Multi-span digital non-linear compensation for dual-polarization quadrature phase shift keying long-haul communication systems
Introduction
Recent numerical and experimental studies have shown that coherent optical QPSK (CO-QPSK) is the promising candidate for next-generation 100 Gbit/s Ethernet (100 GbE) [1]. Coherent detection allows digital signal processing to adaptively compensate for chromatic dispersion (CD) and polarization mode dispersion (PMD), which are both linear effects of fiber. Despite of fiber non-linearities, which are the major limiting factors, next-generation optical systems are employing higher order modulation formats in order to fulfil the ever increasing demand of capacity requirements [2].
DSP techniques are gaining increasing importance as they allow for robust long-haul transmission with mitigation of fiber transmission impairments at the receiver [3], [4]. One of these methods is digital backward propagation (DBP) which can jointly mitigate CD and NL. Pioneering concepts on DBP can be found in [5], [6]. A number of investigations have been done with coherent detection and split-step Fourier method (SSFM) [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. It has been demonstrated that DBP in a single-channel transmission can be improved by using modified split-step Fourier method (M-SSFM) [17], [18]. Modification is done by shifting the non-linear operator calculation point Nlpt (r) along with the optimization of dispersion D and non-linear coefficient γ to optimize the system performance. The parameter Nlpt (r) determines the position of two dispersion (D) blocks in the symmetric split step Fourier method (SSFM). It is also observed in [18] that during each DBP step intensity of the out-of-band distortions becomes higher. The distortion is produced by high-frequency intensity fluctuations in the non-linear sections of DBP algorithm. This limits the performance of DBP in the form of noise. To overcome this problem a low pass filter (LPF) is introduced in each DBP step [18]. Digital LPF limits the bandwidth of the compensating waveform so we can optimize the compensation for the low-frequency intensity fluctuations without overcompensating for the high-frequency intensity fluctuations. But the studies in [18] are limited to single channel transmission with 56 Gbit/s system. Recent investigations [14], [15] shows the suitability of DBP on higher order modulation formats, up to 256-QAM. However actual implementation of the DBP algorithm is now-a-days extremely challenging due to its complexity. The performance is mainly dependent on the computational step-size (h) for multi-channel (WDM) and higher baud-rate transmissions [19], [20].
In order to reduce the computations of the algorithm, by increasing the step-size (i.e. reducing the number of DBP stages per fiber span), a method called correlated DBP (CBP) has been introduced [21]. The investigation of a 100 GHz channel spaced 28 GBaud DP-QPSK transmission system and multi-span CBP shows a reduction of DBP stages by 75%, having the same level of improvement as in the conventional DBP algorithm. In the efforts to reduce the calculation steps per fiber span, there is a trade-off relationship between achievable Q-improvement and algorithm complexity in the DBP. Therefore simplification of the DBP model to efficiently describe fiber transmission especially for polarization multiplexing (POLMUX) signals and an estimation method to precisely optimize parameters are the keys for its future real-time implementation. Especially in the dense wavelength division multiplexed (DWDM) transmission systems, i.e. 50 GHz channel spacing or less where the performance is limited by the inter-play of intra-channel, inter-channel non-linearities. The first experimental demonstration of narrow spaced 10 channel 112 Gbit/s/ch DP-QPSK was reported in [22] and the system performance by using DBP with different baud-rates are investigated in [23]. In [23], investigations show that optimum system performance using DBP is obtained by using 2, 4 and 8 steps per fiber span for 14 GBaud, 28 GBaud and 56 GBaud respectively. A low complexity non-linear compensator scheme [24] with automatic control loop is also investigated. The proposed simple non-linear compensator requires considerably lower implementation complexity and can blindly adapt the required coefficients. In uncompensated links, the simple scheme is not able to improve performance, as the non-linear distortions are distributed over different amounts of CD-impairments. Therefore, the DBP algorithms with less computational efforts and higher improvement in system performance as compared to conventional methods are very attractive.
The conventional DBP techniques are implemented with constant step-size SSFM methods. The use of these methods, however, need the optimization of D, γ and r for efficient mitigation of CD and NL. Also that numerical solution of NLSE with SSFM with constant step-size may cause the spurious spectral peaks. To avoid this numerical artifact and estimating the non-linear phase shift with high accuracy in fewer computations by SSFM, [25], [26] suggest a logarithmic step-size distribution for forward propagation simulations. In the most recent studies logarithmic step-size based DBP (L-DBP) has been investigated to explore the simplified and efficient implementation of backward propagation using SSFM [27]. The basic motivation of implementing logarithmic step-size relates to the fact of exponential decay of signal power and thus NL phase shift in the beginning sections of each fiber span. Therefore requiring more accuracy to estimate NL phase shift phiNL. The logarithmic step-size based DBP algorithm shows overall better system performance than conventional DBP algorithm hence enhancing the non-linear tolerance of the transmission system. The benefit of the logarithmic step-size is the reduced complexity and computational time which is less than conventional M-SSFM based DBP at higher baud rates i.e. 56 GBaud systems. Moreover, in [27] we have investigated transmission systems with diverse baud rates and the results depict: (a) the simplification of DBP algorithm as it eliminates the optimization of the DBP parameters and same forward propagation parameters (FP) parameters can be used to implement logarithmic step-size and (b) additional improvement in system performance in case of L-DBP as compared to conventional DBP method at higher baud rates. Importantly, it is shown in [27], [28], [29], [30] that the logarithmic algorithm works efficiently, both in single-channel and multi-channel transmission, as compared to the conventional methods as described in [17], [18].
