1. Introduction

Chromatic dispersion (CD) and polarization mode dispersion (PMD) are typically compensated using 1-tap equalization in coherent optical orthogonal frequency division multiplexed (CO-OFDM) lightwave systems [1]. Therefore, the reach of CO-OFDM systems is mainly limited by amplified spontaneous emission (ASE) and fiber nonlinearity. Self-phase-modulation (SPM) can be compensated by applying phase modulation proportional to the intensity waveform [2–5]; however, cross-phase-modulation (XPM) is the dominant source of degradation in most dense wavelength division multiplexing (DWDM) systems [6,7]. XPM is commonly regarded as the ultimate limiting factor on the spectral efficiency of lightwave systems [8]; digital XPM compensation requires extensive computational effort [5].

We have recently shown that intensity-driven phase modulation can be used to implement XPM compensation for point-to-point links; however, an additional photodiode is required before the optical demultiplexer to detect the intensity waveform of multiple wavelength channels [9]. Another technique, pilot-based phase noise compensation [10], has been proposed for nonlinearity compensation in CO-OFDM systems [11]. Pilot-based nonlinearity compensation (PB-NLC) does not require any additional hardware as it can be implemented completely using digital signal processing (DSP). However, PB-NLC only improved the nonlinearity threshold by 0.5 dB in a 2000-km dispersion unmanaged link [11] and even less benefit was observed in dispersion managed links [12].

We have previously used simulations to show that PB-NLC is more effective for XPM compensation than for SPM compensation [13], and that SPM compensation prior to PB-NLC significantly improves the nonlinearity-limited performance. In this paper, we experimentally verify that PB-NLC is effective for XPM compensation using a seven-wavelength 17.2-Gb/s CO-OFDM system in a 400-km dispersion managed link. The nonlinearity threshold was increased by ~6 dB. This result was first presented at the European Conference of Optical Communications in Geneva, 2011 [14]. In addition, this paper examines the optimal power of the pilot and optimal bandwidth of the lowpass filter (LPF) that selects the pilot-tone using numerical simulations. The results show that the optimal LPF bandwidth is almost independent of the OFDM signal’s bandwidth. Therefore, the overhead associated with the pilot-tone decreases for higher bandwidth OFDM systems.

2. Experimental setup

Figure 1 shows the experimental setup. Seven wavelengths, spaced 50-GHz apart, were modulated with an OFDM signal. The six outer wavelengths were from distributed feedback lasers (DFB) and the central wavelength was from an external cavity laser (ECL). The OFDM signal was generated in MATLAB using a 128-point IFFT with 78 data-bearing subcarriers, each modulated with 8-QAM, and an 8-sample cyclic prefix. 12 subcarriers either side of DC were zeroed in order to leave a ~2-GHz gap in the center of the OFDM signal, ~1 GHz either side of the pilot. An Arbitrary Waveform Generator (AWG) with two 10-Gsample/s outputs was used to drive the In-phase (I) and Quadrature (Q) inputs of a complex Mach-Zehnder modulator (C-MZM) to generate an 8-GHz wide CO-OFDM signal on each wavelength. The biases of the C-MZM were offset from the null power point to produce a pilot carrying around 20 percent of the total signal power. The data rate was 17.2 Gb/s on a single polarization. The odd and even wavelength channels were separated using interleavers and the odd channels were delayed by one OFDM symbol, to decorrelate neighboring channels. The limited input power into the C-MZM caused the input power into the booster amplifier to be around −31 dBm. This limited the received OSNR to 18 dB for the seven-wavelength system and 22 dB for the single-wavelength system (measured with an Agilent optical spectrum analyzer).

 

Fig. 1 Block diagram showing the experimental setup. The DCM compensates for 90-km of S-SMF; PC-polarisation controller.

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The link comprised 4 × 100-km spans of standard single mode fiber (S-SMF). Each span was followed by a 90-km dispersion compensation module (DCM). The transmission losses of both the S-SMF spans and DCMs were compensated with single-stage EDFAs. The target power of the EDFAs feeding the S-SMF spans was swept from −10 to 14 dBm to investigate the performance of the system at different launch powers. The launch power into the DCMs was 6-dB lower than into the S-SMF spans, to minimize nonlinearities in the DCMs.

