM). Here, the SCMA-OFDM optical signals are allocated to seven channels, which are then coupled into a 2-km-long seven-core optical fiber by a fan-in device. The fiber has good isolation performance, where the best isolation can reach 62.3 dB and the worst isolation can reach 34.9 dB, and the average core insertion loss is approximately 1.5 dB. At the ONU, the output optical signals are collected by a photodiode (PD) and analyzed by a mixed signal oscilloscope (MSO, TekMSO73304DX) with a sampling rate of 50 GSa/s. Finally, the received signals need to be recovered with further analyses performed offline by digital signal processing (DSP) in MATLAB: S/P conversion, remove CP, fast Fourier transform (FFT), PTS phase recovery, SLM phase recovery, SCMA decoder, and bit decryption. After that, we can get the original signals. The number of subcarriers of the OFDM signals is 128, the information entropy of quadrature phase shift keying (QPSK) is 2 bits/symbol. The total bit rate is the subcarrier number × 2 (bits/symbol) × AWG sampling rate × number of cores × overloading factor / (IFFT size + CP size) = 128 × 2 × 10 × 7 × 1.5 / (512 + 128) = 42 Gb/s. The bandwidth of the SCMA-OFDM signals is 10 × 128/512 = 2.5 GHz.
Fig. 8. Proof-of-concept experimental setup of the encrypted SCMA-OFDM PON. DSP, digital signal processor; AWG, arbitrary waveform generator; EA, electrical amplifier; MZM, Mach–Zehnder modulator; EDFA, erbium-doped fiber amplifier; OC, optical coupler; VOA, variable optical attenuator; PD, photodiode; MSO, mixed signal oscilloscope.
As illustrated in Fig. 9(a), the bit error rates (BERs) of the seven cores decrease together with the increase of the received optical power (ROP). Additionally, at the BER of 10−3, the performance gap between the best core and the worst one is only 0.8 dB, verifying the good stability and isolation of the used fiber.
Fig. 9. (a) Bit error rate (BER) performance of encrypted SCMA-OFDM signals for seven-core fiber. (b) BERs of the SCMA-OFDM signals with and without encryption.
For analyzing the superiority of the proposed scheme, we mainly investigate the transmitted signals in the fourth core. The BER performances of the traditional SCMA-OFDM signals and encrypted ones in core-4 are shown in Fig. 9(b). Our scheme is shown to improve the receiver sensitivity by 1.0 dB compared with the traditional SCMA-OFDM signals because the PAPR is reduced significantly. The BER of the illegal ONU that lacks the correct keys remains around 0.5. Even though the public keys are stolen, the private keys are still preserved. The illustration is the constellation diagram of the superposition of four carriers encrypted at the receiver when the ROP is −16 dBm.
Figure 10 depicts BER curves of six users in core-3. It is observed that the six curves show almost the same trend and values with the increase of ROP, illustrating that the transmission performances of six users are practically consistent. The power disparity between the best and the worst users is only 0.3 dB at the BER of 10−3.
Finally, we study the key space with the ROP of −15 dB corresponded to the core-4. Figures 11(a) and 11(b) show the BER with a tiny change in initial value for the sixth-order CNN and Fig. 11(b) is for 3D Lorenz. From Fig. 11(a), it is found that if the initial value of $\{ {x_1},\textrm{ }{x_2},\textrm{ }{x_3},\textrm{ }{x_4},\textrm{ }{x_5},\textrm{ }{x_6}\}$ changes by 10−19, the BER remains unchanged with a correctly decrypted signal. Once $\{ {x_1},\textrm{ }{x_2},\textrm{ }{x_3},\textrm{ }{x_4}\}$ changes by 10−18, 10−17, 10−16, and 10−16, respectively, the BER changes drastically to nearly 0.5. It is worth noting that the BERs are 0.0201 and 0.0109 for ${x_5}$ and ${x_6}$, respectively, when they change by 10−16. In this case, the BER exceeds the FEC limit, so the encryption is still valid. There are 13 parameters for each chaotic sequence including 5${a_{jk}}$, 6${S_{jk}}$, 1${i_j}$, and an initial value x. Six chaotic sequences obtain 78 parameters. As a result, the key space for the sixth-order CNN key is (1016)78 = 101248. The key parameters of the 3D Lorenz system is $(\alpha ,\textrm{ }\gamma ,\textrm{ }\beta ,\textrm{ }x,\textrm{ }y,\textrm{ }z)$. Similarly, it can be estimated that the key space of the 3D Lorenz is ${({10^{15}})^5} \times {10^{14}} = {10^{89}}$. Totally, the key space should be at least ${10^{1248}} \times {10^{89}} = {10^{1337}}$.
We have experimentally demonstrated 42-Gb/s transmission of the encrypted SCMA-OFDM signals over a 2-km seven-core fiber. The proposed encryption method not only reduces the PAPR effectively, but improves the security of the user information with the adoption of the public and private keys. The phase information and the random split position are controlled by the 3D Lorenz chaotic system, avoiding large side information transmission. By implementing the sixth-order CNN and 3D Lorenz, the key space can reach up to 101337. Additionally, the application of the chaotic-SLM-PTS can achieve a 4.3-dB reduction in the PAPR, which is much smaller than the traditional SCMA-OFDM signals when the CCDF is 0.005. The experimental results further verify that our scheme can improve the receiver sensitivity by nearly 1.0 dB at the BER of 10−3.
Funding
National Key Research and Development Program of China (2018YFB1800905); National Natural Science Foundation of China (61720106015, 61727817, 61835005, 61875248, 61935005, 61935011, 61975084, 62035018, 62171227, U2001601); The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (22KJB510031); Jiangsu team of innovation and entrepreneurship; 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.
REFERENCES
1. F. Wang, H. Yao, Q. Zhang, J. Wang, R. Gao, D. Guo, and M. Guizani, IEEE Trans. Netw. Service Manag. 19, 991 (2022). [CrossRef]
2. F. Wang, H. Yao, J. Wang, T. Mai, X. Xin, and M. Guizani, “Hybrid Optical-Electrical Data Center Networking: Challenges and Solutions for Bandwidth Resource Optimization,” IEEE Commun. Mag. [CrossRef]
3. K. Deka, A. Thomas, and S. Sharma, IEEE Trans. Commun. 69, 5043 (2021). [CrossRef]
4. F. Li, J. Yu, Y. Fang, Z. Dong, X. Li, and L. Chen, Opt. Express 22, 8742 (2014). [CrossRef]
5. Y. Liu, Y. Yang, L. Yang, and L. Hanzo, IEEE Trans. Veh. Technol. 70, 2436 (2021). [CrossRef]
6. J. Ren, B. Liu, D. Zhao, S. Han, S. Chen, Y. Mao, Y. Wu, X. Song, J. Zhao, X. Liu, and X. Xin, Opt. Express 28, 39266 (2020). [CrossRef]
7. X. Wang, B. Xu, and H. Zhang, Commun. Nonlinear Sci. Numer. Simul. 15, 99 (2010). [CrossRef]
