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Abstract
In this paper, a novel three-dimensional constellation diagram is proposed for optimizing the spatial coordinates of constellation points using geometric shaping (GS), which improves the constellation figure of merit (CFM) and, as a result, reduces the bit error rate (BER). A three-dimensional carrier-free amplitude phase (CAP) modulated signal transmission at 25.45Gb/s is successfully implemented on a seven-core fiber communication system to verify the performance of the constellation diagram. Compared to the traditional scheme, this method has an average receiver sensitivity gain of 1.4dB at BER ∼1 × 10−3, further, the receiver sensitivity gain difference of 1.3dB between different cores. The experimental results show that this scheme effectively reduces BER without additional communication components, which can be used in short-distance access networks in the near future.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of modern technologies requiring a large number of traffic resources, such as the Internet of Things (IoT), big data, and smart cities, has increased the demands for huge data transmission by end-users. To combat this trend, short-range optical communication systems, primarily intensity modulation/direct detection (IMDD) systems, have gotten a lot of attention, where carrier-free amplitude phase (CAP) modulation has become a widely used modulation scheme with the advantages of simple structure, low loss, high security and high efficiency [1–6]. At the same time, the shortage of spectrum efficiency has become a bottleneck for continually increasing transmission capacity. The geometric shaping (GS) technique has become a popular research direction because it effectively improves the spectrum efficiency and transmission performance of the system. It works in the constellation modulation phase which can change the position of constellation points in the constellation so that they are closer to the central origin. As the average power of the constellation points is reduced, the transmitting optical power at the transmitter is also decreased. Low transmitting power mitigates the nonlinear effects in the fiber that improves the bit error rate (BER) of the shaped signal compared to the unshaped signal. In addition, the low complexity of CAP modulation works well with GS techniques. A design of a constellation with a 256-QAM geometry was described in [7], while [8] proposed a 32-QAM constellation mapping with different geometric configurations using different geometry as a base unit, such as squares, rectangles, and circles. An 8-QAM constellation using two-dimensional spatial coordinate values as a set was proposed in [9]. Similarly, a two-dimensional constellation mapping scheme was proposed in [10], which has a special geometric structural design and honeycomb-like decision regions. However, all these studies are focused on designing constellation mapping considering only a two-dimensional plane. The three-dimensional constellation provides more space for coordinate adjustment and has a larger minimum Euclidean distance (MED) than a two-dimensional constellation at the same average power, which can have better channel conditions when the conditions are permitted [11]. Various improved three-dimensional constellations were reported in [12–13], but these modifications focused on local fine-tuning of the constellation with a square-based unit and were only simulated without experimental validation.
However, the communication capacity of traditional single-mode fiber is approaching the nonlinear Shannon limit with the rapid development of optical communication technologies, and it is inevitable to increase the transmission capacity of the system from new aspects [14–15]. Space division multiplexing (SDM) technology uses multi-core fiber (MCF), few-mode fiber (FMF), or MC-FMF to transmit more signals, which is a new way to increase communication capacity. MCF transmission is one of the most widely used SDM technologies, and the major stumbling block is the inter-core crosstalk, which causes serious signal distortion. Weakly-coupled MCFs, on the other hand, can effectively reduce inter-core crosstalk by rationalizing the number and arrangement of cores, allowing each core of the fiber to be treated as an independent transmit channel, which has proven to be an effective way to break the communication capacity bottleneck. Due to the good compatibility with wavelength-division multiplexing (WDM) technology, SDM is gaining more and more attention [16–19]. In addition, these two technologies are compatible because the constellation mapping is to convert the amplitude and phase of the signal into the coordinate value of the constellation points according to the spatial coordinates table, and geometric shaping is changing the coordinate value of constellation points. Therefore, GS could be used for MCF and FMF transmission scenarios. What’s more, the devices required for SDM inevitably increase the size of the communication system, while GS works on the basic unit of signal modulation avoiding the further increase of system complexity. Under experimental conditions demonstrated in [20] that transmitted 12 channels of 40Gb/s polarization-division-multiplexing quadrature phase-shift keying (PDM-QPSK) signals with ultra-dense WDM-PON using 37 km seven-core MCF. Similarly in [21], the authors demonstrated beyond 100 Gbps SDM-PON systems over 9.6 km 30-core hollow core (HC) fiber without WDM and DSP, which is the first time using commercial 10G-class directly modulated laser. Therefore, SDM technology is seen as an important solution to solve the capacity crisis in the future.
