Open Access
Add to BibSonomy
Abstract
As a combination of direct detection and coherent detection technologies, self-coherent detection has the advantages of low cost and optical field recovery ability. However, most of the self-coherent detection techniques are limited to single sideband (SSB) signals. Recently, carrier-assisted differential detection (CADD) has been proposed to realize complex-valued double sideband (DSB) signals, but it requires a high carrier-to-signal power ratio (CSPR) to mitigate the signal-to-signal beat interference (SSBI). Later, a more cost-effective symmetric CADD (S-CADD) has been proposed while the required CSPR is still high. In order to alleviate the high requirements of CSPR, we propose a scheme based on the joint of digital pre-distortion (DPD) at transmitter and clipping at receiver to further improve the S-CADD system performance. This joint processing can not only solve the problem of non-uniform distribution of subcarrier signal-to-noise ratio (SNR) caused by non-ideal transfer function, but also the error propagation problem caused by enhanced SSBI under low CSPR. After the validation of the 64 Gbaud 16-ary quadrature amplitude modulation (16-QAM) orthogonal frequency division multiplexing (OFDM) signal transmitted over 80 km standard single mode fiber (SSMF), the CSPR required by the proposed scheme to reach the 20% soft decision-forward error correction (SD-FEC) and 7% hard decision-forward error correction (HD-FEC) can be reduced by 1.3 dB and 2.8 dB, respectively, with a comparison of the conventional S-CADD. The results show the potential of the proposed scheme in the short-reach optical transmissions.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous development of current digital technologies, and driven by emerging applications such as cloud computing, smart home, autonomous driving, etc., the data traffic growth in short-range optical networks has been promoted [1–4]. Although coherent detection (CD) has the advantages of high spectral efficiency and high sensitivity over long distances [5], the requirement of expensive narrow-linewidth local oscillator (LO) laser [6] has limited its development in short-range optical transmission. In contrast, the traditional direct detection (DD) does not need the LO laser, so it has the characteristics of simple structure and low cost [7]. However, the traditional DD technology is mainly based on intensity modulation direct detection (IM-DD), which only supports amplitude modulation and detection, and then results in the low spectral efficiency (SE). Moreover, the traditional IM-DD system does not support optical field recovery, so it cannot digitally compensate for the linear signal impairments caused by the fiber links which further limit the transmission distance [8].
In recent years, in order to combine the advantages of DD and CD, a series of cost-effective self-coherent detection schemes have been proposed, which can overcome the frequency-selective fading caused by dispersion [9–12]. Two typical of these methods are Kramers-Kronig (KK) receiver [9,10] and iterative cancellation (IC) receiver [11,12]. But, both schemes are limited to single sideband (SSB) modulation only, thus cannot make full use of receiver bandwidth compared with coherent detection. And the signal-to-signal beat interference (SSBI) generated by the receiver is the main factor affecting the system performance. Although the SSBI can be mitigated by adding a high-power carrier, the high carrier-to-signal power ratio (CSPR) is required for these systems.
Recently, a novel carrier-assisted differential detection (CADD) receiver has been proposed by Prof. William Shieh’s group and experimentally verified widely [13,14]. The optical field recovery of complex value double-sideband (DSB) signal can be realized without the use of optical filters. Compared with SSB signal, it has higher electrical spectral efficiency. However, CADD has the disadvantages of high CSPR requirement and high hardware complexity. To reduce the CSPR of the system, an interleaved CADD and an offset DSB CADD have been proposed in [16–18]. In these reports, the generated SSBI can be isolated from the signal, and the optical field recovery under 3 dB CSPR and 0 dB CSPR have been realized respectively. However, at least half of the spectrum is used to place SSBI, which results in a decrease in spectral efficiency. In addition, a more cost-effective symmetric CADD (S-CADD) scheme has been proposed in [15], which can reduce one PD and one ADC compared with traditional CADD configuration. By comparison, S-CADD has higher receiver sensitivity than CADD. However, the S-CADD system performance is also affected by the non-ideal transfer function like CADD, which still requires a high-power carrier and a frequency gap near the zero-magnitude frequencies of the transfer function to isolate the interference of enhanced SSBI on the desired signal. Therefore, it is very desired to propose a scheme that can ensure high electrical spectral efficiency and reduce the CSPR required by the system.