At the receiver, an optical pre-amplifier fed a Finisar Waveshaper, which selected the central wavelength channel for the signal input of a Kylia dual-polarization optical hybrid with four U²T balanced photodiode pairs. The local oscillator (LO) input to the hybrid was taken from the ECL. The delay of the 400-km link was well in excess of the ECL’s coherence time. The polarization of the signal was aligned to the hybrid’s TE polarization. The In-phase and Quadrature electrical outputs were then digitalized with an Agilent 92804A digital sampling oscilloscope operating at 40 Gsample/s. The signals were then equalized in MATLAB, which involved: (i) SPM compensation [1–3], (ii) downsampling, (iii) PB-NLC [11,13], (iv) 1-tap OFDM equalization [1], and (v) blind carrier phase recovery [15].

3. Optimizing the filter bandwidth of PB-NLC

Figure 2 plots the signal quality Q against the LPF bandwidth for different launch powers. The Q is calculated in two ways: the symbols are derived from the Bit Error Ratio (BER) count; the lines are calculated from the variance of the constellation points around their mean values [3]. A LPF bandwidth of 0 means that the PB-NLC is not used; in this case, blind phase estimation was used to track laser phase noise on a symbol-by-symbol basis. Figure 2(a) is the result for single-wavelength systems, which do not have XPM. The −4 dBm and 0 dBm plots in Fig. 2(a) show that the Q decreases when the bandwidth of the LPF is increased. This is because the noise within the LPF’s bandwidth is also multiplied with the signal, increasing the constellation spread. Thus, in ASE limited cases, a narrow LPF bandwidth is optimum. At a power of 3 dBm, which is in the nonlinearity limited regime, the Q is almost independent of the LPF’s bandwidth. This suggests that PB-NLC is not effective at compensating SPM.

 

Fig. 2 Received Q against the LPF bandwidth for PB-NLC at different optical launch powers.

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Figure 2(b) and Fig. 2(c) are for WDM systems, so include XPM between the WDM channels. At the ASE-limited powers of −6.5 dBm/wavelength, both figures show the Q decreases as the bandwidth of the LPF is increased, which is the same as the single-wavelength system in Fig. 2(a). Figure 2(b) shows that at higher-powers, where Q is limited by nonlinearity, PB-NLC with a 200-MHz LPF provided a 2.3-dB benefit. Figure 2(c) shows that adding SPM compensation before the PB-NLC provides an additional 2.2-dB benefit. PB-NLC improves the nonlinearity-limited performance of WDM systems; the performance is further improved by additional SPM compensation.

Figure 3 shows the optical spectra after 400 km of transmission in the nonlinearity-limited regime for single-wavelength and WDM. These spectra explain why PB-NLC is effective for XPM compensation, but not for SPM compensation. The broad ‘noise’ pedestals around the OFDM signals in both spectra are generated by SPM. Because the SPM products have a wide bandwidth, they are rejected by the electrical filter that separates the pilot from the signal, thus PB-NLC cannot fully compensate for them. In contrast, due to walk-off [9], the XPM products have a much narrower bandwidth, which broadens the pilot as shown in Fig. 3(b). Therefore, the phase shifts due to XPM can be compensated using the pilot’s phase [13].

 

Fig. 3 Received optical spectra measured with an Agilent high-resolution spectrometer: (a) single-wavelength system at 4 dBm launch power; (b) WDM system at 12-dBm launch power (3.5 dBm/wavelength).

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4. System performance versus launch power

Figure 4 plots the received Q against the launch power per wavelength. The dashed black lines indicate the required Q for BER = 10⁻³ (13.6 dB for 8-QAM). Figure 4(a) shows that PB-NLC (□) did not improve the nonlinearity-limited performance of the single-wavelength system. In contrast, intensity-driven SPM compensation (◊) [2,3] increased the nonlinear limit by 4 dB. The maximum improvement in Q at the peaks of these curves was limited experimentally by ASE produced by the booster amplifier after the C-MZM.

 

Fig. 4 Experimental Q against launch power with different nonlinearity compensation methods. A 200-MHz LPF was used in the PB-NLC.

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Figure 4(b) shows that PB-NLC improves system performance for powers greater than −4 dBm/wavelength. Adding SPM compensation prior to PB-NLC (○) increases the nonlinear limit by a total of 6 dB. Using either PB-NLC (□) or SPM compensation (◊), only improves the nonlinearity limit by 2 dB. Therefore, a combination of SPM compensation and PB-NLC (for XPM compensation) is required to improve the nonlinearity-limited performance significantly. Figure 4(b) also shows that PB-NLC reduces the sensitivity of CO-OFDM somewhat, because ASE within the bandwidth of the LPF cannot be removed from the pilot.

