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Abstract
Constellation shaping (CS) has always been a popular research hotspot in optical communication. Recently, most researchers have focussed on using constellation-shaping technology to improve the system's performance, ignoring the additional penalty it brings to the coherent system. This paper proposes a method of constellation truncation using sub-constellation overlap to perform CS on quadrature amplitude modulation (QAM). The experimental results show that compared with the traditional probabilistic shaping 16QAM, the proposed scheme can effectively avoid the extra penalty brought by CS and achieve a gain from 0.5 to 1.5 dB in optical signal-to-noise ratio. To practically verify the proposed scheme's performance, 7-core 16 km fiber span is deployed in the field to experimentally perform space division multiplexed coherent transmission. The wavelength division multiplexing (WDM) of 93 carriers was used to achieve coherent transmission at a net rate of 116.66-Tb/s.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The desire for increased bandwidth and faster optical fiber communication networks has grown increasingly urgent in recent years due to the Internet's explosive growth, making the development of coherent optical communication technology more and more crucial [1]. Currently, coherent receiving technology based on dual-polarization orthogonal amplitude modulation (QAM) is widely used in coherent optical communication systems. QAM can easily achieve coherent transmission of more than 100 Gb/s/carrier [2,3]. By deploying QAM, each symbol carries more bits to improve spectral efficiency and transmission capacity; the system capacity is difficult to approach the Shannon limit since each symbol has the same probability in the standard M-QAM modulation format. Existing studies have shown that in the additive white Gaussian noise channel (AWGN), there is a gap of about 1.53 dB between the standard M-QAM signal and Shannon capacity [4]. In order to further approximate the Shannon limit, many methods have been proposed, such as constellation shaping (CS), and interleaved coding modulation [5–7]. Among them, constellation shaping is one of the most popular methods [8]. The constellation shaping technique is a typical high-order modulation format optimization technique divided into geometric shaping (GS) and probabilistic shaping (PS). GS technology is mainly used to optimize the geometric structure of the mapped constellation diagram so that the average power of signals is relatively reduced when the minimum Euclidean distance of constellation points is certain. Or a relatively large minimum Euclidean distance is obtained when the average power is the same, to improve the performance of the system [9,10]. The basic idea of PS is to reduce the overall transmitting power by changing the transmitting probability of the symbol. Since the outer circle points of the constellation diagram require more power to transmit than the inner circle points do in the high-order modulation, PS technology decreases the transmitting probability of the outer circle points while simultaneously increasing the transmitting probability of the inner points. This boosts the overall efficiency of the system [11,12].
In the current research on constellation shaping, most scholars mainly focus on using constellation shaping to improve the system's performance. On GS, constellation gain is usually achieved by changing the layout of constellation points, such as cross constellation QAM, star constellation QAM, hexagon QAM, etc. [13–15]. According to the report in Ref. [16], the cross constellation has a gain of at least 1 dB compared with the traditional rectangular constellation. The star constellation also performs better than the traditional constellation in the system with limited peak power, and the hexagonal constellation can maximize the minimum Euclidean distance between two adjacent points. Currently, the research direction for GS technology tends to carry out irregular layout optimization of constellation points according to some optimization criteria. For example, in Ref. [17], generalized mutual information is used as an optimization parameter to carry out GS. Due to the development of machine learning and other technologies, many scholars use machine learning technology to optimize the distribution of points in the constellation. In Ref. [18], a particle swarm optimization algorithm was proposed for AWGN and a nonlinear fiber channel to optimize various Amplitude Phase Shift Keying (APSK) constellations. However, the proposed constellation shaping algorithms are based on probabilistic or geometric shaping, rarely combining the two. This is mainly because the position distribution and probability distribution of constellation points are changed after CS. This will cause the performance of the digital signal processing (DSP) algorithm originally used for standard signals in the coherent optical communication system to decline [19–22], such as the frequency offset estimation algorithm based on the fourth power, phase recovery algorithm based on Viterbi and Viterbi (VV) Algorithm, multi-mode blind equalization algorithm. In addition, many reports on constellation shaping algorithms are often based on simulations or back-to-back systems, but in fact, the negative effects of frequency bias and phase bias are more obvious after optical fiber transmission.