In this paper, we propose a novel method based on the joint processing of digital pre-distortion (DPD) at transmitter, and clipping in SSBI iterative elimination algorithm at receiver for the S-CADD systems, which can mitigate the SSBI enhancement caused by the non-ideal transfer function of the S-CADD receiver and the error propagation problem under low CSPR, respectively. We validate our method in the simulation system with 64 Gbaud 16-ary quadrature amplitude modulation (16-QAM) orthogonal frequency division multiplexing (OFDM) signal transmitted over 80 km standard single mode fiber (SSMF). The results show that the error propagation can be effectively eliminated and BER performance can be improved significantly under the low CSPR condition. The realization has been made for the error-free 256Gb/s transmission over 80 km SSMF with the low CSPR range of 2-3 dB. Meanwhile, under the same conditions, the CSPR required by the proposed scheme to reach the 20% soft decision-forward error correction (SD-FEC) and 7% hard decision-forward error correction (HD-FEC) can be reduced by 1.3 dB and 2.8 dB, respectively, with a comparison of the conventional S-CADD methods, which shows the feasibility of our proposed method in the potential short-reach optical transmissions.
2. Basic principle
2.1 S-CADD configuration
Figure 1 shows the general structure of S-CADD receiver, which consists of a 90° optical hybrid, an optical delay line (ODL), and two balanced photo-detectors (BPDs) [15]. We represent the received complex valued DSB signal as C + S(t) with C and S(t) for the carrier and desired signal, respectively. Correspondingly, the signal after ODL and PD detection, can be expressed as follows,
Fig. 1. Schematic of the S-CADD receiver. OC: optical coupler. ODL: optical delay line. BPD: balanced photo-detectors
2.2 System setup
The system configuration built by MATLAB and VPI co-simulation is shown in Fig. 2(a). At the transmitter, the OFDM signals is generated by MATLAB with a fast Fourier transform (FFT) size of 4096 and 2184 sub-carriers filled with 16 QAM symbols. The sampling rate is set to 120 GSa/s corresponding to 64Gbaud 16QAM DSB signal with a raw rate of 256Gb/s. At the receiver, to make a best use of the low-frequency range with considering the device's bandwidth limitations, the signal frequency band is divided into 8 sub-bands on average with each occupying 8 GHz and a 2 GHz guard band is inserted in between neighboring sub-bands referring to the allocation method of signal and guard band in [19]. The ODL is set to 50ps.Thus, the total frequency band occupied by the signal and the guard band is within [-39 GHz, 39 GHz]. Meanwhile, a 256-point circular prefix (CP, 1/16 of one OFDM symbol) at the head of each OFDM symbol has been inserted to alleviate inter symbol interference (ISI) caused by dispersion (CD). The laser is split into two channels, one for modulating the signal and the other as the optical carrier used to control the CSPR through variable optical attenuator (VOA). After the modulation signal combined with the optical carrier, it is amplified by EDFA and fed into the 80 km SSMF with dispersion coefficient of 16e-6 s/m^2 and the nonlinear coefficient of 2.6e-20 m^2/W. And only the additive white Gaussian noise (AWGN) has been considered in the study. At the receiver end after the BPD detection by the S-CADD receiver, the subsequent optical field recovery is processed by offline DSP, including resampling, FFT, channel equalization, SSBI iterative mitigation, symbol decision, and bit error rate calculation. It should be noted that the addition modules shown in Fig. 2(b) and (c) are the operations of DPD and clipping-based SSBI cancellation, which have not been applied in the previously reported CADD systems.