In this paper we have extended our previous investigations [28], [29] and focus on the reduction of required DBP stages as compared to number of fiber spans (multi-span DBP) for transmission link under investigation. We have numerically investigated and implemented a low-pass-filter (LPF) in each L-DBP stage. This is the first investigation of implementing LPF with logarithmic digital backward propagation algorithm for the performance of evaluation of multi-channel transmission. Our results shows efficient compensation of CD and NL in the transmission system with 14 GBaud, 28 GBaud and 56 GBaud rates along with 25 GHz, 50 GHz and 100 GHz channel spacing respectively. Most importantly, by using filtered logarithmic step-size based digital backward propagation (FL-DBP) required number of DBP stages are significantly reduced (decreased computational effort) and also depicts additional improvement in system performance than conventional DBP methods.
Section snippets
Numerical model and digital signal processing module
The DP-QPSK signals are transmitted over 2000 km (25 spans) single mode fiber (SMF) with parameters of α = 0.2 dB/km, D = 16 ps/(nm–km) and γ = 1.2(km− 1.W− 1). In order to investigate the same-capacity and same-bandwidth WDMDP-QPSK transmission systems, the following simulation systems are configured: (a) 20 channel 56 Gbit/s (14 GBaud) with 25 GHz channel spacing, (b) 10 channel 112 Gbit/s (28 GBaud) with 50 GHz channel spacing and (c) 5 channel 224 Gbit/s (56 GBaud) with 100 GHz channel spacing. So that each
Results and discussions
The simulation results for system 1 i.e. 14 GBaud transmission system is given in Fig. 2, as a function of signal input launch power. The Q-value of the system is monitored for LDC, L-DBP and FL-DBP algorithms. In our investigations, we implement the L-DBP algorithm on per span basis i.e. 25 calculation steps for the transmission link. By analysing the results in Fig. 2, DBP algorithms show better performance as compared to LDC showing efficient compensation of dispersion and non-linearities.
Conclusion
We numerically investigate logarithmic step-size distribution method for implementing efficient digital backward propagation (DBP) algorithm using split-step Fourier method (SSFM). The algorithm is evaluated for 2000 km SMF for the following simulation systems; (a) 20 channel 56 Gbit/s (14 GBaud) with 25 GHz channel spacing , (b) 10 channel 112 Gbit/s (28 GBaud) with 50 GHz channel spacing and (c) 5 channel 224 Gbit/s (56 GBaud) with 100 GHz channel spacing, so that each simulation configuration has the
Acknowledgements
The authors gratefully acknowledge the funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the excellence initiative.
References (30)
- et al.
Optics Communications
(December 2011) - et al.
IEEE Journal of Lightwave Technology
(January 2008) - et al.
Nature
(April 2001) - et al.
Optics Express
(March 2007) Advances in Optics and Photonics
(February 2009)- et al.
Optics Letters
(March 2003) - et al.
Optics Letters
(September 1996) - et al.
Optics Express
(January 2008) - et al.
IEEE Journal of Lightwave Technology
(October 2008) - et al.
IEEE Journal of Selected Topics in Quantum Electronics
(September 2010)
IEEE Photonics Technology Letters
IEEE Photonics Journal
Optics Express
Optics Express
Cited by (24)
Performance enhanced down-stream signalling for next generation long-reach 10 Gbit/s passive optical networks
2014, OptikCitation Excerpt :The joint compensation of linear and non-linear transmission impairments is implemented by inversely solving the non-linear Schrödinger equation (NLSE), as in Eq. (1). This method is termed as Digital Backpropagation (BP) [5,6] and it is a topic of high interest in recent years. We have implemented BP algorithm by using the simplest symmetric split-step Fourier method (SSFM) with constant step-size method [6], as in Eq. (2).
Compensation of linear and nonlinear signal distortion by optimized digital backward propagation
2020, Photonische Netze - 13. ITG-FachtagungAll-optical and digital non-linear compensation algorithms in flex-coherent grouped and un-grouped contiguous spectrum based networks
2016, Optical and Quantum ElectronicsSignal processing algorithms for down-stream traffic in next generation 10 Gbit/s fixed-grid passive optical networks
2014, Advances in OptoElectronics