Phase recovery is a critical component in coherent DSP systems. Various carrier phase recovery (CPR) algorithms have been proposed, with blind phase search (BPS) and Quadrature Phase Shift Keying (QPSK) partitioning algorithms being widely used [23–25]. Among them, the BPS algorithm has high estimation accuracy and is considered the benchmark for carrier phase noise estimation. However, the correlation between the estimation accuracy of the BPS algorithm and its testing angle is substantial, and the complexity will be relatively large if a higher estimation accuracy is to be obtained. In Ref. [26,27], the BPS algorithm is compared with the improved QPSK partitioning algorithm, which shows that BPS has the best performance under PS-QAM with low entropy, and on the other hand, the complexity of the BPS algorithm cannot be ignored. Therefore, the QPSK partitioning or an improved QPSK partitioning algorithm is worth studying. However, the current research results show that even if the QPSK Partitioning algorithm is improved, the performance of the BPS algorithm cannot be achieved when the shaping amplitude is further increased [27]. Of course, many scholars have paid attention to the transmission of low-entropy PS-QAM. For low-entropy PS-QAM transmission, researchers often modify the receiving DSP algorithm [28–30], which will undoubtedly increase the complexity of the receiving algorithm. Therefore, this paper deals with the shaping scheme and reduces the influence of PS and GS through reasonable constellation layout and shaping methods. If there is no need to make drastic changes to the receiving DSP algorithm, PS and GS can avoid the additional penalty for the coherent communication system.
In our work, a truncated constellation shaping method based on 16QAM is designed to minimize the additional penalty of constellation shaping in the DSP part of a coherent optical communication system. The constellation is truncated through sub-constellations overlap; the 16 constellation points are compressed to 12, called CS-12QAM in this paper. On this basis, GS is further used to change the distribution of constellation points to meet the needs of the DSP algorithm at the receiving end. Compared to the original constellation, the constellation gain index has improved by 0.012. Experimental results show that the proposed CS-12QAM scheme can effectively reduce the additional penalty brought by PS, and has an optical signal-to-noise ratio (OSNR) gain of 0.5-1.5 dB compared with the traditional PS-16QAM scheme. Finally, the proposed scheme is validated on the field trail, where 16.5 km 7-core fiber is deployed in the coherent optical communication system. We achieved a net rate of 116.66-Tb/s in wavelength division multiplexing (WDM) and polarization-division multiplexing (PDM) systems.
2. Principle
2.1 Analysis of the extra punishment of traditional probability shaping on DSP
In Fig. 1, we simulated the difference between traditional 16QAM constellations and PS-16QAM constellations. We add Gaussian noise to the constellation diagram of the signal sending end, so that we can better see the distribution of constellation points. As we know, the traditional uniform 16QAM constellation distribution is shown in Fig. 1(a), and the emission probability of each constellation point is the same. The constellation distribution of PS-16QAM after PS is shown in Fig. 1(b). Currently, constellation points present a nonuniform distribution, manifested as a small number of points in the outer circle and a large number in the inner circle. Figure 1(c) and Fig. 1(d) are more intuitive representations of the probability distribution of constellation points. In the DSP process, after coherent system transmission, a cascade multi-mode algorithm (CMMA) is generally used to carry out blind equalization [31]. After CMMA, the constellation diagram is circled at this time due to the influence of factors such as frequency offset and phase noise. Here, we simulate the constellation diagram by adding phase noise, as shown in Fig. 1(e) and Fig. 1(f).
As far as we know, QPSK Partitioning improved based on VV algorithm is currently an algorithm with relatively low computational complexity in QAM signal CPR, and is also one of the widely used algorithms [25,32].