Fig. 2. (a) Simulation system configuration. (b) transmitter side DSP modules, and (c) receiver side DSP modules. Inset: optical spectrum of the generated 64GBaud 16QAM DSB signal. EDFA: erbium-doped fiber amplifier. DAC: digital-to-analog convertor. ADC: analog-to-digital convertor. VOA: variable optical attenuator. OC: optical coupler. DPD: digital pre-distortion
2.3 SSBI mitigation based on digital pre-distortion
At present, the performance of CADD receiver is mostly affected by the non-ideal transfer function as shown in Fig. 3(a). Near the zero-magnitude frequencies of the transfer function, SSBI will be seriously enhanced, and then needs to be inserted a guard band. In S-CADD receiver, the SSBI enhanced range, which takes up one-third of a cycle of the transfer function, can be identified by |H(f)|<1. As shown in Fig. 3(a) and (b), the variation trend of SNR with frequency is consistent with that of the transmission function. Namely, the closer the transfer function is to zero-magnitude frequencies, the lower the SNR will be.
Fig. 3. (a) Magnitude of transfer function H(f) for CADD. (b) SNR versus frequency without DPD. (c) optical Spectrum after DPD. (d) SNR versus frequency with DPD. iter.: iteration.
Therefore, with aiming to mitigate the SSBI, we introduce the DPD algorithm to improve the SNR near the zero-magnitude frequencies of the transfer function. And this DPD operation is performed before IFFT at the Tx DSP, can be shown as follows,
where S(f) and ${S_{pre\; }}(f )$ represents signal spectra before and after the DPD, γ represents the DPD coefficient within the range of [0,1). After DPD processing, the signal power becomes higher in the SSBI enhanced range as shown in Fig. 3(c). Therefore, as shown in Fig. 3(d), by adopting the DPD processing, the averaged SNR performance can be improved obviously and then bring the BER performance improvement.2.4 Clipping-based SSBI reconstruction
In the case of low CSPR, the traditional four-iteration process cannot fully converge the system performance, so the number of iterations is further increased. However, the error propagation in the process of iterative SSBI mitigation would be significant. After several iterations, the BER performance deteriorates sharply, leading to the divergent iteration and the failed signal reconstruction. This phenomenon can be interpreted as that a small carrier is not enough to suppress the enhanced SSBI noise, which has an impact on the symbol decision of the desired signal. In particular, the peak sample brought about by enhanced SSBI has a serious impact on the signal. The inaccuracy of the decision signal further leads to the inaccuracy of the SSBI reconstruction and reduces the reliability of the iterative mitigation of the SSBI. With the increase of the number of iterations, these errors will continue to accumulate, and eventually lead to the occurrence of error propagation. In view of this phenomenon, we propose a clipping-based SSBI iteration mitigation scheme as shown in Fig. 4. The iterative closed-loop process includes reload chromatic dispersion (CD), IFFT, clipping, reconstruct SSBI, SSBI scaling factor of β and FFT.
Fig. 4. Clipping-based SSBI iterative mitigation scheme. FFT: fast Fourier transform. IFFT: inverse fast Fourier transform. $\textrm{C}{\textrm{D}^{ - 1}}$: chromatic dispersion compensation. CD: reload chromatic dispersion. β: SSBI scaling factor.
Clipping the signal after each iteration can effectively eliminate the peak sample caused by the estimation error, ensure the boundedness of the system, and maintain the stability of the iteration. Although some clipping noise may be introduced into the desired signal, it can effectively avoid the increase of SSBI noise that may occur in the iterative process and then prevent the occurrence of error propagation [20,21]. The clipping rule is given as follows,
3. Parameter optimization
3.1 Digital pre-distortion coefficient
We firstly optimize the DPD coefficient in the range of [0,1). The degree of DPD transitions from no pre-distortion to full pre-distortion of the receiver response [22]. Note that when γ = 1, there are several infinite discontinuity points in the DPD function, so a close value should be selected as a reference, such as γ = 0.99. The performance comparison results are presented in Fig. 5. Note that in the simulation process, to evaluate the performance of the proposed scheme, 20 iterations are pre-allocated to make the system performance fully converge.
