1. Introduction

Reported experiments focusing on long-haul and ultra long-haul transmission continue to approach the theoretical linear and nonlinear transmission limits as depicted in Fig. 1 . The results of the spectral efficiency versus transmission distance have been plotted to include most noteworthy wavelength-division-multiplexed (WDM) experiments, carried out with various modulation formats, as well as the theoretical linear and nonlinear limits [1, 2]. The linear limit was calculated assuming 80 km standard singlemode fiber spans, EDFA-only amplification (NF=4.5 dB) and a 50 GHz grid with full population of the C-band, while in the case of the nonlinear limit, cross phase modulation is assumed to be the dominant nonlinearity.

 

Fig. 1 Spectral efficiency versus transmission reach for various WDM-experiments employing a variety of modulation formats, fiber types and amplification techniques. The linear limit assumes ASE noise as the only limitation [1], while the nonlinear limit additionally assumes XPM to be the dominant nonlinearity [2].

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Figure 1 highlights that conventional modulation formats such as on-off keying (OOK) [3], differential phase-shift-keying (DPSK) [4] and polarization multiplexed binary phase-shift-keying (PDM-BPSK) [5] as well as quaternary phase-shift keying (PDM-QPSK) [6] have been widely used to demonstrate transmission over distances beyond 2000 km, which is due to their increased resilience towards nonlinear distortions [7] and superior sensitivity in the presence of circularly-symmetric Gaussian noise assuming a 2-dimensional channel [8]. However, an optical wave offers 4 degrees of freedom (2 quadratures in 2 polarizations) and recent work has addressed the question of the optimum modulation format for this higher dimensional channel [9, 10]. After solving a 4-dimensional sphere packing problem, Karlsson and Agrell [9] arrived at a modulation format that provides an asymptotic sensitivity gain of 1.76 dB over BPSK - polarization-switched QPSK (PS-QPSK). PS-QPSK provides maximum power efficiency by transmitting a QPSK symbol in one polarization at a time, with the resultant spectral efficiency limits of 3 bit/s/Hz as opposed to 4 bit/s/Hz for PDM-QPSK and 2 bit/s/Hz for PDM-BPSK.

Previous work, comparing PS-QPSK to PDM-QPSK at 42.9 Gbit/s line-rate showed that PS-QPSK can achieve a more than 3000 km longer maximum reach under WDM conditions [11]. In this paper, we compare experimentally and by means of computer simulations PS-QPSK and PDM-BPSK on an ultra-long-haul transmission link. Section 2 describes the experimental setup for generation, transmission and detection of multichannel PS-QPSK and PDM-BPSK, while section 3 presents a characterization of the computer simulations that have been carried out. In section 4 the receiver sensitivity is compared and experimental transmission results are put into context with previous work [11] as well as relevant simulation results. Section 5 provides a summary and discussion of the paper’s key results.

2. Experimental transmission setup

We used an external cavity laser at 1553 nm with a linewidth of 100 kHz surrounded by 6 DFB-lasers with 50 GHz frequency spacing to compare transmission performance of PDM-BPSK and PS-QPSK. To generate PS-QPSK, an IQ-modulator was driven at 14.3 Gbit/s with two decorrelated 2¹⁵-1 long pseudo-random binary sequences (PRBS) to initially obtain QPSK. It was followed by a polarization switching stage consisting of two parallel Mach-Zehnder modulators (Fig. 2 (a) ). The MZMs were driven at 14.3 Gbit/s with inverse data patterns, to block one or the other polarization, to generate the PS-QPSK format. In case of PDM-BPSK, the underlying BPSK constellation was generated by driving the two arms of the IQ-modulator at 21.45 Gbit/s with inverse PRBS-15 data patterns. The IQ-modulator was followed by a polarization multiplexing stage with a relative delay of 48 symbols yielding PDM-BPSK (Fig. 2 (b)). In Fig. 2 the resulting constellation diagrams of the two formats are shown, illustrating the correlation between X- (red) and Y-polarization (blue) in the case of PS-QPSK, as opposed to no correlation in the case of PDM-BPSK. For both modulation formats, even and odd channels were subsequently separated with a 50 GHz interleaver and recombined with a relative delay of 10 ns to decorrelate neighboring channels.