For QAM modulation format, the signal can be represented as:
where xk represents the kth transmitted signal, Ak represents the amplitude of the kth symbol, and θk represents the phase of the kth symbol.After transmission through the channel, the received signal can be expressed as:
where, yk represents the kth received signal, φk represents the phase noise of the kth signal, and nk represents AWGN of the kth symbol. Usually, we only need to deal with phase noise when doing CPR. The signal is usually processed in the 16QAM modulation format by raising it to the fourth power. After the fourth operation, the received signal can be expressed as:For traditional 16QAM, only the outermost constellation points are usually selected for processing during phase noise estimation, and the modulation phase of these constellation points meets the following requirements:
Therefore, after the 4-power operation, the received signal can be expressed as:
That is, the modulation phase has been removed and only the phase noise is retained. Then the phase noise information can be extracted by taking the Angle function. However, after the traditional PS scheme is used, as shown in Fig. 1(d), the number of constellation points in the outermost ring satisfying formula (4) will be greatly reduced. When the shaping depth is large, the number of points in the outer ring is too small, so phase estimation cannot be carried out adequately. To solve this problem, a new CS scheme is proposed in this paper, which can effectively reduce the additional penalty of PS on DSP in coherent systems.
2.2 Principles of constellation shaping
As shown in Fig. 2, in the first step, 16 constellation points of 16QAM are truncated to 12, forming the 12QAM constellation shown in Fig. 2(b). Here, we innovatively use a sub-constellation overlapping way to truncate 16QAM constellation.
The rearrangement and probability change of constellation can be realized by using the sub-constellation overlap. At the same time, due to the completeness of the number of constellation points, this method can greatly reduce the complexity of adding identification marks and improve the system performance.
It is assumed that the number of bits of the original signal is m, the number of bits mapped by the constellation point after shaping is n, and the number of bits of the sub-constellation identification label is l. In order to recover the source signal at the receiving end, the one-to-one correspondence property of the signal mapping must be guaranteed, so it is necessary to:
This means that $n + l \ge m$, in other words, the number of bits of the reshaped signal must be more than the number of bits of the original signal. If it is equal, it means that the information is rearranged internally, and the probability change is not realized, which does not meet the basic rules of probabilistic shaping.
Assume that the number of mapping constellation after shaping is c, The set of sub-constellations is $\{{{s_1},{s_2},{s_3} \cdots {s_c}} \}$ where s represents a sub-constellation containing s constellation symbol points. At the same time, the number of the subscript represents the priority of the distance from the center of the circle, “1” represents the closest to the center of the sub-constellation, “c” represents the farthest from the center of the sub-constellation. The number of sub-constellations that overlap is denoted by d, then the amount of overlap of each sub-constellation is $\{{{d_1},{d_2},{d_3} \cdots {d_c}} \}$. Combined with the basic idea of sub-constellations overlap, the following requirements should be met:
Formula (7) represents two points: First, the sum of the number of overlapping sub-constellation points must be greater than or equal to the original data's length to ensure its completeness. Secondly, the overlapping sub-constellations should gradually decrease with increased distance from the origin. Otherwise, it does not meet the basic idea of PS. It can be seen that the overlap of sub-constellations will cause problems in the discrimination of the receiving end, so it is necessary to introduce the subset label as the identification marker. Since the number of constellations after shaping is a power multiple of 2, it makes the addition of identification markers the most simplified. From this point of view, since the number of bits of the subset tag is l, it needs to meet:
${d_1}$ represents the maximum overlap number of subsets. When only constellation truncation is carried out, assuming that the truncated sub-constellation contains N constellation points, N constellation points are mixed with other constellation points in the form of “overlap”, so N constellation points contain labels with length of l bit. In M-QAM modulation, the number of bits contained by each constellation symbol can be expressed as $m = {\log _2}M$, where M is the modulation order Assuming that the bits length of the signal to be reshaped is L, the symbol bits length L2 after reshaping can be expressed as:Then the information entropy after shaping can be expressed as:
For the traditional 16QAM constellation, the distance between the constellation points and the origin is taken as a reference, and the constellation is divided into three sub-constellations, as shown in Fig. 3. Constellation points of the same color are in the same sub-constellation. In order to truncate the constellation points, we need to overlap the outermost points onto the inner circle points. Instead of processing according to gray code, we fixed the encoding of the outermost constellation symbols as a four-digit binary code beginning with “01”. While mapping, the matching module reads the long string binary code to be transmitted by 4 four bits per unit, as shown in Fig. 3. When the first two bits are read as “01”, they are replaced with “00”, and a “1” is added after the last bit as a label. All the information is then combined for a normal constellation mapping. In this encoding way, there will be no four-bit unit starting with “01” when mapping again, that is, constellation truncation is realized.
