Digital Backward Propagation Algorithm Research Articles

Evaluation of correlative coding and DP-16QAM n-channel 112Gbit/s coherent transmission: digital non-linear compensation perspective

We numerically report on the complexity reduction of digital backward propagation (DBP) by utilizing correlative encoded transmission (dual-polarization quadrature duobinary) at a bit-rate of 112Gbit/s over 1640km fiber link. The single channel (N=1) and multi-channel (N=10) transmission performances are compared in this paper. In case of multi-channel system, 10 transmitters are multiplexed with 25GHz channel spacing. The fiber link consists of Large A(eff) Pure-Silica core fiber with 20 spans of 82km each. No in-line optical dispersion compensator is employed in the link. The system performances are evaluated by monitoring the bit-error-ratio and the forward error correction limit corresponds to bit-error-ratio of 3.8×10(-3). The DBP algorithm is implemented after the coherent detection and is based on the logarithmic step-size based split-step Fourier method. The results depict that dual-polarization quadrature duobinary can be used to transmit 112Gbit/s signals with an spectral efficiency of 4-b/s/Hz, but at the same time has a higher tolerance to nonlinear transmission impairments. By utilizing dual-polarization quadrature duobinary modulation, comparative system performance with respect to dual-polarization 16-quadrature amplitude modulation transmission can be achieved with 60% less computations and with a step-size of 205km.

Application of a digital non-linear compensation algorithm for evaluating the performance of root-raised-cosine pulses in 112 Gbit s−1 DP-QPSK transmission

In this paper, we numerically investigate the non-linear tolerance of root-raised-cosine (RRC) pulse shaping by interpolating finite impulse response (FIR) filters in conjunction with digital backward propagation (DBP) in coherent 112 Gbit s−1 dual-polarization quadrature phase shift keying (DP-QPSK) transmission. The results depict that RRC pulses are more tolerant to intra-channel non-linearities, i.e. self-phase modulation (SPM), as compared to standard RZ-33 and NRZ pulses. The non-linear threshold point is improved by using RRC pulses by a factor of 2 dB signal input power as compared to RZ pulses and by 4 dB signal launch power as compared to NRZ pulses. The behavior of RRC pulses is also investigated with standard single mode fiber (SMF), non-zero dispersion shifted fiber (NZDSF) and next-generation large Aeff pure silica core fiber (LA-PSCF). Most importantly multi-span DBP is implemented and in the case of RRC pulses the computational efforts of the conventional DBP algorithm are reduced by 80% with a diminutive Q-penalty of 0.74 dB. The duty cycle of the RRC pulses is further optimized for efficient system performance. We have also compared the performance of single-channel transmission with the multi-channel transmission, where the performance is limited due to inter-channel non-linear effects. Furthermore, the non-linear tolerance of RRC pulses is investigated with; (a) different amplifier spacing and (b) variation in transmission link design information for the DBP algorithm.

Efficient compensation of chromatic dispersion and nonlinearities using logarithmic digital backward propagation in N-channel DWDM 1.12Tbit/s DP-QPSK transmission

We propose and numerically investigate the logarithmic step-size distribution for implementing an efficient digital backward propagation (DBP) algorithm using the split-step Fourier method (SSFM). DBP is implemented in N-channel dual-polarization quadrature-phase-shift-keying (DP-QPSK) transmission over 2000 km standard single-mode fiber (SMF) with no in-line optical dispersion compensation. This algorithm is compared with the constant step-size modified DBP (M-SSFM) algorithm in terms of efficiency, complexity and computational time. Furthermore, we investigate the same-capacity and same-bandwidth transmission systems with 14 Gbaud (GBd), 28 GBd and 56 GBd per-channel rates. The logarithmic step-size based DBP algorithm depicts efficient mitigation of chromatic dispersion (CD) and nonlinear (NL) impairment. The benefit of the logarithmic step-size is the reduced complexity and computational time for higher baud rates.

