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Abstract
Sparse code multiple access (SCMA), a new code-domain non-orthogonal technology in the fifth-generation mobile communication (5G), can be modulated by orthogonal frequency division multiplexing (OFDM) to improve the link quality of a single user. In this paper, a high-security SCMA-OFDM multi-core fiber transmission system based on a regular hexagonal chaotic codebook is proposed for next-generation passive optical network (PON). The whole encryption process consists of a regular hexagon chaotic codebook design and frequency domain block scrambling. In designing the regular hexagon chaotic codebook, the optimization of constellation points on orthogonal resources are considered as the starting point. Firstly, the chaos factor generated by the four-dimensional Rossler chaos model is deployed to disturb the mother constellation, and then the corresponding chaotic book is formed by rotating the mother constellation and multiplying the sparse matrix. The designed codebook logically avoids the degradation of transmission performance caused by the rough scrambling of codebook constellation, to find a balance between codebook disturbance and bit error rate (BER). The security and reliability of the transmission system have been verified by performing 42 Gb/s encrypted SCMA-OFDM data transmission experiments in a 2km multi-core fiber. The key space of the encryption scheme can reach 10178, which effectively ensures the security of the transmission system. Furthermore, the performance of the transmission system with a regular hexagon chaotic codebook is improved by 2.5 dB compared with the traditional codebook when the BER is 1 × 10−3. Moreover, the SCMA-OFDM-based transmission architecture and the detection effects of different multi-user detection algorithms in the SCMA-OFDM multi-core fiber transmission system are also studied.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
At present, due to the continuous development and improvement of networking technologies, the core network can provide various broadband services. The development of access networks is relatively lagging, unable to carry large capacity and fast data communication between users and core network. Therefore, the passive optical network (PON) has become a popular access network due to its advantages of low capital costs, low transmission energy consumption, simple network structure, and simple management and maintenance. With the rapid development of the internet of things, mobile Internet, and other new-generation information technologies, the craze for higher spectral efficiency, lower latency, and large-scale connectivity by the end-user is exponentially increasing. Introducing new technologies for the next generation of optical access networks is the need of the hour. Space division multiplexing (SDM) allows signals to be multiplexed in the spatial dimension, thereby increasing system capacity and the number of users. Compared with the inter-mode dispersion and mode coupling of mode multiplexing, SDM based on multi-core fiber is more suitable for application in the access network. Using a weakly coupled multi-core fiber with low inter-core crosstalk, transmission performance can be even comparable to that of using multiple single-mode fibers at the same time. To meet the requirements of large-scale access to next-generation access networks and further tap the potential of multi-core fiber in the access systems, the sparse code multiple access orthogonal frequency division multiplexing (SCMA-OFDM) multi-core fiber transmission system is studied here in this article.
SCMA is a promising non-orthogonal multiple access technology proposed by Huawei [1]. It combines multi-dimensional modulation and sparse spreading techniques to map bit-level data streams directly to a complex domain multi-dimensional codewords in a pre-defined codebook, thus achieving additional shaping gain as well as coding gain. Owing to the non-orthogonal sparse coding overlay scheme, SCMA can support more users under the same number of time-frequency resources, to meet the demand of 5G for massive access. Most of the research in the SCMA is focused on the codebook design on the transmitter side [2] and the multi-user detection algorithm on the receiver side [3,4]. Recently, it has been applied to optical communications. A series of SCMA transmission systems with superior performances [5,6] and multi-user detection algorithms [7] have been proposed and implemented. These results often apply to large-scale access scenarios. In such a large optical access network, hijacking of the data is inevitable, and its security should be worth considering. Digital chaos encryption is used by researchers for secure communications because of its flexibility and stability. Jianxin Ren et al. proposed a probabilistic shaping orthogonal frequency division multiplexing passive optical network based on chaotic constant composition distribution matching by using a four-dimensional hyperchaotic Lv system [8]. Similarly, Mingye Li et al. proposed a novel five-dimensional data-iteration-based encryption model based on a multi-wavelength optical frequency division multiplexing passive optical network (OFDM-PON) by using the hyperchaotic system [9]. In addition, some scholars have also applied it to SCMA encryption, e.g. Ke Lai et al. proposed a novel physical layer transmission scheme with code-word level interleaving at the transmitter by introducing the Tent map [10].