Fig. 5. (a) BER versus γ at different CSPR. (b) CSPR = 3 dB, BER versus iteration numbers at different $\gamma $. (c) BER versus CSPR under conventional scheme and DPD scheme. conv.: conventional. DPD: digital pre-distortion.
At first, the DPD coefficient γ is swept and optimized as shown in Fig. 5(a). The optimal γ is different under different CSPR. When CSPR equal to 3, 5, 7 dB, the corresponding optimal values are 0.4, 0.3, 0.2, respectively. The larger the CSPR, the smaller the optimal DPD coefficient. This can be interpreted as that in the case of a sufficiently large carrier, SSBI has been effectively suppressed, so the performance improvement brought by DPD is limited. As shown in Fig. 5(b), DPD can accelerate iterative convergence and improve BER performance. This is because that the DPD scheme reduces the interference of SSBI near the zero-magnitude frequencies of the transfer function, realizes relatively accurate preliminary symbol decision and reduces the number of iterations. We also compare the relationship between BER and CSPR under conventional and DPD processing as shown in Fig. 5(c). Each data point of the curve with DPD uses the data obtained under the premise of the optimal DPD of each CSPR. The DPD processing has a better optimization effect for low CSPR (3 dB) than for high CSPR (9 dB). Moreover, the optimal CSPR is about 4 dB for the proposed DPD based system while is 6 dB for the conventional based system. Namely, 2 dB CSPR can be reduced by use of the proposed method. When CSPR < 3 dB, the BER performance will degrade sharply, which is caused by the error propagation. Therefore, the performance with low CSPR should be improved and it is the focus of our work in the subsequent part.
3.2 Clipping ratio
As shown in Fig. 6(a), the error propagation phenomenon occurs under low CSPR. When CSPR ≤ 2 dB, we can see that the system performance deteriorates dramatically after several iterations, and no improvement can be obtained in subsequent iterations and even gets worse due to the accumulated errors in the iteration process. This can be understood from the reduction of PAPR of the signal as shown in Fig. 6(b). In the absence of clipping operation, the PAPR of the reconstructed signal rapidly increases after several iterations, which brings serious error accumulation to the iterative closed loop. It can be seen from the figure that PAPR can be effectively stabilized by proper clipping ratio. For CSPR = 2 dB, the BER performance vs. the clipping ratio has been shown in Fig. 6(c). The system performance can be optimized when the clipping ratio = 7 dB. Therefore, the overall estimation error of SSBI can be effectively reduced and error propagation can be avoided when the appropriate clipping ratio is selected.
Fig. 6. (a) BER versus iteration numbers at different CSPR. (b) PAPR versus iteration number with different clipping ratio at CSPR = 2 dB. (c) BER versus clipping ratio at CSPR = 2 dB. conv.: conventional processing. clip.: clipping ratio.
4. Results and discussion
In this section, we validate the performance improvement of the proposed joint processing method of the 256Gb/s S-CADD transmission system shown in Fig. 2. Here, the clipping ratio and the DPD coefficient under different CSPR have been adjusted to the optimal parameters according to the method in the previous chapter.
As shown in Fig. 7, the BER performance vs. CSPR has been compared with the conventional and the proposed methods. Note that there are two points in particular: 1) the abnormal steepness of the curve in the figure is caused by error propagation. And the critical point of error propagation occurs near the steepness region. 2) In the case of large CSPR (> 3 dB), the system performance has not obvious improvement with/without clipping, while it can be significantly improved at low CSPR (< 3 dB) with clipping due to the error propagation effectively eliminated. Moreover, by adopting the DPD scheme, the BER performance of the system in the low CSPR region can be significantly improved, and the critical point of error propagation is slightly shifted to the left (red curve and blue curve). Compared with traditional S-CADD, the CSPRs required by the proposed joint clipping and digital pre-distortion (C-DPD) scheme can be reduced by 1.3 dB and 2.8 dB under the 20% SD-FEC and 7% HD-FEC respectively.
Fig. 7. BER versus CSPR under different conditions. conv.: conventional processing. clip.: clipping ratio. DPD: digital pre-distortion. C-DPD: clipping and digital pre-distortion.