Based on constellation truncation, PS can be realized if the sub-constellation is reassigned and overlapped again. The principle of the mapping scheme that uses sub-constellation overlap to achieve PS is shown in Fig. 4. First, it is necessary to flexibly allocate the sub-constellation according to the needs of the information points after the final shaping and the actual situation. And constellation overlapping labels is introduced to distinguish the overlapping information. The maximum number of overlaps determines the bit length of the constellation overlap label. This way, combining information bits and constellation overlapping labels constitutes the probabilistically shaped information bits. The selection of the sub-constellation and the length of the constellation overlap label determine the overall effect of probabilistic shaping, that is, the degree of concentration of the shaped information relative to the average energy value of the information. The more overlapping sub-constellations near the origin, the better the shaping effect. However, the increase in overlapping times will increase the number of bits of constellation overlapping labels, reducing information transmission efficiency. At the same time, the more detailed the sub-constellation division, the stronger the information variability and flexibility in the shaping process. This will also increase the length of information bits of the sub-constellation and reduce the practicality of PS. In this way, to improve the effect of PS, it is necessary to make a reasonable and adequate balance between the number of elements in the sub-constellation set and the number of sub-constellation overlaps.
Fig. 4. The principle of mapping scheme for probabilistic shaping by using sub-constellation overlap
Compared with the traditional PS method using constant composition distribution matching (CCDM) [33], the sub-constellation overlap method has lower complexity. And because the selection and superposition of sub-constellations are artificially defined, shaping can be more flexible and not limited to the Maxwell-Boltzmann distribution.
After constellation truncation, the constellation obtained is shown in Constellation-B in Fig. 3. Obviously, because the sub-constellation of the outer ring is directly overlapped to the inner ring, the constellation points of the outer ring that meet the phase requirements of the QPSK Partition algorithm disappear. Therefore, it is necessary to further optimize the constellation by GS.
In this paper, we adopt the direct design method for GS. First, construct a square with the origin as the primary center, and distribute the four constellation points on the four vertices of the square. Next, build an equilateral triangle based on each side of the square, and then distribute the next four constellation points at the vertex of each equilateral triangle. Finally, the last four constellation points were arranged on the phase line that met the phase requirements of QPSK Partition algorithm. The distance between the four constellation points and the vertex of the square was the same as the length of the square side. The final result is shown in Fig. 2(c).