 

Fig. 2 Transmitter used for WDM transmission of (a) PS-QPSK and (b) PDM-BPSK.

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The WDM-signal was launched into a single-span recirculating loop with 80.24 km of standard single mode fiber (SMF) and an accumulated chromatic dispersion of 1347 ps/nm per recirculation [12]. The loop was gated with two acousto-optic modulators whose insertion losses, as well as the span loss of 15.4 dB, was compensated for by EDFAs with noise figures of 4.5 dB and a fixed output power of 17 dBm. Variable optical attenuators were used to set the launch power into the span and balance the loop. A Mach-Zehnder filter was employed to flatten the gain profile of the EDFAs and avoid out of band noise accumulation.

The signal was detected with a phase and polarization-diverse coherent receiver using a pair of balanced PINs to receive each quadrature. The local oscillator was an ECL with 100 kHz linewidth whose frequency was tuned to ensure that the frequency offset did not exceed 1 GHz. The signal was digitized with a digital sampling oscilloscope with an electrical bandwidth of 16 GHz and processed offline. After the signal had been de-skewed, normalized and resampled, chromatic dispersion was compensated digitally. For PS-QPSK, a polarization-switched constant modulus algorithm equalizer with least-mean squares updating was used [13], followed by a modified Viterbi & Viterbi phase recovery [11]. In the case of PDM-BPSK, joint equalization and phase-recovery was performed in a similar manner to that described in [14] for PDM-QPSK.

3. Simulation of the transmission performance

The experimental results obtained were verified by transmission simulations using MATLAB. All 7 co-polarized WDM-channels carried 2¹⁵ symbols based on different pseudo-random symbol sequences. The limited transmitter bandwidth was emulated with a 5th -order electrical Bessel filter. A 2nd order Gaussian optical filter with a 3dB bandwidth of 40 GHz has been used to model the interleaver frequency response. Laser phase noise was modeled as a Wiener process and the transmitter laser linewidth was set to be 100 kHz, as in the experiments. Residual implementation penalty of the experimental setup was modeled by adding different amounts of noise to the electrical driving signals.

Table 1 shows the parameters used in the simulations to correspond to the experimental values. The EDFAs were set to operate in saturation with a fixed output power of 17 dBm; with a subsequent attenuator used to obtain the required optical power levels. The signal propagation in the fiber was modeled with the symmetrical split-step Fourier method [15], which has been extended with the wave-plate to take polarization mode dispersion into account [16]. The optical loop filter was modeled as a 2nd order Gaussian filter with adjustable bandwidth to accommodate the full optical spectrum.

Table 1. Fiber and link parameters

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After transmission, the incoming signal was detected with a phase- and polarization diverse digital coherent receiver. The linewidth of the LO was set to 100 kHz and a negligible frequency offset between transmitter and LO-laser was assumed. The limited receiver bandwidth dominated by the bandwidth of the ADCs was modeled with a filter employing measured frequency responses of every channel of the digital sampling oscilloscope used in the experiment [17]. Additional quantization noise was added by simulating ADCs with an effective number of bits equal to 5. Subsequent DSP includes chromatic dispersion compensation, equalization and digital phase estimation as described in Section 2. Monte-Carlo error counting was performed to determine the BER, which serves as the performance metric to determine the achievable reach at a given launch power.

4. Transmission results at 42.9Gbit/s

Figure 3 shows back-to-back measurements of the receiver sensitivity for (a) PDM-BPSK and (b) PS-QPSK. The results are plotted on a double-log scale and fitted linearly to ease comparison between the formats, as well as against theoretical sensitivity limits. Single channel PDM-BPSK shows an implementation penalty of 0.4 dB at BER = 3.8 × 10⁻³ compared to 0.8 dB for PS-QPSK. Adding more WDM channels to the signal resulted in an additional penalty of 0.2 dB in both cases, which was due to coherent crosstalk induced by neighboring channels. Taking this into account the different implementation penalties result in a reduction of the theoretical sensitivity advantage of PS-QPSK over PDM-BPSK (0.75 dB reduces to 0.4 dB at a BER of 3.8 × 10⁻³).