In order to research the number of iterations required for error-free transmission in the S-CADD receiver of the proposed scheme, the relationship between the BER performance vs. iterations was measured, as shown in Fig. 8. As mentioned earlier, in the case of CSPR = 2 dB and no clipping, error propagation will occur, and BER performance deteriorates rapidly after several iterations. After adding clipping, BER performance can be slowly optimized with the increase of iterations without error propagation, but more iterations are required. After adopt C-DPD scheme, the BER performance of the system is greatly improved. Compared with only clipping scheme, BER performance converges faster and requires fewer iterations to achieve the same BER. For the C-DPD scheme, when the number of iterations is 16, the system performance tends to be stable.
Fig. 8. CSPR = 2 dB, BER versus iteration numbers under different conditions. conv.: conventional processing. clip.: clipping ratio. DPD: digital pre-distortion. C-DPD: clipping and digital pre-distortion.
The BER vs. OSNR has been shown in Fig. 9 when CSPR = 2 dB and the number of iterations is 16. Obviously, the error propagation leads to performance deterioration at low CSPR without clipping. Even if the OSNR is high enough and without distortion in the transmitter, no improvement can be obtained without clipping. However, the BER performances can be significantly improved when the clipping operation is applied in the receiver without distortion. And, the improvement is further significant when C-DPD scheme is used. Compared with only clipping scheme, the C-DPD scheme can realize an OSNR gain of 3 dB for 20% SD-FEC limit and 5.1 dB for 7% HD-FEC limit respectively. The difference of OSNR gain under the two FEC thresholds is originated from the dominant noise under the different OSNR condition. At the 20% SD-FEC threshold, the ASE noise is the main factor affecting the performance, while at the 7% HD-FEC threshold, the main factor affecting the performance is the residual SSBI. Since the C-DPD scheme has a better SSBI mitigation effect than the clipping scheme only, the gain under the 7% HD-FEC threshold is more significant than that under the 20% SD-FEC threshold.
Fig. 9. CSPR = 2 dB, Iteration = 16, BER versus OSNR under different conditions. conv.: conventional processing. clip.: clipping ratio. DPD: digital pre-distortion. C-DPD: clipping and digital pre-distortion.
5. Conclusion
In summary, we propose a joint SSBI mitigation method to improve system performance for the two issues of the non-uniform distribution of subcarrier SNR caused by non-ideal transfer function, and the error propagation caused by enhanced SSBI. By adopting the proposed joint mitigation method, we can realize the optical field recovery of S-CADD under low CSPR without sacrificing electrical spectral efficiency. Through the simulation, the DPD coefficient and clipping ratio have been optimized to improve the system performance corresponding to the required CSPR, iteration number, and OSNR sensitivity. Compared with traditional S-CADD, the CSPR required by the proposed scheme to reach the 20% SD-FEC and 7% HD-FEC can be reduced by 1.3 dB and 2.8 dB, respectively. Therefore, this scheme provides an effective method for optical field recovery under low CSPR. The results show that the proposed scheme can be used to improve the performance of short-reach optical interconnect.
Funding
National Key Research and Development Program of China (2023YFB2906304); National Natural Science Foundation of China (62022029, U22A2087); Guangdong Introducing Innovative and Entrepreneurial Teams of “The Pearl River Talent Recruitment Program” (2019ZT08X340); Guangdong Guangxi Joint Science Key Foundation (2021GXNSFDA076001); Guangdong Basic and Applied Basic Research Foundation (2023A1515010877).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. F. Al-Turjman, E. Ever, and H. Zahmatkesh, “Small cells in the forthcoming 5 G/IoT: traffic modelling and deployment overview,” IEEE Commun. Surv. Tutorials 21(1), 28–65 (2019). [CrossRef]
2. L. Jiang, L. Yan, A. Yi, et al., “Integrated components and solutions for high-speed short-reach data transmission,” Photonics 8(3), 77 (2021). [CrossRef]
3. C. Kachris, K. Kanonakis, and I. Tomkos, “Optical interconnection networks in data centers: recent trends and future challenges,” IEEE Commun. Mag. 51(9), 39–45 (2013). [CrossRef]
4. B. Briscoe, A. Brunstrom, A. Petlund, et al., “Reducing internet latency: a survey of techniques and their merits,” IEEE Commun. Surv. Tutorials 18(3), 2149–2196 (2016). [CrossRef]
5. K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightwave Technol. 34(1), 157–179 (2016). [CrossRef]
6. T. Gui, X. Wang, M. Tang, et al., “Real-time demonstration of 600 Gb/s DP-64QAM Self-Homodyne coherent bi-direction transmission with un-cooled DFB laser,” Proc. Optical Fiber Communication Conference, paper Th4C.3 (2020).