In this paper, we propose a high-security SCMA-OFDM multi-core fiber transmission system based on a regular hexagonal chaotic codebook by using PON transmission architecture and introducing Logistic chaos models. In chaotic encryption of the codebook, considering that any small perturbation to the mapped constellation points can have a significant impact on the bit error rate (BER) [11], we attempt to find a breakthrough point from the design process of codebook. In the multi-stage optimization process, the chaotic model can be used to rotate the special mother constellations randomly in a certain range when the structure of the codebook is determined. Experimental results show that this method can improve transmission security without degrading transmission performance. Then, we further enhance the security of physical layer data transmission by implementing secondary encryption of the frequency domain signal after chaotic coding through a chunking cycle. Experiments show that our encrypted transmission scheme brings a gain of around 2.5 dB to the system compared with the classical Huawei codebook [12] at a BER of $1 \times {10^{ - 3}}$. The scheme also achieves the expected encryption effect very well and has high key sensitivity.
2. Principles
2.1 Encrypted SCMA-OFDM Transmission Architecture
The detailed architecture of the proposed encrypted SCMA-OFDM transmission is depicted in Fig. 1, the whole structure includes the SCMA-OFDM-PON transmission module and encryption module. In this module, it is considered that an SCMA-OFDM system consists of Z OFDM subcarriers. In the SCMA block, J users share K subcarriers. Therefore, $Z$ subcarriers can be evenly divided into ${N_B} = Z/K$ SCMA blocks of size $K$. A single SCMA encoder is discussed in detail since each SCMA block is encoded using the same codebook. Here the chaotic codebooks generated by the encryption module are deployed. An SCMA encoder can be regarded as a map from ${\log _2}^M$ bits to a $K$-dimensional complex codebook of size $M$. There are ${d_v}({d_v} < K)$ non-zeros elements in a codeword. All J users superimpose the transmitted codewords on $K$ subcarriers to achieve overload communication and the overloading factor of the code is defined as $\lambda \textrm{ = }J/K$. The encrypted SCMA signal is then generated by cyclically scrambling the synthesis matrix of the ${N_B}$SCMA blocks using the frequency domain and symbol perturbation factors generated by the encryption module. As complex signals cannot be transmitted directly in short-range intensity modulation/direct detection (IM/DD) systems, we need to use special operations to convert the complex signal into a real signal. A common approach is the Discrete MultiTone (DMT) modulation used in the literature [13]. It performs Hermite transform on the frequency domain signal before the Inverse Fast Fourier Transform (IFFT), such that the transformed time domain symbols are all real numbers. Instead of DMT modulation, we perform digital up-conversion after OFDM modulation. This step includes interpolation, filtering, and mixing. First, the signal is interpolated 4 times, and the spectrum is extended 4 times accordingly. Then, the interpolated signal is filtered. At last, the filtered signal is mixed with the high-frequency signal to complete up-conversion. The entire process is implemented by digital signal processing (DSP), which effectively avoids additional devices and noise interference. At the receiving end, it is necessary to perform digital down conversion before OFDM demodulation and transform the real signal into a complex signal. The process of digital down-conversion is mixing, filtering, and extracting. In the SCMA decoding operation of the demodulated signal, we use the common message passing algorithm (MPA). The essence of MPA is the iterative update of external messages between resource nodes and variable nodes. Its working principle is shown in Fig. 2.
Compared with Maximum A Posteriori (MAP) [1], the algorithm does not require exhaustive detection of codebook combinations for all users. It uses the sparsity of the SCMA codebook to select local probability updates on each sub-channel according to the criterion of conditional probability. Although the algorithm can reduce the computational complexity from $O({{M^J}} )$ to $O({{M^{{d_f}}}} )$ while approaching the MAP decoding effect, this complexity is still the main bottleneck of the system. For this reason, optimization algorithms such as SD-MPA [3] and Log-MPA [4] have been proposed one after another. All these algorithms have shown good detection results in the wireless domain, but they are not effectively deployed in optical communications. Several of these typical optimization algorithms will be experimentally verified in Section 3, which helps us to better discover the performance differences of different detection algorithms in optical communications.