In this paper, we propose a new design of a three-dimensional constellation diagram, which can be disassembled into a superposition of several two-dimensional structures can be further that considered as a combination of several base cells, which simplifies the complex 3D constellation. The origin of the coordinates is chosen as one of the constellation points, and constellation points at the same level form structure of regular triangle, which make the constellation points closely surround the central origin. Compared to the traditional ones, the redesigned constellation has lower average energy at the same MED, which effectively reduces the BER of transmission. Based on the scheme, we successfully implemented three-dimensional 16-CAP transmission over a 2 km 7-core fiber.
2. Principle
The performance of the constellation is determined by MED and average energy. MED is defined as the minimum distance between constellation points and has a close relationship with noise immunity signal. The average energy is defined as the distance between the constellation points and the origin measuring the required transmitting power. However, increasing the MED will lead to the rise of average power, and the deterioration of both parameters will weaken the performance of BER. To find an optimal solution, the performance of the constellation is comprehensively evaluated by CFM [22]:
Where d is the square of the MED and P is the average power of the constellation point. CFM reflects the connection between constellation performance and these two indicators, which facilitates the subsequent design of a specially shaped constellation.The distribution of the traditional 16-ary three-dimensional constellation is shown in Fig. 1. To describe the construction of the three-dimensional constellation easily, constellation points with the same distance between grid origin and the point can be defined as the same energy level. The constellation consists of two cubes, the eight vertices of the inner small cube form the constellation point group at the first energy level, with a minimum distance of 4 between adjacent points. The eight vertices of the outer larger cube form the constellation point group at the second energy level and the distance between the vertex on the inner small cube is 8.6. We named this geometric shape of the constellation as Cube-shaped-16-CAP, and the specific three-dimensional spatial coordinates and constellation point mapping rules are shown in Table 1. The CFM of Cube-shaped-CAP-16 is calculated to be 0.4726 with Eq. (1).
Table 1. Three-dimensional spatial coordinates and mapping rules of Cube-shaped-16-CAP constellation
To design a new constellation, it is necessary to consider both MED and average power. Since only increasing the MED between constellation points results in deteriorating the average power, moreover, a decrease in average power will lead to a deteriorate the BER performance, therefore a three-dimensional constellation is often designed with a fixed MED. At the same time, basic cell should be confirmed for the irregular structure of constellation. As shown in Fig. 2, regular triangles and regular tetrahedrons are often chosen as the basic cell, because they are geometric figures which have the closest distance between vertices and the center in two-dimensional and three-dimensional spaces with fixed MED. Under the condition discussed above, the three-dimensional constellation diagram is reconstructed by GS. The constellation points are as close as possible to the origin of the coordinates and the CFM is increased to obtain a constellation with high performance.
Fig. 2. Distance between vertices and the center of different geometric figures with fixed edge lengths in (a)two-dimensional (b)three-dimensional.