Multi-span digital non-linear compensation for dual-polarization quadrature phase shift keying long-haul communication systems

We have numerically investigated a method to reduce the complexity of the digital backward propagation algorithm (DBP). A filtered logarithmic step-size based split-step Fourier method (SSFM) is investigated in this paper to digitally compensate chromatic dispersion (CD) and non-linearities (NL) in dual-polarization quadrature phase shift keying (DP-QPSK) systems. The algorithm was evaluated for coherently-detected multiple channel DP-QPSK system over un-compensated transmission links with diverse baud-rates i.e. 14GBaud, 28GBaud and 56GBaud. The results depict efficient mitigation of CD and NL, therefore improving the non-linear threshold point (NLT) by 4dB. Furthermore by implementing a low-pass-filter (LPF) in each DBP stage, the required number of DBP stages are significantly reduced (multi-span DBP) by 75%. The results delineate improved system performance of logarithmic step size based filtered DBP (FL-DBP) both in terms of efficiency and complexity which will be helpful in future deployment of DBP algorithm with real-time signal processing modules for non-linear compensation.

Impact of channel baud-rate on logarithmic digital backward propagation in DP-QPSK system with uncompensated transmission links

We numerically investigate the impact of channel baud-rate on the performance of logarithmic step-size based spilt-step Fourier method (SSFM). This algorithm is used to implement digital backward propagation (DBP) to efficiently compensate fiber chromatic dispersion (CD) and non-linearities (NL). The DBP method is implemented in N-channel dual-polarization quadrature phase shift keying (DP-QPSK) transmission over 2000 km standard single mode fiber (SMF) with no in-line optical dispersion compensation. We investigate the same-capacity and same-bandwidth transmission systems with 56 Gbit/s/ch (14 GBaud), 112 Gbit/s/ch (28 GBaud) and 224 Gbit/s/ch (56 GBaud). Each system has the bandwidth occupancy of 500 GHz with a total transmission capacity of 1.12 Tbit/s. Moreover, we have also compared the multiple channel transmission performance with single channel transmission to quantify the impact of inter-channel (cross-phase modulation ‘XPM’ and four-wave mixing ‘FWM’) and intra-channel (self-phase modulation ‘SPM’) non-linearities. The logarithmic step-size based DBP algorithm (L-DBP) depicts efficient mitigation of CD and NL impairments. The benefit of the logarithmic step-size is the reduced complexity and computational time for higher baud-rate transmission systems.

Optimized digital backward propagation for phase modulated signals in mixed-optical fiber transmission link

The parametric optimization of Digital Backward Propagation (DBP) algorithm for mitigating fiber transmission impairments is proposed and numerically demonstrated for phase modulated signals in mixed-optical fiber transmission link. The optimization of parameters i.e. dispersion (D) and non-linear coefficient (γ) offer improved eye-opening (EO). We investigate the optimization of iterative and non-iterative symmetric split-step Fourier method (S-SSFM) for solving the inverse non-linear Schrödinger equation (NLSE). Optimized DBP algorithm, with step-size equal to fiber module length i.e. one calculation step per fiber span for obtaining higher computational efficiency, is implemented at the receiver as a digital signal processing (DSP) module. The system performance is evaluated by EO-improvement for diverse in-line compensation schemes. Using computationally efficient non-iterative symmetric split-step Fourier method (NIS-SSFM) upto 3.6 dB referenced EO-improvement can be obtained at 6 dBm signal launch power by optimizing and modifying DBP algorithm parameters, based on the characterization of the individual fiber types, in mixed-optical fiber transmission link.

Numerical evaluation of the functional boundaries of digital backward propagation algorithm for mitigating non-linear impairments in phase encoded transmission

We numerically evaluate the robustness of digital backward propagation (DBP) algorithm for the mitigation of fiber transmission impairments in phase encoded transmission. We have investigated DBP algorithm by varying physical parameters of transmission i.e. bit rates, modulation formats, fiber transmission length and fiber spans of unequal length. The system performance is evaluated by Q-factor. Through the imperative evaluation of the effective transmission impairments mitigation at different instants, we identify functional limits of DBP algorithm. These methodological studies could be used in next generation optical networks to formulate flexibility in the algorithm to adopt and identify changes in the physical network paths.