2.2 High-security transmission scheme based on regular hexagon chaotic codebook
The encryption module is divided into codebook encryption and block scrambling encryption. We introduce the Rossler four-dimensional hyperchaotic model and one-dimensional Logistic chaotic model in the encryption module. The Rossler chaotic model is a hyperchaotic system defined by a fourth-order differential equation. Its function is defined as follows:
Fig. 3. Chaotic model (a) phase diagram of Rossler chaotic map (b) bifurcation diagram of a Logistic map
Firstly, the codebook is chaotically encrypted, and to reduce the impact of chaotic encryption on the transmission performance, the detailed design process of the SCMA codebook is considered here [2]. The overall structure of the SCMA codebook can be represented by a factor graph matrix defined as $F = ({{f_1},{f_2}, \cdots ,{f_J}} )$. Its optimization steps include mapping matrix, constellation points, multi-dimensional mother constellation, and constellation function operators. The mapping matrix ${V_j}$ determines the set of resources occupied by the layer j. Its non-zero rows correspond to the index of the non-zero elements of the binary indicator vector ${f_j}$. Each useŕs narrowband data is converted to spread spectrum by multiplying the mapping matrix. The mapping matrix depends on the structure of the SCMA codebook. And a good codebook can be obtained if the SCMA codebook structure is optimized by combining multi-dimensional constellation and constellation function operations. Due to the sparsity of the SCMA codebook, the optimization of constellation points and multi-dimensional mother constellation can follow the principle of maximizing the minimum Euclidean distance (MED). The most common method is to maximize the MED between the mother constellation [14] or to maximize the MED between the constellation points superimposed on the orthogonal resources [15]. Here a structured encryption scheme for resource-level constellation is designed to maximize the MED of constellation points based on lattice theory. Phase rotation is used as the constellation function operator during this process. The constellation pool of each multiplexed resource is superimposed by ${d_f}$ complex constellation sets ${S_u}(u = 0,1, \cdots ,{d_f})$ corresponding to the user. The cardinality of ${S_u}$ is M. Among all elements, ${S_0}$ are reals and other ${S_u} = {e^{j{\theta _u}}}{S_0}$. ${S_0}$ is expressed as:
For the selection of the rotation parameters ${\theta _u}$, we divide them into ${\theta _u}^{\prime}$ and $\Delta {\theta _u}$, so that an approximate average plane angle (${180^\circ }$) angle can be achieved. ${\theta _u}^{\prime}$ is the rotation angle of the mean plane angle, while $\Delta {\theta _u}$ is the randomly generated rotation angle based on the chaotic model. Considering that too large $\Delta {\theta _u}$ will cause the MED of the constellation pool on the multiplexed resource to become sharply smaller, the range of $\Delta {\theta _u}$ is controlled to be $[{0{\kern 1pt} {\kern 1pt} ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {{10}^\circ }} ]$. In addition, to further enhance the difficulty of decoding the codebook, we also consider the rotation direction of $\Delta {\theta _u}$. This design can achieve secure transmission of information in the physical layer without degrading transmission performance compared to [16]. The constellation pool of chaotic codebook is designed in the following way:
λ Use ${S_0}$ as a basic constellation set
λ Obtain the rotation angle of the average plane angle $\{{{\theta_1},{\theta_2}, \cdots ,{\theta_{{d_f} - 1}}} \}$:
λ Generate four groups of sequences $\{{{x_n},{y_n},{z_n},{w_n}} \}$ by Rossler chaotic model. Then extract the first two groups to generate chaotic factors X and $Y$. The specific operations are as follows:
λ Parity judgment for chaos factor $Y$. The directional key is generated by the following mapping relationship:
λ Using the chaos factor $X$ as the rotation key, the following operation is performed to obtain the rotation parameter ${\theta _u}$:
λ Calculate $\{{{S_1},{S_2}, \cdots ,{S_{{d_f} - 1}}} \}$ based on ${S_u} = {e^{j{\theta _u}}}{S_0}(u = 1,2, \cdots ,{d_f} - 1)$
In sum, the design of the constellation pool for the chaotic codebook is summarized as follows:
To facilitate performance comparison with the Huawei codebook, we use the factor graph matrix of the codebook (as shown in Fig. 4(a)), where ${S_u}$ is assigned to non-zero locations in a Latin order, $M = 4,J = 6,K = 4,{d_v} = 2,{d_f} = 3$. Latin order requires that there are no identical vectors in the row and column directions of the codebook matrix. The use of Latin order enables the receiver to distinguish the individual user messages that collide on each resource block with a lower BER. Every user selects the set of constellations on the corresponding layer of the constellation pool as his constellation points according to the factor graph. Its mapping relationship is shown in Fig. 4(b). The whole process of forming a regular hexagon chaotic codebook can be vividly shown in Fig. 5.