5. Optimization of the design parameters

Numerical simulations were conducted to investigate the overhead associated with PB-NLC in higher data rate systems. Three systems were simulated: EXP, 40G and 100G. EXP used an OFDM symbol identical to that of the experimental system. The 40G and 100G systems also used the same OFDM symbol rate and cyclic prefix length; however, they used 104 data-bearing subcarriers and 254 data-bearing subcarriers respectively. A linewidth of 100 kHz was used for both the laser at the transmitter and the LO. The optical link was identical to the experiment, consisting of 4 × 100 km spans of S-SMF, each followed by a 90 km DCM. The simulated S-SMF had 16 ps/nm/km of CD, 0.2 dB/km of loss, a nonlinearity constant of 2.6 × 10⁻²⁰ m²/W and an effective core area of 80 µm². The noise figures of the EDFAs were set to 6 dB and the power into the DCMs was 6 dB lower than into the SMF spans. The residual dispersion per span was 160 ps/nm.

Figure 5 shows the simulated spectra of the central wavelength at the receiver for the EXP and the 100G systems. XPM broadens the pilot by around ± 500 MHz in both systems. This suggests the required gap around the subcarriers and the bandwidth of the pilot selecting LPF can be designed independently of the bandwidth of the OFDM sidebands.

 

Fig. 5 Simulated optical spectra after 400 km: (a) EXP system at 0 dBm/wavelength; (b) 100G system at 2 dBm/wavelength.

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The bandwidth of the LPF and the power allocated to the unmodulated pilot are parameters that need to be optimized for the PB-NLC. To find globally optimal parameters, sweeps of both the LPF bandwidth and pilot power must be performed at several launch powers. This is because the optimal bandwidth of the LPF is different for the linear regime, where ASE dominates, and the nonlinear regime, where fiber nonlinearity dominates.

We first optimized the LPF bandwidth for a large pilot power of 0.3 × sideband power. Note that the total transmitted power is the pilot power plus the sideband power. The power of the pilot was chosen to be sufficient to give good results. Figure 6(a-c) plots the received Q against the LPF bandwidth at different launch powers for the three different bit rates. It is desirable to use the narrowest LPF bandwidth that allows effective XPM compensation. A narrower-bandwidth filter requires fewer nulled subcarriers and less pilot power, thus a narrower total channel bandwidth and a better sensitivity. Figure 6(a-c) show that the Q at the optimal transmit power is close to maximum for a LPF bandwidth of 500-MHz for all three systems. This suggests that the optimal filter bandwidth is independent of the OFDM sideband bandwidth. Further increases in the LPF bandwidth will only produce small improvements. The optimal LPF bandwidth was lower in the experiment because the noise floor caused by the low power into the booster amplifier. We therefore use a filter bandwidth of 500 MHz for all systems simulations from hereon in.

 

Fig. 6 (a-c) Simulated received Q against LPF bandwidth of pilot filter for the three different systems. (d) Simulated received Q against pilot power for all three systems.

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In the ASE-limited region, the filtered pilot will also contain ASE. Thus there are two sources of signal degradation: ASE at the optical frequencies of the subcarriers and the ASE close to the pilot, which is multiplied with the signal when phase modulation is applied. Therefore, it is important to optimize the ratio of pilot and signal powers. In contrast, in the nonlinearity limited region, fiber nonlinearity is the dominant cause of signal degradation. Given that the OFDM sideband is rejected by the pilot’s LPF, the effectiveness of XPM compensation is independent of the pilot power; however, a stronger pilot reduces the available power for the OFDM sideband so the nonlinearity mixing is weaker. This means the nonlinearity-limited performance will always improve with increasing pilot power, simply because the signal is weaker for a given launch power. Therefore, to achieve optimal transmission performance, the pilot power should be optimized at ASE limited powers.

Figure 6(d) plots the received Q against pilot power for the three bit-rates at ASE-limited launch powers. The optimal pilot power is: 30% of the OFDM sideband power for the EXP system, 25% for the 40G system and 15% for the 100G system. This shows that the optimal ratio of pilot to sideband power decreases as the bandwidth of the OFDM sideband increases.

6. Conclusion

These experiments show that PB-NLC works well for compensating XPM if SPM is compensated separately, prior to XPM compensation; the nonlinear limit of the central wavelength of a seven-wavelength system was increased by 6 dB. For a single-wavelength system, the nonlinearity limit was not increased, confirming that the PB-NLC is not effective for SPM compensation. To implement PB-NLC, bandwidth and power must be allocated to the pilot. Although this is a significant overhead for low-bandwidth systems, numerical simulations showed that the overhead decreases for higher-bandwidth OFDM signals. In fact, the required pilot bandwidth is independent of the OFDM sideband’s bandwidth and the optimal ratio of pilot-to-signal power also decreases for higher-bandwidth OFDM signals.