 

Fig. 3 Back to back measurements of the bit-error rate with varying OSNR for (a) PDM-BPSK and (b) PS-QPSK.

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To characterize the transmission performance of both modulation formats, 7 WDM channels were launched into a recirculating loop and the launch power per channel was varied between −14 and 4 dBm to determine the maximum transmission distance at BER=3.8×10⁻³. Figure 4 shows the experimental as well as the simulation results. Previous work on 7-channel WDM-transmission of 42.9 Gbit/s PDM-QPSK [11], extended by simulations to provide additional information on the relative performance of PS-QPSK, is also included, for comparison.

 

Fig. 4 Reach as a function of launch power at BER = 3.8 × 10⁻³ for PDM-BPSK, PS-QPSK and PDM-QPSK [11]. Markers show experimental results while lines denote simulated performance.

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The experimental results show lower maximum reach than predicted by the computer simulations, which we attributed to small inaccuracies such as e.g. in EDFA noise figure and nonlinear fiber coefficient, as well as the absence of a loop synchronous polarization scrambler. Furthermore, the loop has to be rebalanced for each launch power, which can affect the amount of noise added per recirculation. All these effects tend to accumulate with an increased number of recirculations, especially if, like in this case, a single span loop is used [12]. However, experimental results and simulations were in good agreement concerning the general trend as well as transmission performance in the linear and nonlinear regimes.

Despite showing similar optimum launch powers of −3.5 dBm, in experiment, and −4 dBm in simulation, PS-QPSK clearly outperformed PDM-QPSK with a maximum reach of 13,640 km compared to 10,350 km, corresponding to an increase of 30% (28% in simulation). However, PDM-BPSK shows a 1-1.5 dB higher optimum launch power, which translated into 14,040 km maximum reach, corresponding to an increase of less than 3% compared to PS-QPSK (29% in simulation).

The improved sensitivity of PS-QPSK with respect to PDM-BPSK observed in the back-to-back measurements translated into a 0.4 dB improvement in the linear region of the reach curve (0.7 dB improvement with respect to PDM-QPSK). On the nonlinear part of the reach curve, PDM-BPSK was ~1.5 dB more resilient towards nonlinearities than PS-QPSK, in both experiment and simulation. However, PDM-QPSK showed a similar penalty of ~1.5 dB and 3 dB in the nonlinear region, compared to PS-QPSK and PDM-BPSK, respectively. We attributed this effect to an increased walk-off (relative to the symbol period) as a result of increasing symbol-rates: 10.7 GBd for PDM-QPSK, 14.3 GBd for PS-QPSK and 21.45 GBd for PDM-BPSK.

In terms of the DSP complexity, it is worth mentioning that the number of FIR-filter taps required to compensate for chromatic dispersion scales with the square of the symbol-rate. Therefore, PDM-BPSK requires an approximately 125% longer FIR-filter than PS-QPSK. For transmission over 170 spans this corresponds to 1498 taps as opposed to 3371 taps [18], which is equivalent to 2048 and 4096 taps when ceiled to the nearest power of two for implementation with the ‘overlap and save’ technique. Furthermore, the lower symbol-rate of PS-QPSK would lead to 33% lower electrical bandwidth requirements for transmitter and receiver-side electronics compared to PDM-BPSK.

5. Conclusions

Ultra-long-haul transmission of PS-QPSK and PDM-BPSK formats at 42.9 Gbit/s was studied and compared for the first time. WDM-transmission over an uncompensated SMF link employing 80 km spans, with EDFA-only amplification and phase and polarization-diverse coherent detection, was investigated experimentally and by means of computer simulations. Due to its reduced resilience to nonlinearities, PS-QPSK resulted in a lower transmission distance of 13,640 km compared to 14,040 km for PDM-BPSK. However, due to its reduced symbol-rate, PS-QPSK offers the benefits of reduced receiver complexity and lower bandwidth requirements for transmitter and receiver electronics which makes it potentially attractive for ultra-long-haul transmission.