Ezra Ip

Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation

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.

Coherent detection in optical fiber systems

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

Feedforward Carrier Recovery for Coherent Optical Communications

We study a carrier-synchronization scheme for coherent optical communications that uses a feedforward architecture that can be implemented in digital hardware without a phase-locked loop. We derive the equations for maximum a posteriori joint detection of the transmitted symbols and the carrier phase. The result is a multidimensional optimization problem that we approximate with a two-stage iterative algorithm: The first stage is a symbol-by-symbol soft detector of the carrier phase, and the second stage is a hard-decision phase estimator that uses prior and subsequent soft-phase decisions to obtain a minimum mean-square-error phase estimate by exploiting the temporal correlation in the phase-noise process. The received symbols are then derotated by the hard-decision phase estimates, and maximum- likelihood sequence detection of the symbols follows. As each component in the carrier-recovery unit can be separately optimized, the resulting system is highly flexible. We show that the optimum hard-decision phase estimator is a linear filter whose impulse response consists of a causal and an anticausal exponential sequence, which we can truncate and implement as an finite-impulse- response filter. We derive equations for the phase-error variance and the system bit-error ratio (BER). Our results show that 4, 8, and 16 quadrature-amplitude-modulation (QAM) transmissions at 1 dB above sensitivity for BER = 10-3 is possible with laser beat linewidths of DeltanuTb = 1.3 X 10-4, 1.3 X 10-4, and 1.5 x 105 when a decision-directed soft-decision phase estimator is employed.

Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion

In this paper, we consider a fractionally spaced equalizer (FSE) for electronic compensation of chromatic dispersion (CD) and polarization-mode dispersion (PMD) in a dually polarized (polarization-multiplexed) coherent optical communications system. Our results show that the FSE can compensate any arbitrary amount of CD and first-order PMD distortion, provided that the oversampling rate is at least 3/2 and that a sufficient number of equalizer taps are used. In contrast, the amount of CD and PMD that can be corrected by a symbol-rate equalizer only approaches an asymptotic limit, and increasing the number of taps has no effect on performance due to aliasing that causes signal cancellation and noise enhancement.

Mode-division multiplexed transmission with inline few-mode fiber amplifier

We demonstrate mode-division multiplexed WDM transmission over 50-km of few-mode fiber using the fibers LP01 and two degenerate LP11 modes. A few-mode EDFA is used to boost the power of the output signal before a few-mode coherent receiver. A 6×6 time-domain MIMO equalizer is used to recover the transmitted data. We also experimentally characterize the 50-km few-mode fiber and the few-mode EDFA.

Nonlinear Compensation Using Backpropagation for Polarization-Multiplexed Transmission

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.

Fiber Impairment Compensation Using Coherent Detection and Digital Signal Processing

Next-generation optical fiber systems will employ coherent detection to improve power and spectral efficiency, and to facilitate flexible impairment compensation using digital signal processors (DSPs). In a fully digital coherent system, the electric fields at the input and the output of the channel are available to DSPs at the transmitter and the receiver, enabling the use of arbitrary impairment precompensation and postcompensation algorithms. Linear time-invariant (LTI) impairments such as chromatic dispersion and polarization-mode dispersion can be compensated by adaptive linear equalizers. Non-LTI impairments, such as laser phase noise and Kerr nonlinearity, can be compensated by channel inversion. All existing impairment compensation techniques ultimately approximate channel inversion for a subset of the channel effects. We provide a unified multiblock nonlinear model for the joint compensation of the impairments in fiber transmission. We show that commonly used techniques for overcoming different impairments, despite their different appearance, are often based on the same principles such as feedback and feedforward control, and time-versus-frequency-domain representations. We highlight equivalences between techniques, and show that the choice of algorithm depends on making tradeoffs.

101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation

Record capacity transmission of 101.7-Tb/s (370×294-Gb/s) is performed over 3×55 km SSMF using PDM-128QAM-OFDM modulation and pilot-based phase noise mitigation. Achieved spectral efficiency of 11 bits/s/Hz is the highest reported to date for WDM transmission.

Terabit Optical Access Networks Based on WDM-OFDMA-PON

Next-generation optical access networks are envisioned to evolve into a converged, high-speed, multiservice platform supporting residential, business, mobile backhaul, and special purpose applications. Moreover, bandwidth demand projections suggest that terabit aggregate capacity may need to be reached in such next-generation passive optical networks (PON). To satisfy these requirements while leveraging the large investments made in existing fiber plants, a wavelength division multiplexed (WDM)-based long-reach PON architecture combined with a multiple access technology that features a passive last-mile split, large per-λ speeds, and statistical bandwidth multiplexing can be exploited. In this paper, the first terabit PON based on hybrid WDM orthogonal frequency division multiple access (OFDMA) technology is proposed and experimentally verified. To enable high-speed, long-reach transmission with simplified optical network unit (ONU)-side digital signal processing, multiband OFDMA with ONU-side sub-band selectivity is proposed. Design challenges and tradeoffs between analog and digital domain sub-band combining and selection are also discussed. Finally, the experimental setup and results of the first 1.2 Tb/s (1 Tb/s after overhead) symmetric WDM-OFDMA-PON over 90 km straight single-mode fiber and 1:32 passive split, featuring multiband OFDMA, digitally selective ONUs, and a coherent-receiver OLT are presented and analyzed. By supporting up to 800 ONUs with 1.25/10 Gb/s guaranteed/peak rates and exhibiting a record rate-distance product achieved in long-reach PON, the demonstrated architecture may be viewed as promising for future converged terabit optical metro/access.

Multimode fiber amplifier with tunable modal gain using a reconfigurable multimode pump

We propose a method for controlling mode-dependent gain in a multimode Erbium-doped fiber amplifier by tuning the mode content of a multimode pump. The resulting device is suitable for mode-division multiplexed transmission.