Optical fiber transmission is impacted by linear and nonlinear impairments. We study the use of digital backpropagation (BP) in conjunction with coherent detection to jointly mitigate dispersion and fiber nonlinearity. We propose a noniterative asymmetric split-step Fourier method (SSFM) for solving the inverse nonlinear Schrodinger equation (NLSE). Using simulation results for RZ-QPSK transmitted over terrestrial systems with inline amplification and dispersion compensation, we obtain heuristics for the step size and sampling rate requirements, as well as the optimal dispersion map.

Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation

Fibre-optic communications systems have traditionally carried data using binary (on-off) encoding of the light amplitude. However, next-generation systems will use both the amplitude and phase of the optical carrier to achieve higher spectral efficiencies and thus higher overall data capacities(1,2). Although this approach requires highly complex transmitters and receivers, the increased capacity and many further practical benefits that accrue from a full knowledge of the amplitude and phase of the optical field(3) more than outweigh this additional hardware complexity and can greatly simplify optical network design. However, use of the complex optical field gives rise to a new dominant limitation to system performance-nonlinear phase noise(4,5). Developing a device to remove this noise is therefore of great technical importance. Here, we report the development of the first practical ('black-box') all-optical regenerator capable of removing both phase and amplitude noise from binary phase-encoded optical communications signals.

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All-optical phase and amplitude regenerator for next-generation telecommunications systems

Recent progress in coherent optical communication, a field revived by advances in digital signal processing (DSP), is reviewed. DSP-based phase and polarization management techniques make coherent detection robust and practical. With coherent detection, the complex field of the received signal is fully recovered, allowing compensation of linear impairments including chromatic dispersion and polarization-mode dispersion using digital filters. In addition, fiber nonlinearities can also be compensated by using backward propagation in the digital domain.

Recent advances in coherent optical communication

Digital backpropagation (BP) is a universal method for jointly compensating dispersion and nonlinear impairments in optical fiber and is applicable to signals of any modulation format. In this paper, we compare single carrier (SC) versus orthogonal frequency-division multiplexing (OFDM) for polarization-multiplexed transmission. We show that at realistic data rates and transmission distances, polarization mode dispersion does not significantly degrade the performance of BP and can be mitigated by a post-BP linear equalizer. Dispersion unmanaged transmission can significantly reduce nonlinearity, and in this transmission regime, SC and OFDM have similar nonlinear tolerance. Multichannel BP is effective at mitigating interchannel nonlinearity for point-to-point links.

Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission

Backpropagation has been shown to be the most effective method for compensating intra-channel fiber nonlinearity in long-haul optical communications systems. However, effective compensation is computationally expensive, as it requires numerous steps and possibly increased sampling rates compared with the baud rate. This makes backpropagation difficult to implement in real-time. We propose: (i) low-pass filtering the compensation signal (the intensity waveform used to calculate the nonlinearity compensation) in each backpropagation step and (ii) optimizing the position of the nonlinear section in each step. With numerical simulations, we show that these modifications to backpropagation improve system performance, reducing the number of backpropagation steps and reducing the oversampling for a given system performance. Using our ‘filtered backpropagation’, with four backpropagation steps operating at the same sampling rate as that required for linear equalizers, the Q at the optimal launch power was improved by 2 dB and 1.6 dB for single wavelength CO-OFDM and CO-QPSK systems, respectively, in a 3200 km (40 × 80km) single-mode fiber link, with no optical dispersion compensation. With previously proposed backpropagation methods, 40 steps were required to achieve an equivalent performance. A doubling in the sampling rate of the OFDM system was also required. We estimate this is a reduction in computational complexity by a factor of around ten.

Improved single channel backpropagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems

A universal post-compensation scheme for fiber impairments in wavelength-division multiplexing (WDM) systems is proposed based on coherent detection and digital signal processing (DSP). Transmission of 10 x 10 Gbit/s binary-phase-shift-keying (BPSK) signals at a channel spacing of 20 GHz over 800 km dispersion shifted fiber (DSF) has been demonstrated numerically.

Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing.

For original paper see Ben-Ezra et al., ibid., vol.17, no.9, p.1803 (2005). The authors point out that in the above letter, the rate equation model (REM) for quantum-dot (QD) semiconductor optical amplifiers (SOAs) is incorrect because the rate of carrier transition from the excited state (ES) of QD to the wetting layer (WL) was given by Nwh/tau2w, proportional to the carrier density in the WL (Nw).

Comments on “Theoretical Analysis of Gain-Recovery Time and Chirp in QD-SOA”

A method of designing a complementary filter pair is proposed to reduce error accumulation in the split-step backward propagation for distributed impairment compensation of wavelength-division-multiplexing transmission. The complementary filter pair is designed so that the individual errors of the two filters cancel each other. A 12 times 100 Gb/s 16-ary quadrature amplitude modulation transmission system in nonzero dispersion-shifted fiber is simulated using such a filter pair. The required filter length is halved by the complementary filter pair design for a transmission distance of 1200 km.

Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission

All-optical clock recovery from 40 Gbit/s non-return-to-zero (NRZ) data has been experimentally demonstrated by using a fibre-pigtailed Fabry–Perot filter and a self-pulsing two-section gain-coupled distributed feedback laser. The recovered clock has a measured root-mean-square (RMS) timing jitter of 1.2 ps. Error-free performance has been achieved in back-to-back bit error ratio (BER) tests using the optically recovered clock.

All-optical clock recovery of NRZ data at 40 Gbit/s using Fabry-Perot filter and two-section gain-coupled DFB laser

An all-optical carrier synchronization (carrier-phase and polarization recovery) scheme from binary phase-shift keying signals is proposed and demonstrated for the first time. The proposed scheme uses a degenerate optical parametric oscillator which has a phase-sensitive amplifier as a gain block.

Xiaoxu Li

Papers

Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing.

Comments on “Theoretical Analysis of Gain-Recovery Time and Chirp in QD-SOA”

Complementary FIR Filter Pair for Distributed Impairment Compensation of WDM Fiber Transmission

All-optical clock recovery of NRZ data at 40 Gbit/s using Fabry-Perot filter and two-section gain-coupled DFB laser

All-Optical Carrier Synchronization Using a Phase-Sensitive Oscillator