1. Introduction

In the past 40 years, mobile communication has experienced a great leap forward development from 1G to 5G. In particular, 5G network realizes massive device access, ultra-low delay and higher transmission rate. Non orthogonal multiple access (NOMA) is one of the key technologies of 5G, which superimposes the information of different users non orthogonally and decodes it at the receiver (multi-user detection). Sparse code division multiple access (SCMA) technology, which was put forward by Huawei Co., Ltd [1], has attracted extensive attention in the industry. Its biggest feature is the combination of modulation and spread spectrum, which can realize “overload” under the condition of limited resources, and the number of users that can be supported is much larger than the number of orthogonal channels.

Researchers have done a lot of work on SCMA in the field of mobile communication, mainly focusing on codebook design and multi-user detection [2–5]. In recent years, some researchers have applied SCMA in the field of optical communication. For example, a novel non orthogonal optical multicarrier access system based on filter bank and SCMA is proposed in Ref.6. In this paper, completed the experiment of a 60 km single-mode optical fiber link multicarrier SCMA system based on 73.68 GB / s filter bank, which verified the feasibility of this method. Unfortunately, optical coherent transceivers are expensive and are not the first choice for cost sensitive access networks. The reference [7] proposed a SCMA scheme for the next generation passive optical networks which is based on intensity modulation and direct detection. The experiments verify the feasibility of SCMA-PON, in which the multidimensional codewords of every six users are superimposed on four OFDM subcarriers, and the overload rate reaches 150%. In addition, space division multiplexing technology based on multi-core fiber (MCF) and few-mode fiber (FMF) has proved to have great advantages such as compactness and spatial parallelism. The reference [8] proposed 4×4 multiple input multiple output (MIMO) 7-core fiber wireless communication system which is based on sparse code multiple access (SCMA) and OFDM / OQAM technology. 11.04 Gb/s 4 × 4 MIMO SCMA-OFDM/OQAM signals are successfully transmitted on the uplink and downlink of 20 km 7-core optical fiber and 0.4 m air distance.

In this paper, we study the feasibility of using SCMA coding in multi-core optical fiber transmission system. The scheme we proposed in this paper uses the core of multi-core fiber as the orthogonal resource block of SCMA, and verifying its transmission performance through a transmission experiment on 2 km 7-core fiber. In addition, the traditional SCMA-OFDM system has a high complexity when using message passing algorithm (MPA) in multi-user detection. We propose a novel SCMA-OFDM transmission system based on multi-core fiber to reduce the detection complexity by increasing the dimension. The proposed method can be used in multi-core non orthogonal optical access network system to serve more users at the same time.

2. Principle

2.1 Optical SCMA coding transmission system based on multi-core fiber

SCMA, as a new NOMA scheme, directly maps the bit stream data into multi-dimensional codewords. It makes modulation and spread spectrum complete in one step, which brings greater freedom to the user's codebook design and greatly improves the spectral efficiency (SE). SCMA signal is formed by linear superposition of codewords from J users. And each codeword is mapped from ${\log _2}|M |$ bits, where M represents the number of codewords in the codebook. The mathematical definition of SCMA coding is ${\mathrm{\mathbb{B}}^{{{\log }_2}(M)}} \to \textrm{X}$, where X represents K-dimensional complex codewords and K represents the number of orthogonal resources.

Figure 1 shows the principle of the proposed optical SCMA coding transmission system with 6 users and 4 cores. At the transmitter, the principle of SCMA encoder is shown in Fig. 2. 6 users have different exclusive codebooks. Every two bits correspond to the 4-dimensional sparse complex codewords in the codebook and correspond to 4 constellation points. The codewords (namely X₁, X₂, X_3, X_4, X_5, X₆) from six users add each other to obtain the transmitted codeword Y₁. The constellation of SCMA signal on each core is shown in the illustration of Fig. 2. The SCMA encoded signal can be expressed as:

 

Fig. 1. The principle of the proposed SCMA transmission system based on 4 modes fiber.

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Fig. 2. The principle of the SCMA encoding.

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The codeword Y₁ coded by SCMA encoder constitutes a discrete complex signal ${Y_K}$ (K = 1,2,3,4, represent the occupied 4 cores respectively). ${Y_K}$ cannot be transmitted directly in intensity modulation with direct detection (IM/DD) system. In order to enable it to be transmitted in IM/DD system, this paper converts the complex signal into real signal by digital up-conversion processing. The real signal can be restored by digital down conversion at the receiver. The whole process is processed in the electrical field without additional devices, which is easy to realize. Digital up conversion technology is transmitted through digital modulation of baseband signal to medium and high frequency, which is the core technology in radio communication and can also be applied in optical transmission system [9]. The principle of digital up conversion and down conversion is also shown in the blue box of Fig. 1. The steps of digital up conversion include interpolation, digital filtering and up conversion. Suppose the frequency of the signal ${Y_K}$ is f, the sampling frequency is f_s, the frequency of the mixed signal is F, the sampling frequency is F_s and $f < F,\textrm{ }{f_s} < {F_s}$. The sampling satisfies the Nyquist sampling theorem.