7. K. Zhong, X. Zhou, J. Huo, et al., “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018). [CrossRef]
8. Q. Hu, D. Che, Y. Wang, et al., “Advanced modulation formats for high-performance short-reach optical interconnects,” Opt. Express 23(3), 3245–3259 (2015). [CrossRef]
9. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]
10. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers–Kronig receivers,” Adv. Opt. Photon. 11(3), 480–517 (2019). [CrossRef]
11. C. Sun, D. Che, H. Ji, et al., “Investigation of single-and multi-carrier modulation formats for Kramers–Kronig and SSBI iterative cancellation receivers,” Opt. Lett. 44(7), 1785–1788 (2019). [CrossRef]
12. S. T. Le, K. Schuh, M. Chagnon, et al., “1.72Tb/s virtual-carrier assisted direct-detection transmission over 200 km,” J. Lightwave Technol. 36(6), 1347–1353 (2018). [CrossRef]
13. W. Shieh, C. Sun, and H. Ji, “Carrier-assisted differential detection,” Light: Sci. Appl. 9(1), 18 (2020). [CrossRef]
14. C. Sun, T. Ji, H. Ji, et al., “Experimental demonstration of complex-valued DSB signal field recovery via direct detection,” IEEE Photon. Technol. Lett. 32(10), 585–588 (2020). [CrossRef]
15. Y. Zhu, L. Li, Y. Fu, et al., “Symmetric carrier assisted differential detection receiver with low-complexity signal-signal beating interference mitigation,” Opt. Express 28(13), 19008–19022 (2020). [CrossRef]
16. T. Ji, C. Sun, H. Ji, et al., “Field recovery at low CSPR using interleaved carrier assisted differential detection,” Proc. Optical Fiber Communication Conference, paper W4A.3 (2020).
17. T. Ji, C. Sun, H. Ji, et al., “Theoretical and experimental investigations of interleaved carrier-assisted differential detection,” J. Lightwave Technol. 39(1), 122–128 (2021). [CrossRef]
18. P. Qin, C. Bai, Z. Wang, et al., “Offset double sideband carrier assisted differential detection with field recovery at low carrier-to-signal power ratio,” Opt. Express 30(26), 48112–48132 (2022). [CrossRef]
19. J. Li, Z. Wang, H. Ji, et al., “High electrical spectral efficiency silicon photonic receiver with carrier-assisted differential detection,” Proc. Optical Fiber Communication Conference, paper Th4B.6 (2022).
20. S. T. Le, V. Aref, K. Schuh, et al., “30 Gbaud 128 QAM SSB direct detection transmission over 80 km with clipped iterative SSBI cancellation,” Proc. Optical Fiber Communication Conference, paper M4F.2 (2020).
21. S. T. Le, V. Aref, K. Schuh, et al., “Power-efficient single-sideband transmission with clipped iterative SSBI cancellation,” J. Lightwave Technol. 38(16), 4359–4367 (2020). [CrossRef]
22. X. Li, H. Ji, L. Liu, et al., “Asymmetric self-coherent detection with mitigated SSBI enhancement using partial pre-compensation,” Proc. Eur. Conf. Opt. Commun., paper 1–4 (2022).