In this paper, the MED of constellation points is designed as 4, which is the same as the constellation of Cube-shaped-16-CAP. The new constellation is shown in Fig. 3. It is difficult to make full use of space while designing a constellation directly from a three-dimensional perspective, whereas it is much easier to consider it from a two-dimensional perspective. Therefore, we divide the three-dimensional constellation into three levels based on the z-axis coordinate, with red, orange, and purple lines connecting the constellation points of the same level. Space resources of the red level could be fully utilized because z-axis coordinate value of constellation points on red level is zero, so the points on red level have lower energy compared with the points on upper and lower levels which have the same value of x-axis and y-axis. Each level can be considered as a two-dimensional constellation, and distance between adjacent levels is 3.2660, which is the height of the regular tetrahedron with side length 4. First of all, six regular triangles with side length 4 are made around the origin of coordinates to make a regular hexagon, which also has the same side length as regular triangles. The seven constellation points of the red level are formed by its six vertices and central point, and the z-axis coordinate of the red level constellation point is 0. Regular hexagon is chosen to be the structure of red level because it has the shortest distance between the constellation points and the origin compared with the regular triangle shaped structure of orange level and purple level. Furthermore, make regular tetrahedrons upwards from any three spaced regular triangles as the base; the three vertices at the top form the constellation points on the orange level. In addition, make regular tetrahedrons downwards from the three regular triangles and the three vertices form the constellation points on the purple level. At last, select the triangle in the previous step and make a regular tetrahedron downwards to get the last three constellation points on the purple level. We named this new three-dimensional constellation scheme as Hierarchical-16-CAP, and the specific three-dimensional spatial coordinates and constellation point mapping rules are shown in Table 2. The CFM value of Hierarchical-16-CAP is 0.8889, which is an improvement over Cube-shaped-16-CAP, according to Eq. (1). The designed mapping rule will have a significant impact on transmission BER because the constellation points are tightly clustered in the center, resulting in a large increase in the number of adjacent points close to the central constellation point. Although the irregular shape of the Hierarchical-16-CAP prevents its mapping rule from becoming a Gray mapping, the performance gain from the increased CFM will compensate for and outweigh the BER loss in this respect if the used mapping rule is as close to a Gray mapping as possible.
Table 2. Three-dimensional spatial coordinates and mapping rules of Hierarchical-16-CAP constellation
3. Experimental setup and results
To verify the effect of the Hierarchical-16-CAP constellation diagram, experiments are carried out as shown in Fig. 4. The original data is first mapped onto the constellation point coordinates at the offline transmitter. The symbols will then be up-sampled and fed into three mutually orthogonal shaping filters for processing and synthesis, yielding a 3D-CAP-16 signal in the end. The coded and modulated data is first fed into an arbitrary waveform generator (AWG, TekAWG70002A), before being sent at a rate of 10GS/s. An electrical amplifier (EA) amplifies the electrical signal before sending it to a Mach-Zehnder modulator (MZM) for loading onto the optical carrier. The emitting light∼1550nm is modulated by the MZM with the electrical signal from the AWG before being fed into a 1:8 power splitter (PS), which divides the signal into seven equal parts. Finally, each component is fanned into the seven-core fiber's corresponding cores. After 2 km in the 7-core fiber, the signal is demodulated by the fan-out device. To compensate for transmission power loss, an EDFA is used. A VOA is placed in front of PD at the receiver to adjust the optical power. After converting into an electrical signal the data file is collected by the mixed-signal oscilloscope (MSO, TekMSO73304DX). The process at the offline receiver is the reverse of the previous steps, consisting of matched filtering, down-sampled and de-mapping, which turn the constellation points coordinate into a binary bitstream to obtain the original data.
Fig. 4. Experimental setup (AWG: arbitrary waveform generator; EA: electrical amplifier; MZM: Mach-Zehnder modulator; PS: power splitter; MCF: multicore fiber; EDFA: Erbium-doped fiber amplifier; PD: photodiode; MSO: mixed-signal oscilloscope).
The cross-sectional view of the seven-core weakly coupled multicore fiber used in this paper is shown in Fig. 4, where the fibers are arranged in a hexagonal configuration with the highest spatial utilization. The transmission loss of MCF is less than 0.3 dB/km, while the average insertion loss of fiber is about 1.5 dB and crosstalk of less than -50 dB between adjacent cores.
