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We investigate experimentally the validity of testing all-optical OFDM and Nyquist WDM systems using interleaved test channels derived from only two data sources. These “odd and even” channels are insufficiently decorrelated, so experiments underestimate the inter-carrier interference (ICI). Additionally, numerical simulations demonstrate that using odd and even channels generates stronger nonlinear distortions during transmission, causing an unrealistically large penalty in the nonlinearity-limited region.
©2012 Optical Society of America
1. Introduction
Most experimental demonstrations of optical transmission systems at 400-Gb/s, 1-Tb/s and beyond combine multiple sub-bands to form superchannels [1–4]. All-optical orthogonal frequency division multiplexing (AO-OFDM) [1] and Nyquist wavelength division multiplexing (N-WDM) [5] are two examples of multi-sub-band systems. Sub-bands are used because of the bandwidth limitations of the data modulators and digital-to-analogue converters (DAC). To reduce the number of modulators, the sub-bands in these experimental systems are typically cloned from the outputs of only one [2] or two [3] modulators.
Insufficient decorrelation between the sub-bands will produce unrealistic results [6], so various methods of decorrelating the sub-bands have been proposed. A common method is odds-and-evens [3, 4], where all of the odd-numbered channels carry the same information as one another, as do the even channels. Experimental proof-of-concept demonstrations have used odds-and-evens for AO-OFDM [1, 3] and N-WDM [7, 8]. While odds-and-evens ensures that the received channel is different to its closest neighbors, the neighbors on either side are identical with one another. This was shown to under-estimate inter-carrier-interference (ICI) of a three-subcarrier coherent WDM system [6].
In this paper, we experimentally investigate the effect of using odds-and-evens in AO-OFDM and N-WDM superchannels. Two cases are considered: (a) without any cyclic prefix (CP) for OFDM or guard band (GB) for N-WDM; (b) with 20% CP/BG, which was sufficient to prevent ICI. Our results show that using odds-and-evens overestimates the performance of both AO-OFDM and N-WDM without a CP/GB, as in a coherent WDM system [6]. Odds-and-evens underestimated the performance of AO-OFDM with a 20% CP. Of the cases tested, odds-and-evens only accurately predicted the performance of N-WDM with a 20% GB [9].
Additionally, we used numerical simulations to investigate the effect of using odds-and-evens on degradation caused by fiber nonlinearity. Our results show that using odds-and-evens causes a penalty in the nonlinearity limited region. At 5 Gbaud, this penalty is ~2.3 dB, but reduces with increasing channel spacing and baud rate.
Our observations are important when comparing modulation formats for next-generation transmission systems and estimating the capacity of optical links.
2. Experimental description
We constructed two ten-channel systems: odds-and-evens and decorrelated. In both, each channel carries a 5-Gbaud 16-QAM signal. 16-QAM is a good compromise between reach and spectral efficiency [10]. Channel(s) means subcarrier(s) in the OFDM systems.
Figure 1(a) shows the decorrelated system setup. The ‘parent’ channel is generated by modulating the output of an Agilent external cavity laser (ECL) with a Sumitomo complex Mach-Zehnder modulator (C-MZM), driven from a Tektronix arbitrary waveform generator (AWG), with 10-Gsample/s In-phase and Quadrature outputs. Two samples per symbol were used to ensure near-square pulses for AO-OFDM and near-sinc pulses for N-WDM. A 50-tap FIR filter was used to shape the N-WDM channels. Each transmitted block contained 93,000 symbols. This parent channel was duplicated optically using a serrodyne loop [2]. Each round trip produces a ~140-ns delay (~700-symbols) and a frequency down-shift of 5 GHz for no CP/GB, or 6 GHz for a 20% CP/GB. The delay advantageously decorrelates the channels. A tunable optical delay is inserted in the loop to align the symbol transitions of the channels, which is required for AO-OFDM [1]. A Finisar Waveshaper limits the loop’s bandwidth to ten channels as shown in Fig. 2(a) . The optical signal-to-noise ratio (OSNR) decreases for each recirculation due to an accumulation of the noise. This degradation was minimized by operating the EDFAs inside the serrodyne loop at a high ( + 17 dBm) output power.
Fig. 1 Block diagram of the experimental setup: (a) fully decorrelated channels; (b) ‘odd and even’ channels.
Fig. 2 Optical spectra measured with an Agilent high-resolution spectrometer: (a) decorrelated 6-GHz spaced N-WDM; (b) odds-and-evens 6-GHz spaced AO-OFDM.
