Nonlinearity aware bisection-based sphere shaping for optical digital subcarrier multiplexing systems.

In this paper, a nonlinearity-tolerant sphere shaping is proposed based on the parallel bisection structure. Compared to enumerative sphere shaping (ESS), the bisection-based sphere shaping (BS-SS) can achieve a lower average energy and rate loss at the same blocklength by selecting all preferential sequences. The nonlinearity-tolerant BS-SS (BS-SS-NLI) can mitigate the fiber nonlinearity by reducing the energy variation, which is demonstrated in the simulations with probabilistically shaped, single channel, dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) for a multi-span long-haul transmission over 2500 km of standard single-mode fiber (SSMF) applying digital subcarrier multiplexing (SCM), comparing with recent literature kurtosis-limited ESS (K-ESS) and list-encoding constant composition distribution matching (L-CCDM). The BS-SS-NLI can provide 0.25 dB effective signal-to-noise ratio (SNR) gain over ESS and 0.39 dB gain over L-CCDM. The achievable information rate (AIR) can be improved ∼0.1 bits/4D-symbol by BS-SS-NLI over ESS.

Maximizing the information throughput of ultra-wideband fiber-optic communication systems.

Maximized information rates of ultra-wideband (typically, beyond 100~nm modulated bandwidth) lumped-amplified fiber-optic communication systems have been thoroughly examined accounting for the wavelength dependencies of optical fiber parameters in conjunction with the impact of the inelastic inter-channel stimulated Raman scattering (SRS). Three strategies to maximize point-to-point link throughput were proposed: optimizations of non-uniformly and uniformly distributed launch power per channel and the optimization based on adjusting to the target 3 dB ratio between the power of linear amplified spontaneous emission and nonlinear interference noise. The results clearly emphasize the possibility to approach nearly optimal system performance by means of implementing pragmatic engineering sub-optimal optimization strategies.

Digital backpropagation accounting for polarization-mode dispersion.

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

DSP algorithms for recovering single-carrier Alamouti coded signals for PON applications.

Alamouti space-time block code (STBC) combined with a simple heterodyne coherent receiver enables phase diverse coherent detection without any optical polarization tracking. While such a system consisting of only a 3-dB coupler and a single balanced photodiode has been recently demonstrated using orthogonal frequency-division multiplexed (OFDM) signals, herein we report the first application to single-carrier systems. Applicability of such technique for single-carrier systems is not straightforward since specialized digital signal processing (DSP) algorithms are required for data recovery. In this paper, we address the implementing issues and DSP algorithms applicable for single-carrier (SC) Alamouti STBC based simplified heterodyne receivers. Polarization-insensitive operation of the proposed scheme and its performance are verified by means of simulation for a 12-Gbits/s quadrature phase-shift keying (QPSK) transmission system.

Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multi-channel digital back-propagation.

Superchannel transmission spaced at the symbol rate, known as Nyquist spacing, has been demonstrated for effectively maximizing the optical communication channel capacity and spectral efficiency. However, the achievable capacity and reach of transmission systems using advanced modulation formats are affected by fibre nonlinearities and equalization enhanced phase noise (EEPN). Fibre nonlinearities can be effectively compensated using digital back-propagation (DBP). However EEPN which arises from the interaction between laser phase noise and dispersion cannot be efficiently mitigated, and can significantly degrade the performance of transmission systems. Here we report the first investigation of the origin and the impact of EEPN in Nyquist-spaced superchannel system, employing electronic dispersion compensation (EDC) and multi-channel DBP (MC-DBP). Analysis was carried out in a Nyquist-spaced 9-channel 32-Gbaud DP-64QAM transmission system. Results confirm that EEPN significantly degrades the performance of all sub-channels of the superchannel system and that the distortions are more severe for the outer sub-channels, both using EDC and MC-DBP. It is also found that the origin of EEPN depends on the relative position between the carrier phase recovery module and the EDC (or MC-DBP) module. Considering EEPN, diverse coding techniques and modulation formats have to be applied for optimizing different sub-channels in superchannel systems.

Spectrally shaped DP-16QAM super-channel transmission with multi-channel digital back-propagation.

The achievable transmission capacity of conventional optical fibre communication systems is limited by nonlinear distortions due to the Kerr effect and the difficulty in modulating the optical field to effectively use the available fibre bandwidth. In order to achieve a high information spectral density (ISD), while simultaneously maintaining transmission reach, multi-channel fibre nonlinearity compensation and spectrally efficient data encoding must be utilised. In this work, we use a single coherent super-receiver to simultaneously receive a DP-16QAM super-channel, consisting of seven spectrally shaped 10GBd sub-carriers spaced at the Nyquist frequency. Effective nonlinearity mitigation is achieved using multi-channel digital back-propagation (MC-DBP) and this technique is combined with an optimised forward error correction implementation to demonstrate a record gain in transmission reach of 85%; increasing the maximum transmission distance from 3190 km to 5890 km, with an ISD of 6.60 b/s/Hz. In addition, this report outlines for the first time, the sensitivity of MC-DBP gain to linear transmission line impairments and defines a trade-off between performance and complexity.