Firstly, ${Y_K}$ is interpolated by m times. 0 is inserted at the interval, and the interpolated signal is ${Y^{\prime}_K}$. The interpolated spectrum is the m-times periodic extension of the original spectrum, $m\ast {f_s} = {F_s}$. Then filter the interpolated signal ${Y^{\prime}_K}$. Since all the information of the spectrum has been included in the principal value interval of the spectrum, taking the principal value interval of the periodic continuation signal of ${Y^{\prime}_K}$ is equivalent to filtering ${Y^{\prime}_K}$. The signal after filtering is ${Y^{\prime\prime}_K}$. At this time, the frequency range of ${Y^{\prime\prime}_K}$ is 0-f_s and the sampling frequency is F_s. It can be seen that the function of interpolation filtering is to maintain the set SCMA signal frequency and adjust the sampling frequency of SCMA signal to mix with high-frequency signal. When mixing, you only need to multiply the filtered signal and the high-frequency signal and take the real part:

After the signal ${s_{DUC}}$ is transmitted through multi-core fiber channel, at the receiver, the received optical signal is converted into an electrical signal. Then the electrical signal needs to be restored to multi-dimensional constellation after digital down conversion. As shown in Fig. 1, the steps of digital down conversion are complex mixing, filtering and decimation. Due to the sparsity of SCMA codebook, message passing algorithm (MPA) is usually used for approximate optimal detection [10]. Fig. 3 shows the factor graph of the codebook in Fig. 2 and the flow chart of MPA algorithm. There are two kinds of nodes in the factor graph: user nodes (UNs) and core nodes (CNs). The working principle of MPA is to pass the probability called message along the edge between nodes, and iteratively update the possibility of the received SCMA codeword. For the message passing method between UNS and SNS, can refer to [10,11]. The first step of MPA is the initial calculation of conditional probability. The second step is transferring the probability of SCMA codeword from CNs to UNs. Relatively speaking, in the third step, the probability of SCMA codeword is transferred from UNs to CNs. Then the second and third steps are performed iteratively. After N times iterations, the correct binary data can be recovered by the maximum possible codeword.

 

Fig. 3. (a) Factor graph (b) MPA algorithm flow block.

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2.2 SCMA-OFDM transmission system based on multi-core fiber

SCMA encoding actually improves the use efficiency of orthogonal resource blocks. For optical communication systems, orthogonal resource blocks can be orthogonal frequency domain, mode, time domain and so on. Therefore, we consider the joint orthogonal frequency domain and fiber core domain to encode for further improving the transmission efficiency. For a SCMA system, reducing the complexity of MPA detection algorithm at the receiver has always been the focus of research. The complexity of MPA can be roughly expressed as:

In the formula, M represents the symbol modulation order, d_f represents the number of users superimposed on each resource block, K represents the number of resources, and N_iter represents the number of iterations. From this, we can see that the main ways to reduce the complexity of the algorithm are: reducing N_iter, M, and d_f. In a SCMA-OFDM transmission system on multi-core fiber, we can use different fiber cores to reduce d_f, which is the number of users superimposed in the frequency domain.

Figure 4 shows the principle of the proposed SCMA-OFDM transmission system based on multi-core fiber. In most SCMA-OFDM systems, orthogonal subcarriers are usually divided into N groups, and each group uses K subcarriers to transmit data of J users. Here, we use the codebook in section 2.1 to form three groups, which are corresponding to three fiber cores respectively. Each group has two-dimensional codewords after SCMA encoder by reorganizing the factor matrix. Specifically, the decomposition rule of factor matrix F is shown in Fig. 5

 

Fig. 4. The principle of the proposed SCMA-OFDM transmission system based on multi-core fiber.

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Fig. 5. (a) Factor matrix; (b)Factor graph; (c) Factor graph of recombination

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The row of the factor matrix represents the orthogonal resource block K, the column of the factor matrix represents the user J, and the element 1 in the matrix represents that the user is connected to the resource in the factor graph. Fig. 5 (a) represents the factor matrix of the factor graph in Fig. 5 (b). As can be seen from Fig. 5, part I is the superposition of codewords when K = 1, 2 and J = 1, 2, 3. Part II is the superposition of codewords when K= 3, 4 and J = 4, 5, 6. Part III is the codeword superposition of the rest, which forms resource blocks c₅ and c₆. Thus, a 4-dimensional codeword becomes three 2-dimensional codewords. MPA can still be used.

