We demonstrate a two-fold reach extension of 16 GBaud 16–Quadrature Amplitude Modulation (QAM) wavelength division multiplexed (WDM) system based on erbium doped fiber amplifier (EDFA)-only amplified standard and single mode fiber -based link. The result is enabled by transmitter-side digital backpropagation and frequency referenced carriers drawn from a parametric comb.
© 2015 Optical Society of America
The ever increasing growth in data traffic resulting from the widespread adoption of high-bandwidth applications and services is soon to consume the transmission capacity of the legacy Wavelength Division Multiplexing (WDM) systems . In particular, the issue here is two-fold: in addition to a more-efficient information packing in a given (or available) bandwidth, the energy consumption associated with reach is of particular concern, whereas avoidance of (optical-to-electrical-to-optical - OEO) repeaters, used periodically in long-haul links to regenerate / re-create the transmitted signals upon exhaustion of the signal integrity is also of particular interest in this respect . In consequence, an immense research efforts are being dedicated to increasing the capacity limits, as well as the reach of fiber optic links. Historically, the capacity-reach limits were imposed by linear impairments such as Chromatic Dispersion (CD) and Polarization Mode Dispersion (PMD) . However, the development of the digital signal processing (DSP)-enabled coherent receiver has enabled efficient digital equalization techniques for arbitrary amounts of CD and PMD , both of which are unitary transformations, making them even more appealing for digital processing. Presently, however, the information carrying capacity of fiber optic links is limited by the Kerr nonlinearity, which essentially works so as to couple the wavelength-allocated information channels and becomes increasingly detrimental to the integrity of the information as the signal powers are increased [5–12]. As a practical compromise between the OSNR limitation , on the one hand, and nonlinear impairment, on the other, the current systems are engineered so as to operate near the onset of nonlinear effects. Solutions such as Ultra Large Effective Area Fibers (ULAF)  have been successful in the sense that they allow higher signal launch powers by reducing the fiber nonlinearity, however, signal transmission is still performed avoiding the nonlinear regime. More recently, research into digital compensation of nonlinear effects has become an active research area, albeit with limited applicability and success. The mid-span optical phase conjugation (OPC) gained significant interest in the early 2000’s [14, 15], and has been successfully revived recently [16–18]. The OPC, however, does not compensate the effects of Third Order Dispersion (TOD) and requires both a symmetric dispersion map and a symmetric power evolution throughout the link, making it ineffective in commercially deployed systems. Another relatively new Nonlinearity Compensation (NLC) technique that has been recently introduced is Phase Conjugated Twin Wave (PCTW) transmission [19, 20]. Although highly successful in laboratory demonstrations, the drawback to PCTW, is that it cannot make efficient use of the available degrees of freedom (bandwidth and polarization resources) essentially limiting the spectral efficiency to a fraction of what can be achieved employing polarization multiplexing.
A promising approach to digital NLC is Digital Back Propagation (DBP) [21, 22]. DBP essentially computes the inverse of the Nonlinear Schrodinger Equation (NLSE), governing the propagation in optical fibers , thereby reversing the propagation effects. In principle, the DBP allows a full elimination of distortions arising from the joint effect of CD and signal-signal Kerr-mediated interactions , however, experimental demonstrations, in this respect, have had limited success in multichannel systems [25–28], with the exception of [29, 30] which have for the first time demonstrated appreciable reach extension by 85% and 100%, respectively, by detecting one whole super-channel with a single detector and relying on DBP to compensate nonlinear effects in conjunction with adaptive forward error correction coding. The missing link in the multi-channel DBP efforts has been singled out recently in . In this contribution we demonstrate the effectiveness of DBP based on transmitter pre-compensation and employing frequency referenced carriers (FRC’s), which enabled achieving for the first time, to the best of our knowledge, a two-fold reach enhancement for a multichannel coherent transmission system with independently modulated and independently detected channels.
2. Experimental demonstration
The DBP processing block can be implemented either at the transmitter, where the signal is pre-distorted before transmission, or at the receiver, where the received signal is equalized after detection. Of these two approaches, transmitter-DBP has the fundamental advantage that the input to the computational engine is noiseless, whereas in contrast, the input to the receiver-DBP will be polluted by the Amplified Spontaneous Emission (ASE) noise accumulated in transmission. Thus, in principle, the transmitter-side DBP should avail a better performance than its receiver counterpart. It is important to note, however, that in order to achieve maximum NLC, the optical carrier waves must be frequency referenced to one another, so as to ensure a deterministic and known walk-off between the channels in the cross-phase modulation (CPM) interaction . In practice, frequency referencing can be accomplished by an optical frequency comb [32–40]. In particular, parametric frequency combs have been demonstrated as capable of generating virtually arbitrary numbers of carriers as well as exhibiting an outstanding performance as carriers for coherent modulation formats [36–40].