Next, we perform the second block scrambling encryption on the SCMA encoded matrix [17]. The rows of the matrix represent the subcarrier frequencies and the column represents the SCMA symbols. Here, we define eight matrix block formats: $16 \times 6$, $4 \times 15$, $8 \times 15$, $8 \times 30$, $16 \times 30$, $4 \times 30$, $8 \times 6$, $16 \times 15$, which correspond to eight index values from 0 to 7 respectively. The whole block encryption is divided into the following two steps:
- (1) The sequences $({{z_u},{w_u}} )$ generated by the Rossler chaotic model are used for the following calculations to produce the index value T and divide the data into several matrices with the corresponding size of $A \times B$.
- (2) The one-dimensional Logistic chaotic sequence ${q_n}$ is calculated as follows, and the chaotic parameters r and c are obtained to scramble the rows and columns in turn. The corresponding block scrambling flow chart is shown in Fig. 6. Firstly, r rows are cyclically disrupted upwards, then c columns are cyclically disrupted to the left. The receiver can achieve decryption by reverse operation.
The entire chaotic encryption process does not involve too much interference at the constellation points, and the receiver can reverse the encrypted information with the known key to achieving the correct recovery of the message.
3. Experiment setup and results
In order to verify the high-security SCMA-OFDM transmission system, the IM/DD system is deployed as shown in Fig. 7. In the experiment, a continuous wave laser with a wavelength∼1550nm was used as the light source, and the power was set to 14.5 dBm. At the OLT transmitter, the encrypted SCMA-OFDM signal is generated by offline DSP. Then an arbitrary waveform generator (AWG, TekAWG70002A) with a sampling rate of 10 GSa/s is used for digital-to-analog conversion of the encrypted signal. An electrical signal through the electric amplifier is injected into the MZM to complete the IM. Before the optical signal is coupled into the seven-core fiber through the 1:8 splitter and fan-in device, it needs to be further amplified by the commercial erbium-doped fiber amplifier. At the receiving end, the optical network unit (ONU) is divided into legal access and illegal access. In the case of legal ONU, the received optical power is adjusted by using a variable optical attenuator and converting the received optical signal into an electrical signal through a photodiode. Then, the obtained electrical signal is passed through a mixed-signal oscilloscope (MSO, TexMSO73304DX) with a sampling rate of 50 GS/s. After analog-to-digital conversion, the received data is decrypted by using the same key as the transmitter. Users with illegal access will not be able to get the correct data through offline DSP because they do not know the key.