The three partially superimposed codewords are modulated simultaneously, and then sent to three different fiber cores for transmission. The process of OFDM modulation is shown in the dotted line at the transmitter in Fig. 4. Complex conjugation is taken for each codeword respectively in order to generate real data after IFFT and facilitate the modulation of IM/DD system. After complex conjugation, IFFT and cyclic prefix are added to complete OFDM modulation. N groups of data are sent to OFDM modulation module in sequence, converted into 3-channel electrical signals in parallel and series, and then converted into optical signals, which are sent to 3 cores of seven core optical fiber for transmission. After the optical signal converting into electrical signal at the receiver, it needs OFDM demodulation first. Then MPA detection was performed in the order of N groups. It is particularly noteworthy that during MPA detection, only two codewords of part I and part II need to be iterated to recover the bit data of all users, which greatly reduces the amount of data and complexity of iterative operation. But this will sacrifice some BER performance. When using I, II and III parts for message transmission, it will increase a certain amount of calculation, but it can traverse all nodes to improve the BER performance. We will name MPA1 and MPA2 in the above two methods. In the section 3.2, their performance will be verified experimentally.

3. Experimental setup and results

3.1 Experimental of SCMA transmission system based on 7 core fiber

Figure 6 shows the block diagram of SCMA transmission system based on seven-core fiber. In this experiment, a weakly coupled 7-core fiber is adopted and the cross-section image is depicted in Fig. 6(a). The core pitch and cladding diameter are set as 41.5 µm and 245 µm respectively to ensure the long-term reliability of transmission and reduce bending loss as much as possible [12]. The attenuation coefficient of the fiber used in this article is less than 0.3 dB/km at 1550 nm. And the average insertion loss of each fiber core is measured about 1.5 dB, crosstalk between adjacent cores is less than -50 dB. The schematic diagram of the fiber Fan-in device is shown in Fig. 6(b). The signals are multiplexed spatially through a Fan-in device consisting of seven thin cladding fibers wrapped by glass capillaries.

 

Fig. 6. Experimental setup (AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; VOA: variable optical attenuator; MCF: multicore fiber; PD: photodiode; MSO: mixed signal oscilloscope). (a) Cross-section of MCF, (b) schematic diagram of the 7-core fiber Fan-in device.

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In this experiment, a continuous wave laser (CW) with an optical power of 15 dBm is used as the light source, and the center of the light source is 1550 nm. The beam splitter is used to divide the light source into four channels. This paper uses the codebook which is proposed by Huawei [1] is used for SCMA encoding. The SCMA signal generates four digital signals through offline digital signal processing (DSP). Then the SCMA signals are uploaded to arbitrary signal generator (Tektronix, AWG70002A), with a sampling rate of 10 GSa/s. The generated 4-channel analog signal modulates the electrical signal to the 4-channel optical carrier through 4 Mach-Zehnder modulators (MZM). Then, the four optical signals are further amplified by commercial erbium-doped fiber amplifier (EDFA). Four optical signals are coupled into four random cores of 7-core optical fiber through fan-in device. After 2 km MCF transmission, the optical received power is adjusted by a variable optical attenuator (VOA) and detected by a photodiode (PD) with a band width of 40 GHz to convert the optical signal into an electrical signal. Then it is sampled by a mixed signal oscilloscope (Tektronix, MSO73304DX) with a sampling rate of 50 GS / s. The sampled SCMA signal is transmitted to the computer for offline DSP. Traditional MPA [10] is used for multi-user detection to recover the data. In the digital upconversion of this experiment, we use an interpolation of 4 times. We assume that the frequency of the high frequency carrier signal used for mixing is 10⁶ Hz. Digital downconversion uses the same parameters.

The total transmission bitrate of the system is: ${baud rate} \times {bit per symbol} \times {J / K} = {{30G} / s}$. Fig. 7(a) shows the BER performance of SCMA signal in back-to-back (BKB) transmission and 2 km MCF transmission. The dotted line in the Fig. 7(a) is the forward error correction (FEC) limit (BER is 3.8 × 10−3). It can be clearly seen that the FEC limit can be reached when the sensitivity of the receiver is −13 dBm and−10 dBm in the case of back-to-back and 2 km MCF respectively. The influence of optical fiber dispersion caused by MCF with transmission distance of 2 km on SCMA signal can be ignored. Fig. 7 (b) shows the SCMA signal constellation on the four cores at the transmitter, and Fig. 7 (c) and Fig. 7 (d) show the constellation after 2 km MCF at -8 dBm and –14 dBm respectively. Obviously, when the received optical power is -14 dBm, the signal constellation is chaotic, and the BER is only 0.123.