The detail of the DBP block is shown in Fig. 1. The data to be transmitted on each of the WDM channels are mapped to a desired modulation format and are subsequently combined and passed to a full-field (back-propagating) NLSE engine taking into account the transmission link parameters. Subsequently, the NLSE full-field output is channelized into spectral slices and independent, but fully-synchronously pre-distorted waveforms are generated for each channel. In this experiment, an internally developed graphics processing unit (GPU)-assisted NLSE solver was used as the DBP computational engine . The DBP engine served to calculate the inverse to the actual propagation in the physical link – thus mirror-imaged power evolution (to that of the physical link) and taking into account opposite signed fiber parameters (dispersion and nonlinearity), as well as reciprocals of amplifier gain and attenuation, as explained in detail in . The calculation was based on a symmetric split-step NLSE solver with 0.01 degrees allowed phase variation, wherein blocks of 216 symbols were processed using 4 samples per symbol, a frequency resolution of ~48 kHz and a time resolution of ~7.8 fs. The full schematic of a system employing transmitter-side DBP is shown in Fig. 2.
The 3-channel WDM DBP-transmitter implementation is presented in Fig. 3. A 25 GHz-pitched narrowband parametric frequency comb was generated following the guidelines found in . Two Distributed Feedback (DFB) lasers served as comb seeds that were injection locked to spectral lines of a phase-modulated External Cavity Laser (ECL) with 3 kHz linewidth. The optical comb was demultiplexed using a Waveshaper optical processor (OP), availing mutually coherent optical carriers with OSNRs in excess of 45 dB and sub-5 kHz linewidth. Different shift-register initial conditions were used to generate three pseudo-random bit sequences (PRBS) that were subsequently gray mapped to 16-Quadrature Amplitude Modulation (QAM) symbols. Transmitter DSP consisted of raised-cosine filtering using 4 samples-per-symbol, 128 filter taps and roll-off factor of 0.1 was applied prior to the DBP computation to constrain the spectral occupancy. Three Digital to Analog Converters (DAC)  were used to generate the electrical pre-distorted signals at the rate of 64 GS/s. The DACs exhibited clock feed through, which generated a tone at 16 GHz that was filtered using 4th order electrical Bessel filters. The pre-distorted 16 GBaud 16-QAM signals were cast onto the optical carriers by means of nested Mach-Zehnder modulators (NMZM), passively coupled, and a polarization beam splitter (PBS) was used to ensure that all channels were co-polarized. The time alignment of all channels was controlled to within 5 ps and was accomplished by means of optical delay lines and synchronous triggering of the DACs. It is important to note that all carriers were frequency referenced but no effort was made to control the channel’s relative optical phases .
The transmitter was particularly optimized to accurately replicate the full-field output of the DBP-block. To characterize the back-to-back performance, generated pre-compensated optical waveforms of all channels were asynchronously acquired using a coherent receiver in a homodyne configuration. Subsequently, the full optical field was digitally reconstructed and virtually propagated using the same NLSE computation as in the DBP-block. The constellations generated by virtual propagation were then characterized in terms of the worst case Q-factor, and an optimum pre-emphasis profile was found and applied to correct any non-ideal frequency and phase responses of the filters, electrical amplifiers and electro-optic modulators .
The transmission experiment was performed in a recirculating loop implemented as shown in Fig. 4. A single 85 km span of Standard Single-Mode Fiber (SSMF) with 16 ps/nm/km dispersion, nonlinear coefficient of 1.22 w−1km−1and total attenuation of 15.95 dB served as the transmission fiber inside the loop. Fiber loss was compensated by an Erbium Doped Fiber Amplifier (EDFA) with 4.5 dB noise figure and a second EDFA was employed to compensate the loop-associated losses and allow a wide range of launch powers. A 1 nm-wide WDM Optical Filter was used to remove the out-of-band ASE noise before launching the signals into the fiber. The combined loss of the loop components from amplifier B to amplifier A was 9.5 dB and the loop-associated optical signal-to-noise ratio (OSNR) with respect to the channel launch power and number of loops are shown in Fig. 5.
After transmission, the signals were independently filtered, down converted using a local oscillator (LO) with <100 kHz linewidth and were coherently detected. The coherent receiver consisted of an integrated 90-degree hybrid and a pair of balanced detectors with 40 GHz Bandwidth. The electrical signals were digitized using a real time oscilloscope at the rate of 100 GS/s and offline processing was performed on a personal computer running MATLAB. Receiver DSP operated on blocks of 216 symbols using 4 samples per symbol and consisted of the standard filtering chain for coherent receivers , including receiver front-end correction, timing recovery, carrier frequency and phase estimation and least mean squares (LMS) adaptive equalization relying on the constant modulus algorithm (CMA) for pre-convergence. The bit-error rate (BER) measurements were performed by error counting in a sufficient collection of samples satisfying the 90% confidence interval , and Q-factors were extracted from BER measurements. The chosen Forward Error Correction (FEC) BER threshold was 1.1x10−3 (Q2 = 9.7 dB), corresponding to a simple Reed-Solomon (255,233) code.