Figure 1(b) shows the odds-and-evens system. Five spectral lines, spaced at twice the channel spacing (i.e. 10 or 12 GHz), were generated by overdriving a Covega optical phase modulator. The powers of these lines were equalized with a Waveshaper before all five lines were modulated with the same RF signal as the parent channel of the decorrelated system. The five modulated optical channels were split into two paths: one path was shifted in frequency by the channel spacing (5 or 6 GHz), amplified and recombined with the unshifted path to obtain the spectrum shown in Fig. 2(b). Again, a tunable optical delay was used to align the symbol transitions so that the even channels were delayed by exactly 80 ns (400 symbols) relative to all of the odd channels.
The same coherent receiver was used for all systems, comprising a Kylia optical hybrid, four U2T balanced photodiode pairs and another ECL tuned to the frequency of the desired channel. A polarization controller enabled a single-polarization receiver to be used; however, these results could be generalized to a dual-polarization system. An Agilent 40 GSample/s real-time sampling oscilloscope was used as the analogue to digital converter (ADC). After digitization, the signal was resampled in MATLAB to 10 GSample/s for N-WDM (two-times oversampling) and to 20 GSample/s for AO-OFDM (four-times oversampling). Next, a blind self-tuning equalizer separated the channels. A constant modulus algorithm (CMA) was used to roughly converge each channel, which was initialized with a filter response to reject neighboring channels [11]. This was followed by a decision-directed radius directed equalizer (DD-RDE) to fine-tune the equalizer taps [12]. The initial 20,000 symbols were discarded to ensure the equalizer had converged to a steady-state. Blind carrier phase recovery was then used to compensate for laser phase noise [12].
We wish to investigate the upper limit of performance of the AO-OFDM and N-WDM systems. Therefore, the measurements were taken with the maximum possible OSNR; that is, back to back, which resulted in more than 30-dB OSNR for all cases. For reference, an N-WDM system with 10-GHz channel spacing, which would not be affected by ICI, had an average received signal quality, Q, of 20.4 dB with our experimental setup. Throughout this paper, Q is the signal-to-noise ratio (SNR) measured from the received constellation [13]; 16-QAM requires a Q of 16.5 dB for a BER of 10−3.
3. Experimental results for back-to-back systems
3.1 5-GHz channel spacing
Figure 3(a) shows the performance of each channel for AO-OFDM using a 5-GHz channel spacing. There is no CP/GB, so both AO-OFDM and N-WDM will have ICI because perfectly square pulses and perfect Sinc pulses are impossible to practically implement. The received Q of the odds-and-evens AO-OFDM (■) is ~20 dB for all channels. This small reduction from the reference 10-GHz spacing experiment suggests that the degradation due to linear ICI is negligible. In contrast, the first channel in decorrelated AO-OFDM (●) has Q = 18.2 dB, the second channel has Q = 13.3 dB, and the equalizer did not converge for all other channels.
Figure 3(b) shows the performance of the N-WDM system with 5-GHz channel spacing. The average Q of the odds-and-evens system is 16.9 dB, 3.5-dB lower than the 10-GHz reference. The average Q for the decorrelated system was 14.5 dB; 2.4 dB lower than the odds-and-evens system. Thus the odds-and-evens overestimates the performance somewhat [6]. Note that the well confined spectrum of N-WDM means that ICI can only be generated by a channel’s closest neighbors. Therefore, the unrealistic benefit from odds-and-evens must be caused by the two closest neighbors being identical [6].
Overall, the results in Fig. 3 demonstrate that odds-and-evens under-estimates ICI for both AO-OFDM and N-WDM if the channels are spaced at the baud-rate.
3.2 6-GHz channel spacing
Figure 4 shows the performance of AO-OFDM and N-WDM for 6-GHz channel spacing, which allows for a CP or GB. The decorrelated results show that the ICI in both systems is negligible. Figure 4(a) shows the odds-and-evens AO-OFDM performs ~2 dB worse than the decorrelated system. This is because the correlated neighboring channels interact with the blind equalizer, preventing it fully converging. Using a different equalizer optimization method, such as using a training sequence, may aid convergence and avoid this penalty.
Figure 4(b) shows that the performance of the middle channels is similar for odds-and-evens and decorrelated signals. The Q of the decorrelated system’s channels decreases with index, because higher index channels have accumulated more noise during their multiple passes through the EDFA of the recirculating loop. The Q’s, averaged over all channels, are 20.0 dB for both systems, which is close to the reference system with 10-GHz spacing.
3.3 Summary
Table 1 shows a summary of the average Q’s of all the experimental systems. Of all the systems tested, the only system where using odds-and-evens channels and decorrelated channels produced similar results was the N-WDM system at 6-GHz channel spacing. At 5-GHz spacing, Odds-and-evens overestimated the performance for both AO-OFDM and N-WDM, showing that odds-and-evens systems do not accurately predict the ICI.