BER curves for Cube-shaped-16-CAP and Hierarchical-16-CAP in core1 for b2b and after 2 km transmission are shown in Fig. 5. It can be seen that there is a loss of about 0.4 dB when the BER is $1 \times {10^{ - 3}}$ in the signal after transmission, which is not only signal attenuation caused by dispersion and noise interference, but also additional loss due to the optical interface of the multiplexer device. The received optical power at BER of $1 \times {10^{ - 3}}$ for Cube-shaped-16-CAP and Hierarchical-16-CAP is -20.6dBm and -22.2dBm respectively, and the improved solution achieves a sensitivity gain of 1.6dB. According to the figure, although the BER of Cube-shaped-16-CAP is slightly lower than Hierarchical-16-CAP when the received optical power is low, the improved scheme has an obvious advantage when the optical power is between -24dBm and -20dBm. BER performance for both schemes are deteriorating and featuring non-linear variation at low optical received power, because noise interference is very serious at low optical power, which makes the constellation points at the receiver widely shift. Due to the dispersion of constellation points, Cube-shaped-16-CAP is slightly less likely to be misjudged than Hierarchical-16-CAP. Figure 5 (a)-(d) also shows a comparison of constellation diagrams of Cube-shaped-16-CAP and Hierarchical-16-CAP signals after 2 km and b2b transmission at -22dBm. As stated in the principle the advantage of using the specially designed constellation diagram outweighs the disadvantage.
Fig. 5. BER curves of Cube-shaped-16-CAP and Hierarchical-16-CAP in core-1 for b2b and 2 km transmission.
In addition, BER curves of Hierarchical-16-CAP in 7 core fiber after 2 km transmission are shown in Fig. 6. The received optical power from core1 to 7 is -22.2 dBm, -22.0 dBm, -21.3 dBm, -20.9 dBm, -21.2 dBm, -21.3 dBm, and -21.4 dBm at BER of $1 \times {10^{ - 3}}$, respectively, with a difference of 1.3 dB between the best core1 and the worst core4. The performance of cores has a degree of randomness because it is related to the manufacturing process. Besides, some factors such as external disturbances may also be responsible. From the result, the performance difference is controlled within an appropriate range, and each core can be regarded as an independent communication channel to use, which can greatly expand the communication capacity from the spatial dimension.
Furthermore, BER curves of Cube-shaped-16-CAP and Hierarchical-16-CAP in core 1 to core 7 are shown in Fig. 7. Due to the different transmission performance of cores, the modulation gain between the two constellation diagrams is also different, which is 1.6dB, 1.5dB, 1.4dB, 1.3dB, 1.3dB, 1.5dB, and 1.4dB at BER of $1 \times {10^{ - 3}}$, respectively. When the BER is $1 \times {10^{ - 3}}$, the average optical power gain of the Hierarchical-16-CAP is 1.4dB higher compared with the Cube-shaped-16-CAP. The figure also shows the constellation diagram at -21dBm at the receiver for both constellation schemes.
4. Conclusion
A novel 16-ary 3D-CAP constellation diagram is proposed in this paper to reduce the average power by changing the coordinates of the constellation points in three-dimensional space while keeping the MED constant, allowing the constellation diagram to achieve better BER performance at the same bit rate. A 7-core fiber transmission experiment has been successfully carried out and the result shows that Hierarchical-16-CAP achieves an average optical power gain of 1.4dB at a BER of $1 \times {10^{ - 3}}$ compared to the traditional Cube-shaped-16-CAP. It can be seen that space division multiplexing has good compatibility with GS, and the new constellation modulation scheme is effective in reducing the BER in the case of large-scale MCF communication transmission in the future.
Funding
National Key Research and Development Program of China (2018YFB1800901); National Natural Science Foundation of China (61875248, 61835005, 61727817, 62035018, U2001601,61975084, 61720106015, 61935011, 61935005); Open Fund of IPOC (BUPT); Opened Fund of the State Key Laboratory of Integrated Optoelectronics (IOSKL2020KF17); 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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