Two transmission scenarios were investigated. In the first case, only linear impairment compensation was applied, i.e. the DBP pre-compensation block at the transmitter was disabled and Electronic Dispersion Compensation (EDC) was applied at the receiver by means of a T/2-spaced Finite Impulse Response (FIR) filter (where T is the symbol period), with the number of taps chosen following the guidelines found in . In the second case, both linear and nonlinear impairment compensation was employed at the transmitter side, i.e. the DBP pre-compensation block was enabled, leaving no need for any further dispersion compensation at the receiver.
A comparison between the spectra of the ideal signal and the modulator output is presented in Fig. 6. The waveform shown is the center channel pre-distorted signal for transmission over 3000 km and 1 dBm launch power. The spectrum of the modulator output without digital pre-emphasis is shown in Fig. 6(a). It can be seen that the frequency response of the components in the transmitter exhibit a roll-off that attenuates the signal at high frequencies. Figure 6(b) shows the spectrum of the output of the modulator for the appropriate pre-emphasis fully matching the ideal – numerically calculated pre-distortion spectrum. We note that the particular example shown is that for a highest power tried in the experiment, where the nonlinear pre-distortion departs the most from the EDC-only counterpart. Furthermore, Fig. 7 shows the back-to-back constellations prior to (Fig. 7(a)) and after successful application of the pre-emphasis (see Fig. 7(b)). Quantitatively, the pre-emphasis yielded 9.3 dB of performance improvement. The results shown in Figs. 6 and 7 are of particular importance for NLC and serve to evaluate the ability of precise waveform shaping, which plays a crucial role in the pre-compensation of nonlinear effects.
The transmission performance for all channels is presented in Figs. 8 and 9. The linear reach (i.e. using EDC only) for the chosen FEC threshold was 1530 km, whereas the optimum launch power per channel was −7 dBm. At this distance the improvement in Q-factor provided by DBP was 2.3 dB for the center channel, while the optimum launch power per channel was found to be −3 dBm.
The attempt to double the transmission distance to 3060 km at the former optimum average power level (effectively in the linear regime) resulted in the measured performance of the center channel corresponding to the Q-factor of 7.7 dB, i.e. below the required forward error correction threshold of 9.7 dB. In sharp contrast, employing DBP improved the Q-factor to 10.4 dB, for the optimum launch power per channel increased from −9 dBm to −3 dBm. We can conclude that DBP effectively enabled the transmission within the nonlinear propagation regime, and was able to take advantage of the increased OSNR provided by the higher launch power. Figure 10 shows a comparison between the constellations and eye diagrams captured at 1530 km using EDC and at 3060 km obtained by the DBP with FRC’s, exhibiting virtually the same performance at twice as long a distance, which was made possible by digital NLC for the first time, to the best of our knowledge and is in full agreement with theoretical predictions from . The important ramifications of this demonstration are three-fold: (i) The obtained result without a doubt demonstrates the ability of reversing signal-signal interaction in propagation; (ii) Owing to the fact that phases of the transmitted channels have not been tracked, nor controlled, these results further corroborate the prediction of  that phase stability plays a minor role in NLC; (iii) Although not directly aimed at in the particularly realized setting, this experimental result also clearly warrants the re-definition of the established capacity bounds in fiber optic transmission, which nearly universally considered the nonlinear interaction as an irreversible impairment. Finally, it must be observed that the 100% reach extension (with respect to the ordinary EDC-only transmission), i.e. doubling of the linear reach, was made possible by the full-complexity NLS calculation, which is prohibitively complex for real-time implementation. Nevertheless, this results represents a strong motivation for an active pursuit of more efficient methods for NLS integration amenable to ASIC implementation.
We have, for the first time, to the best of our knowledge, demonstrated the effectiveness of employing frequency referenced carriers in transmitter-side DBP-based compensation of nonlinearities. In particular, the linear reach of a 16 QAM 16 GBaud system of 1530 km was doubled to 3060 km at the same bit-error-ratio of 1.1x10−3. In essence, the reliance on FRC’s allowed transmission in the previously forbidden nonlinear regime, by permitting us to take advantage of the increased signal OSNR while compensating for the ensuing nonlinear distortions using DBP, and, in this instance, achieving doubling of the attainable transmission reach.
Although the demonstration was based on only three channels, its extension to a larger channel count, as well as polarization-multiplexed systems is straightforward. The demonstrated reach extension directly corresponds to avoidance of a repeater layer and for the first time allows 16-QAM transmission beyond 3000 km (at a fixed conservative FEC threshold) . More importantly, this result directly implies attainability of higher information capacities in fiber optic links than those currently established. As implied by the physical channel interaction and the joint processing necessary for its reversal, the pursuit for capacity needs to rely on multi-user / multiple input – multiple output (MIMO) cooperative processing . By the same token, a significant effort is necessary for a development of error-control coding techniques relying on multi-user/MIMO methods for the attainment of the full multi-user capacity for the systems in which complete crosstalk cancellation is not attained.
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