Table 1. Summary of received signal qualities: red – odds-and-evens underestimated ICI; orange – odds-and-evens interacted with the equalizer; green – odds-and-evens produced correct result.
4. Simulation results for an 800-km link
Yang et al. [14] showed that concatenating the same 8-GHz band of electrically generated CO-OFDM channels increased the effect of fiber nonlinearity on the estimated system performance; the correlation between the transmitted channels caused the nonlinear products of each channel to add coherently. This phenomenon could also occur in AO-OFDM and N-WDM superchannels. We use numerical simulations to investigate N-WDM superchannels with a 20% GB, which is the case where the odds-and-evens and decorrelated systems gave identical linear performance.
We simulated a ten-channel N-WDM system. The analogue electronics and optics, including the fiber, were simulated using VPItransmissionMaker v8.7; the digital signal processing (DSP) of the transmitter and receiver were implemented in MATLAB. Symbol rates of 5 Gbaud (6-GHz spacing), 10 GBaud (12-GHz spacing) and 20 GBaud (24-GHz spacing) were obtained by adjusting the DAC/ADC rates. A rectangular filter at the Nyquist frequency of each DAC was used to remove the image of the DAC. The test link had 10 × 80-km fiber spans. The fiber attenuation was 0.2 dB/km; CD was 16 ps/nm/km and the nonlinearity constant, γ, was 1.3 /W/km. The split-step Fourier method is used to simulate fiber nonlinearity. The loss of each span was compensated with EDFAs with a noise figure of 6 dB. Ideal lasers, modulators and coherent receivers were assumed, to identify the degradation caused by the link. The number of transmitted symbols per channel was 32268. The DSP algorithms in MATLAB were identical to those in Section 2, except that carrier phase compensation was removed.
Figure 5 shows the averaged Q of the middle two channels against the launch power per channel into each fiber span. The dashed black line shows the FEC limit for a BER of 10−3. The decorrelated systems are shown by the solid markers (▲●■) and the odds-and-evens systems are shown by the hollow markers (∆○□). At all baud rates, the odds-and-evens and the decorrelated systems have very similar performance in the ASE limited region, where the launch power is low. This is as expected since the ICI is negligible due to the GB/CP. Also, the required launch power increases by 3 dB with each doubling of the baud rate, which agrees with standard theory.
At a launch power of −6 dBm/channel the 5-Gbaud system is mainly limited by fiber nonlinearity. Here, the Q of the odds-and-evens is 2.3-dB lower than the Q of the decorrelated; the nonlinear threshold of the odds-and-evens is also 1.3-dB lower. This shows that the correlation between the channels increases the nonlinear distortion generated in the link, as in [14]. For the 10-Gbaud system, the penalty in Q at nonlinearity-limited powers, say at −4 dBm/channel, is reduced to 1.3 dB. This is further reduced to 0.7 dB for the 20-Gbaud system (at −2 dBm/channel). The increased channel spacing allows CD to induce walk-off between the channels, thus decorrelating them. These simulation results suggest that odds-and-evens generates more nonlinear distortion. However, for a channel spacing of >24 GHz, the difference in performance between odds-and-evens and decorrelated is within 1 dB. These results are also likely to be relevant to single-carrier nonlinear transmission [10, 15]
For each doubling in baud rate, a 3-dB increase in the launch power per channel produces the same spectral density. Figure 5 shows that the nonlinearity threshold increases at less than 3 dB per doubling in baud rate. The two main reasons for this are: (i) the total superchannel bandwidth increases; and (ii) the optimum channel granularity for an 800-km link without inline CD compensation is ~6 Gbaud [16, 17].
7. Conclusions
Our experimental results show that using odds-and-evens to test a design can significantly affect the accuracy of linear performance estimates for both AO-OFDM and N-WDM superchannels. In the case of no CP/GB, using odd and even channels provides a significant, but unrealistic, benefit for both AO-OFDM and N-WDM, as it decreases the estimated ICI. Therefore, odds and evens does not accurately indicate the likely penalty from ICI.
Simulation results show the additional correlation between the channels when using odds-and-evens increases the degradation due to fiber nonlinearity. This overestimate of degradation is reduced for larger channel spacings (when the baud rate is also increased) because of the increased decorrelation caused by CD. This second result is consistent with the findings in [14] for electrically generated CO-OFDM systems with numerous channels in each OFDM band.
In conclusion, decorrelation between test channels is crucial if accurate estimates of the linear and nonlinear performance of AO-OFDM and Nyquist-WDM systems are required.
Acknowledgments
This work is supported the Australian Research Council’s (ARC) Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems, CUDOS, (Project CE110001018) and the ARC’s Discovery scheme (DP1096782).
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