In AWGN channel, the gain index of constellation map can be expressed as:
3. Experimental setup and results
3.1 Experiment A: performance analysis of CS-12QAM
In order to verify the performance of our proposed scheme, we first conducted experiments on a coherent optical transmission system, as shown in Fig. 5. At the transmitter, a tunable external cavity laser (ECL) with a linewidth of ∼100 kHz was used to transmit optical signals with a wavelength of 1550 nm. After the polarization beam splitter (PBS), the optical carrier was modulated by IQ modulators (IQM). The IQMs were driven by a four channelled arbitrary waveform generator (AWG) operating at 64 GSample/s, generating 16QAM signals at 32 GBaud. The two modulated signals were transmitted in the 20 km standard single-mode fiber (SMF) after passing through the polarization beam combiner (PBC). An erbium-doped fiber amplifier (EDFA) is first used at the receiving end to enlarge the optical signal. Then EDFA-2 is used as a noise source to enter the receiver with the signal light through the optical coupler (OC). A variable optical attenuator (VOA) was used to adjust the noise. After coherent reception using a local oscillator (LO), the four-way signal of the PDM was digitized through a high-speed digital storage oscilloscope (DSO) with an acquisition rate of 80 GS/s. The collected signals were processed by offline digital signal processing (DSP). The detailed DSP process is shown in Fig. 5. The DSP part adopted the conventional algorithm without any additional adjustment due to CS, so the performance gap between the CS-12QAM and the traditional PS-16QAM scheme can be equitably compared. For blind equalization, the CMMA was used, and the quadratic-power algorithm was deployed for frequency offset compensation and phase recovery. In our algorithm, because only the points of the outer ring are used, we set the selection radius to 3.1 and the length of the filter during the unwrap process to 250. Finally, the multiple input multiple output (MIMO) algorithm based on least mean square was used for polarization demultiplexing [34], and the bit error rate (BER) after demodulation was used as the performance index of the system.
Firstly, we used the CS method proposed in this paper and the traditional PS method to generate 16QAM information with four probability distributions of information entropy of 3.6 bits/symbol, 3.5 bits/symbol, 3.3 bits/symbol, and 3.2 bits/symbol, respectively.
As shown in Fig. 6, constellation points have different distributions under different information entropy. It should be noted that when the information entropy is 3.6 bits/symbol, CS-12QAM proposed in this paper is uniformly distributed because the distribution of constellation points is not uniform after truncation of the 16QAM constellation employing sub-constellation overlap. Therefore, some constellations are overlapped again by adding labels, and finally, a uniform CS-12QAM constellation is obtained.
We experimented to directly reflect the difference between the proposed scheme in this paper and the traditional PS scheme, as shown in Fig. 6, under the above four kinds of information entropy. The power value of EDFA-2 was changed to adjust the size of the introduced noise. The oscilloscope analyzed the optical OSNR, and the BER curve based on OSNR was finally obtained to compare the performance. All the data obtained in this paper were averaged by combining the X and Y channels of dual polarization after data collection 5 times to ensure the reliability of the experimental results.
As shown in Fig. 7(a) and 7(c), when the information entropy of the two schemes is fixed at 3.6 bits/symbol, the BER of the two schemes is not very different, and the BER vs OSNR curve is very stable. This is because the constellation of CS-12QAM presents a uniform probability distribution at this time, so no additional gain of PS is obtained. When the information entropy is 3.5 bits/symbol, the performance of CS-12QAM is slightly better than that of the traditional PS-16QAM. This performance gap is mainly due to the GS. However, when the probability shaping amplitude is further increased, the performance of the two schemes changes significantly. Figure 7(b) and 7(d) show that under 3.3 bits/symbol, the performance of CS-12QAM is further improved.
In contrast, that of PS-16QAM is barely improved or even slightly deteriorated, caused by the extra penalty from PS to DSP in the coherent optical communication system. When the shaping amplitude was further increased to 3.2 bits/symbol, the curves of both schemes showed significant dithering. Especially for the PS-16QAM scheme, the gain from probabilistic shaping has almost completely disappeared, and the penalty is more obvious. Especially when OSNR is low, it is difficult for data to be decoded correctly. For our proposed CS-16QAM, the performance also reaches the limit state at 3.2 bits/symbol. At this time, the phase recovery effect of CS-12QAM is also volatile. When the OSNR is low, the noise in the channel will mask this situation. When OSNR is improved, the channel noise has little influence on the system's overall performance, and the unstable factors are exposed in the phase recovery process. In Fig. 7(b), it can be seen that the BER curve has significant jitter when the OSNR reaches 20 dB. If we optimize the parameters of the QPSK partitioning algorithm, we can further improve the performance.