Fig. 7. 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; PS: power splitter; VOA: variable optical attenuator; PD: photodiode; MSO: mixed-signal oscilloscope)
Firstly, an experimental study has been conducted of different SCMA-OFDM transmission architectures. The transmission scheme with up and down-conversion, and the scheme based on the Hermitian conjugate structure are employed for data transmission on core 3 without encryption, the data rate transmission rate is kept at 42 Gb/s. The experimental result of Fig. 8 shows that compared with the Hermitian conjugate transmission scheme, the performance of the transmission scheme with up and down-conversion is improved by about 1 dB at the BER∼$1 \times {10^{ - 3}}$. There is no big difference between the two transmission architectures. The only obvious difference is that the transmission scheme with up and down-conversion is interpolated in the time domain and the transmission scheme based on the Hermitian conjugate structure is interpolated in the frequency domain.
Secondly, we experimentally measure the BER performance of the encrypted SCMA-OFDM signal in different cores, the result is shown in Fig. 9. With the increase of received optical power, the BER of different cores tends to decrease. Moreover, the performance difference between the best core and the worst core is about 1 dB. Compared with legal users, Fig. 10 shows that illegal users are unable to obtain any useful information from encrypted signals because of the lack of corresponding keys and the BER remains around 0.5 at various receiving optical power. It is worth mentioning that since both legitimate users and illegal users will receive similar constellations, the receiving end cannot determine from the constellation diagrams whether the data has been encrypted or not. Hence the encryption process is hidden as well.
Thirdly, the key space of the proposed encryption scheme is calculated conservatively, which can be divided into three parts: the control parameters, the initial values, and the iteration steps of $Rossler$ and $Logistic$ chaos models. According to the experimental result in Fig. 11, we estimate that the key space of our encrypted transmission scheme is ${({1 \times {{10}^{17}}} )^5} \times {({1 \times {{10}^{16}}} )^3} \times {10^{15}} \times {10^{14}} \times {10^{13}} \times {10^3} \times {10^0} = {10^{178}}$. This order of magnitude is almost impossible to break through violence, so it can provide a good level of security for data transmission at the physical layer.
Finally, the transmission performance of the regular hexagonal chaotic codebook is tested. Figure 12 describes the BER performance of data transmission in core 7 using Huawei codebook and chaos codebook respectively. It is found that when the BER is $1 \times {10^{ - 3}}$, the system using a regular hexagonal chaotic codebook can improve nearly by 2.5 dB compared with the Huawei codebook. All this is attributed to the larger minimum Euclidean distance (MED) of the chaotic codebook. When passing through the fiber channel, it can reduce the influence of adjacent constellation points and then can prevent the interference of noise. In addition, we also experimentally test the detection effects of different multi-user detection algorithms. Take the experimental result of core 1 as an example. Figure 13 shows that the MPA algorithm is still relatively superior in optical communications, which is similar to the result in the wireless field. However, the other two algorithms Log-MPA and SD-MPA reduce the computational complexity at the expense of transmission reliability.
Fig. 12. (I) BER curves of Huawei codebook and chaos codebook after 2km MCF transmission. (II) Resource constellations at the transmitter using Huawei codebook(a); Resource constellations using Huawei codebook when the received optical power is −7dBm(b) and −17dBm(c) respectively; Resource constellations at the transmitter using chaos codebook (d); Resource constellations using chaos codebook when the received optical power is −7dBm(e) and −17dBm(f) respectively;
4. Conclusion
This paper proposes a high-security SCMA-OFDM multi-core fiber transmission system based on a regular hexagonal chaotic codebook. The transmission scheme includes a chaotic codebook and the domain block scrambling in the frequency domain, which can effectively improve the security of the system and prevent data from being broken by violence. This scheme is experimentally proven to be able to achieve 42 Gb/s data transmission in a seven-core fiber of 2 km. At the same time, a regular hexagonal chaotic codebook can bring a significant improvement to the transmission performance of the system. Therefore, this encrypted transmission scheme has a bright prospect for future applications in non-orthogonal optical access networks. In addition, the universality of different multi-user detection algorithms is experimentally verified. SD-MPA and Log-MPA can also detect the information of each user in optical communications. Although their computational complexity is reduced compared with MPA algorithm, their detection effect is still not as good as MPA algorithm under the same BER. This is no different from wireless communication.
Funding
National Key Research and Development Program of China (2018YFB1800901); 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.
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