Estimating divergently routed nonlinearly interfering channel powers using cross phase modulation.

The deployment of coherent transceivers in legacy networks requires significant investment in installation. We propose a method enabling autonomous (re-)configuration of an optical channel, which would be advantageous in legacy networks and necessary in proposed future networks utilizing a flexible frequency grid and software defined components such as reconfigurable optical add drop multiplexers (ROADM). We consider potential interfering optical channels propagating with the prospective channel along part of the fiber link which are dropped before arrival at the receiver. The method uses a commercially available line card transmitting a 40Gbit/s polarization multiplexed quadrature phase shift keying (PM-QPSK) probe channel to characterize an optical channel. The power of the nearest neighboring channels is then inferred by examining its bit error rate (BER) which is impacted by cross phase modulation (XPM) from the aggressor channels. In a 4 node network with 2 ROADMs using up to 6 aggressor OOK channels, we successfully deduce the neighboring channel power down to -2 dBm, and an extra improvement down to -3.5 dBm is gained, by measuring at an offset to the international telecommunication union (ITU) grid which also reveals inequality in neighbor channel powers.

Differential carrier phase recovery for QPSK optical coherent systems with integrated tunable lasers.

The performance of a differential carrier phase recovery algorithm is investigated for the quadrature phase shift keying (QPSK) modulation format with an integrated tunable laser. The phase noise of the widely-tunable laser measured using a digital coherent receiver is shown to exhibit significant drift compared to a standard distributed feedback (DFB) laser due to enhanced low frequency noise component. The simulated performance of the differential algorithm is compared to the Viterbi-Viterbi phase estimation at different baud rates using the measured phase noise for the integrated tunable laser.

Pulse-shaping versus digital backpropagation in 224Gbit/s PDM-16QAM transmission.

We investigate the transmission performance of 224Gbit/s polarization-division-multiplexed 16-state quadrature amplitude modulation (PDM-16QAM) for systems employing standard single mode fiber (SSMF) and erbium doped fiber amplifiers (EDFAs). We consider the effectiveness of return-to-zero (RZ) data pulses with varying duty cycles and digital backpropagation (DBP) in reducing nonlinear distortion in wavelength-division- multiplexed (WDM) links with 3, 5, 7 and 9 channels. Similar improvement in transmission reach of 18-25% was achieved either by pulse-carving at the transmitter or by DBP, yielding maximum transmission distances of up to 1760km for RZ-pulse-shapes and 1280km for NRZ.

Blind adaptive equalization of polarization-switched QPSK modulation.

Coherent detection in combination with digital signal processing has recently enabled significant progress in the capacity of optical communications systems. This improvement has enabled detection of optimum constellations for optical signals in four dimensions. In this paper, we propose and investigate an algorithm for the blind adaptive equalization of one such modulation format: polarization-switched quaternary phase shift keying (PS-QPSK). The proposed algorithm, which includes both blind initialization and adaptation of the equalizer, is found to be insensitive to the input polarization state and demonstrates highly robust convergence in the presence of PDL, DGD and polarization rotation.

Generation and long-haul transmission of polarization-switched QPSK at 42.9 Gb/s.

We demonstrate, for the first time, the generation and transmission of polarization-switched QPSK (PS-QPSK) signals at 42.9 Gb/s. Long-haul transmission of PS-QPSK is experimentally investigated in a recirculating loop and compared with transmission of dual-polarization QPSK (DP-QPSK) at 42.9 Gb/s per channel. A reduction in the required OSNR of 0.7 dB was found at a BER of 3.8 x 10(-3), resulting in an increase in maximum reach of more than 30% for a WDM system operating on a 50 GHz frequency grid. The maximum reach of 13640 km for WDM PS-QPSK is, to the best of our knowledge, the longest distance reported for 40 Gb/s WDM transmission, over an uncompensated link, with standard fiber and amplification.

Ultra-long-haul transmission of 7×42.9 Gbit/s PS-QPSK and PDM-BPSK.

We investigated ultra-long-haul transmission of polarization-switched QPSK (PS-QPSK) and polarization-division-multiplexed BPSK (PDM-BPSK) at 42.9 Gbit/s experimentally as well as by means of computer simulations. PDM-BPSK allowed transmission distances in excess of 14,040 km to be achieved, compared to 13,640 km for PS-QPSK. However, PS-QPSK offers a significant reduction in receiver complexity due to the lower symbol-rate.