Through our analysis, in the coherent system, the additional penalty of DSP mainly comes from the phase recovery part of DSP. With the increase of the shaping depth, fewer and fewer constellation points satisfy formula (4). Consequently, the phase recovery stage of the conventional PS-16QAM frequently has problems obtaining the proper phase noise.
In our experiment, the receiver collects about 60 data frames in a time slot through DSO for decoding, and each small frame contains 8192 symbols. The BER of each small frame is recorded separately, and their average value is taken as the BER of this experiment. Through our observation, when PS-16QAM is subjected to the additional penalty brought by probabilistic shaping, the BER of small frames tends to appear large jitter.
When the information entropy is 3.3 bits/symbol, and the OSNR is fixed at 16 dB, the error code number (ECN) jitter of CS-12QAM and PS-16QAM in a large frame, is shown in Fig. 8(a) and (b), respectively. When there is a surge in the number of error codes, it indicates the phase recovery error. As seen from Fig. 8(a), when the information entropy is 3.3 bits/symbol, the ECN of CS-12QAM still shows a stable state, while the ECN of PS-16QAM shows irregular jitter. This jitter is mainly due to the inaccuracy of phase estimation. Due to the role of PS, there are fewer points for phase recovery, so there are often inaccurate phase estimates.
For PS-16QAM, when the information entropy is 3.2 bits/symbol, data jitter under different OSNRs is recorded, the ECN in Fig. 9(a), (b) and (c) shows the ECN jitter when the OSNR is 14 dB, 16 dB, and 20 dB, respectively. Illustration (d) shows the ECN jitter of CS-12QAM when OSNR is 16 dB. It can be seen that when the shaping depth is large enough, the CS-12QAM will also be affected, but compared with the traditional PS-16QAM, it still has a great performance improvement.
Further, to explore the relationship between the two schemes’ influence on the PS penalty and the shaping depth, we monitored the change of BER by changing the shaping depth when the OSNR was fixed at 17 dB. Here, we selected a set of data and used the BPS algorithm to carry out CPR on PS-16QAM as the comparison of our experiment. The number of test angles of the BPS algorithm was set to 32. As shown in Fig. 10, the shaping amplitude gradually increases with entropy decrease. In the beginning, BER will show a gradual decline due to the gain brought by PS. The BER of BPS-PS-16QAM has been on a steady downward trend, but there is a clear difference between the other two groups. It can be seen that both sets of curves using the QPSK Partitioning algorithm have inflection points. This is because when the shaping depth is too large, the number of outer circle points used for phase recovery will be too small, and the additional penalty of probabilistic shaping on the QPSK partitioning algorithm will start to appear. In the PS-16QAM scheme, the inflection point is 3.5 bits/symbol, while in the CS-12QAM scheme, the inflection point is 3.2 bits/symbol. This indicates that compared with the traditional PS-16QAM, the CS-12QAM scheme proposed in this paper can have a larger shaping depth without additional punishment, so it has better anti-noise performance.
3.2 Experiment B: transmission over field deployed 7-core fiber
The above experimental analysis shows that the CS-12QAM proposed in this paper has certain advantages over the traditional PS-16QAM in performance. On this basis, we carried out further experimental verification in the field deployed of 7-core fiber. Figure 11(a) shows that the field-deployed armoured optical fiber cable of four 7-core optical fibers surrounds Guangzhou Higher Education Mega Center through an underground tunnel. The length of the optical fiber cable is 16.5 km, of which 16.4 km is in the tunnel. The remaining 0.1 km is in the laboratory, allowing access to the 7-core fiber at either end of the cable. During the deployment process, due to the diameter of the fiber cable, the length of a spooled cable is usually limited to a few kilometers, so our 7-core fiber cable is fused every 3 km. This puts a high demand on fusion technology because even minor deviations can increase losses, reducing communication performance. Compared with the test environment in the laboratory, the deployment of long-distance optical fibers in the field will inevitably produce splicing losses due to many fusion points, accumulating into a more significant value. Therefore, during cable deployment, it is necessary to reduce the fusion loss of each core at each point. Our experiment reduced the average fusion loss of the 7-core fiber to ∼0.3 dB per fusion point. The cross-section of the 7-core fiber we used is shown in Fig. 11(b), with a cladding diameter of 200 ± 5 μm and a core spacing of 62 ± 2 µm. To make each core uncoupled, a low-refractive index trench is introduced around each core, thereby limiting optical energy to the core as much as possible and reducing cross-talk between cores. We measured crosstalk values as low as -70 dB. The final transmission attenuation per core after installation is about 0.2 dB/km, with similar performance to commercial SMF.