 

Fig. 7. (a)The measured BER curves of BKB and after 2km MCF transmission; (b)The constellation at transmitter; The constellation at receiver when the received optical power is -8 dBm(c) and -14 dBm(d).

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3.2 Experimental of SCMA-OFDM transmission system based on 7 core fiber

In order to further improve the quantity of access subscriber, SCMA-OFDM transmission system is introduced. This paper uses the multi-core of fiber to reduce the complexity of MPA detection at the receiver. The specific principle is explained in detail in Section 2.2. The experimental procedure is the same as Section 3.1. The difference lies in that the SCMA encoding at the transmitter is superimposed in the way shown in Fig. 8. The codewords are superimposed into three parts I, II and III. We find that when stacking codewords in parallel, the number of constellation points in the part III will be reduced. This is because the codewords in these two lines just don't contain the imaginary part. This will make the receiver unable to correctly detect the original constellation point of users. Therefore, when decomposing the factor graph, we should pay attention to whether the receiver can demodulate correctly. The three parts are respectively processing parallel-serial conversion after OFDM to generate three rows of data S₁, S₂, S₃. The three rows of data fan in three cores of a 7-core fiber for transmission. The specific process is shown in Fig. 8 where X_{j, k} represents the codeword mapped by the j-th user on the k-th subcarrier. All the key system parameters are provided in Table 1.

 

Fig. 8. The proposed superposition scheme.

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Table 1. System parameters.

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Figure 9(a) shows the BER performance of the original MPA and the proposed MPA1 and MPA2 after 2 km MCF transmission. The dotted line in the figure is the FEC limit. Among them, MPA1 is a simplified MPA algorithm proposed in Section 2.2. The algorithm only needs to pass messages to part I and II, and the complexity is reduced to $O({N_{iter}}\sum\limits_{i = 1}^{{K / 2}} {{M^{{d_f} \times {2 / 3}}}} )$. MPA2 transmits messages to part I, II and III with the same complexity as MPA1, but the amount of calculation will increase by one group. As can be seen from Fig. 9(a), the original MPA, MPA1 and MPA2 reach the FEC limit when the receiving optical power is about -11.5 dBm, -9.5 dBm and -12.5dBm respectively. Fig. 9 (b) is the signal constellation at transmitter. And Fig. 9(c) and (d) are signal constellation when the received optical power -8dBm and -14dBm respectively by using MPA1. It can also be seen from Fig. 9 (a) that when the received optical power is -9 dBm, the original MPA has roughly the same BER performance as MPA1. If the received optical power continues to be improved, the BER performance of MPA1 will be better than that of the original MPA. This is because if the optical power continues to be increased, the possibility of light leakage to other cores in multi-core fiber will raising, which will cause the increasing of the crosstalk between the cores. MPA1 disperses the number of superimposed users on the one subcarrier. Originally, three user codewords were superimposed on one subcarrier. and totally uses four subcarriers. While codewords of two users are superimposed on one subcarrier and totally uses six subcarriers when using MPA1. During demodulation, the original crosstalk is weakened due to the spread spectrum of SCMA encoding, and the BER performance is improved. This conclusion is more obvious than MPA2. As can be seen from Figure 9(a), since MPA2 traverses all nodes, the BER performance is greatly improved compared with the original MPA. Although the amount of calculation is more than one group of calculations compared with MPA1, the overall complexity is still lower than the traditional MPA algorithm.

 

Fig. 9. (a)The BER performance of the original MPA and the proposed MPA1 and MPA2 after 2km MCF transmission; The signal constellation at the transmitter by using MPA4(b); the received optical power -8dBm (c) and -14dBm (d) respectively by using MPA1.

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4. Conclusions

We have proved the feasibility of SCMA encoding scheme in multi-core fiber transmission. By experiments, we verify the possibility of non-orthogonal transmission using cores of multi-core fiber as orthogonal resource blocks. The experiment uses a traditional codebook to encode data that exceeds the number of resource block users. Mapping bit steam into multi-dimensional codewords and superimpose it on 4 cores of 2 km weakly coupling 7-core fiber for transmission. It is successfully demodulated at the receiver at 30 Gb/s. In addition, we also experimentally verify the MCF transmission system of SCMA-OFDM. By using different cores, we reduce the complexity of MPA detection algorithm at the receiving end, and this method helps to suppress crosstalk between core and improve the BER performance. This scheme has great prospects in the future non orthogonal optical access network system.