Estimating OSNR of equalised QPSK signals.

We propose and demonstrate a technique to estimate the OSNR of an equalised QPSK signal based on the radial moments of the complex signal constellation. The technique is compared through simulation with maximum likelihood estimation and the effect of the block size used in the estimation is also assessed. The technique is verified experimentally and when combined with a single point calibration the OSNR of the input signal was estimated to within 0.5 dB.

Burst Mode Receiver for 112 Gb/s DP-QPSK with parallel DSP.

A burst mode 112 Gb/s DP-QPSK digital coherent optical receiver with parallel DSP suitable for implementation in a CMOS ASIC with a 218.75 MHz clock speed is presented. The receiver performance is validated in a five channel 50 GHz grid WDM burst switching experiment using a commercially available wavelength tunable laser as the local oscillator. A new equalizer initialization scheme that overcomes the degenerate convergence problem and ensures rapid convergence is introduced. We show that the performance of the tunable local oscillator is commensurate with burst mode coherent reception when differential decoding in employed and that required parallel DSP implementation does not seriously impair the polarization and frequency tracking performance of a digital coherent receiver under burst mode operation. We report a burst acquisition time of less than 200 ns.

A comparison of modulation formats for passive optical networks.

The sensitivity of the four-dimensional modulation format, polarization-switched quadrature phase shift keying (PS-QPSK), is compared with polarization division multiplexed QPSK (PDM-QPSK), binary phase shift keying (PDM-BPSK) and 8-ary quadrature amplitude modulation (PDM-8QAM) at a constant bitrate (12.5 Gbit/s) using a preamplified signal to improve receiver sensitivity. The sensitivity without preamplification is also obtained. PS-QPSK is found to maintain a sensitivity advantage over the reference formats in line with theory with an absolute sensitivity of -52.7 dBm (4.2 photons/bit), assuming hard decision FEC.

A long-reach ultra-dense 10 Gbit/s WDM-PON using a digital coherent receiver.

We investigate the impact of channel spacing and nonlinear transmission over 120 km of standard single mode fiber for a 10 Gbit/s long-reach wavelength division multiplexed passive optical network (WDM-PON). We employed polarization division multiplexed quadrature phase shift keying (PDM-QPSK), which allowed data transmission at 3.125 GBaud, including a 25% overhead for forward error correction. To receive this spectrally efficient modulation format, a digital coherent receiver was employed, allowing for both frequency selectivity and an increased sensitivity of -45 dBm (25 photons/bit).We investigated a channel spacing as low as 5 GHz, for which the loss budget was 48.6 dB, increasing to 54.0 dB for a 50 GHz grid.

Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation.

The impact of phase to amplitude noise conversion for QPSK, 16-QAM, and 64-QAM coherent optical systems are investigated with electronically-compensated chromatic dispersion (CD). The electronic equalizer is shown to convert the phase noise from the local oscillator (LO) to amplitude noise, limiting the amount of CD that can ideally be compensated digitally. The simulation results demonstrate that the performance of coherent systems can significantly be degraded with digitally compensated CD and LO phase noise. The maximum tolerable LO linewidth is also investigated for the different modulation formats and found to become increasingly stringent for longer transmission distance and higher symbol rate.

Characterization of long-haul 112Gbit/s PDM-QAM-16 transmission with and without digital nonlinearity compensation.

In this paper long-haul, single channel, polarization multiplexed 16-state quadrature amplitude modulation (PDM-QAM-16) transmission at 112 Gbit/s is investigated. Novel digital signal processing techniques are used to perform carrier phase estimation and symbol estimation, in combination with nonlinear digital backpropagation. The results obtained demonstrate that the use of digital nonlinear backpropagation increases the optimum launch power from -4 dBm to -1 dBm with a consequent increase in maximum reach from 1440 km to 2400 km, which is a record transmission distance for QAM-16 reported to date for an SMF link with EDFAs only. Furthermore, experimental measurements are supported by simulations, based on the link used in the experiment.

Digital filters for coherent optical receivers.

Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

Electronic compensation of chromatic dispersion using a digital coherent receiver.

Digital signal processing (DSP) combined with a phase and polarization diverse coherent receiver is a promising technology for future optical networks. Not only can the DSP be used to remove the need for dynamic polarization control, but also it may be utilized to compensate for nonlinear and linear transmission impairments. In this paper we present results of a 42.8Gbit/s nonlinear transmission experiment, using polarization multiplexed QPSK data at 10.7GBaud, with 4 bits per symbol. The digital coherent receiver allows 107,424 ps/nm of chromatic dispersion to be compensated digitally after transmission over 6400km of standard single mode fiber.