At the transmitter, as shown in Fig. 12, a tunable ECL with a line width of ∼100 kHz was used as the light source for the test channel. 93 C-band ECLs were used as the light source in the dummy channels, with WDM intervals set to 50 GHz. The test and dummy channels were modulated independently by a dual-polarization IQ modulator, respectively. The IQ modulators were driven by two AWGs, operating at 64 GSample/s and producing a 16QAM signal at 32 GBaud. After modulation, the dummy channel's signal was divided into two beams. One beam entered the 1 × 8coupler after the EDFA and was then injected into the channels of the other six cores. For the other one, the light with the same frequency as a waveshaper filtered out the test channel, coupled with the test channel and injected into the test core channel. After transmission through field deployed 7-core fiber with a length of 16.5 km, the obtained spectrum is shown in the illustration in Fig. 12. At the receiving end, a waveshaper was used to select the wavelength of the test channel and fed into the coherent receiver. After analog-to-digital conversion through DSO, DSP processing is carried out offline.
In the actual test, we tested 19 wavelengths in core 4 (middle core) and core 5 (side core) of the 7-core fiber. As shown in Fig. 13, BER values of all wavelengths are below the 20% soft-decision FEC threshold of 2.4 × 10−2, which is equivalent to the transmission of 116.66-Tb/s (3.5 × 2 × 7 × 93 × 32 × 80%) based on 7-core fiber under 93-WDM. Because we used 93 wavelengths, and there would be some differences in the power of these wavelengths, the spectrum could not be completely flat (the spectrum is shown in the illustration in Fig. 12), so there is a particular gap between different wavelengths of BER. And since we are using a C-Band amplifier, the gain of the amplifier is also uneven. The gain effect of the amplifier is better near the central wavelength of the C-band, while the gain effect is slightly worse at the edge of the band. Therefore, the overall BER will show that the central part is better and the two sides are slightly weaker. To our knowledge, this is the first detailed report of a coherent transmission system based on probabilistic shaping in a field-deployed 7-core fiber. The results are more trustworthy when performed in field-deployed optical fibers rather than in a laboratory.
4. Conclusion
We propose a scheme of QAM constellation truncation based on sub-constellation overlap. By using sub-constellation overlap, 16QAM is truncated to 12QAM. On this basis, the constellation is geometrically reshaped to reduce the extra penalty of PS on the coherent system DSP at the transmitting end. The experimental results show that CS-12QAM has an OSNR gain of 0.5-1.5 dB compared with the traditional PS-16QAM under the change of shaping depth. And when the additional penalty of PS becomes apparent, the depth of the CS-12QAM is 0.3 bits/symbol, more than the traditional PS-16QAM. Furthermore, the performance of CS-12QAM is verified in the field deployed seven-core fiber. Using CS-12QAM, coherent transmission with a net rate of 116.66-Tb/s is achieved through PDM-93-WDM-7-Core.
Funding
National Key Research and Development Program of China (2021YFB2800904); National Natural Science Foundation of China (61835005, 61935005, 62171227, 62205151, 62225503, U2001601); Jiangsu Provincial Key Research and Development Program (BE2022055-2, BE2022079); The Natural Science Foundation of the Jiangsu Higher Education Institutions of China (22KJB510031); 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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