We experimentally investigate the effect of self-phase modulation on direct-detection orthogonal frequency division multiplexed (OFDM) transmission at 11.1 Gb/s over 960km and 1600km uncompensated standard single-mode fiber links. We show that for long-haul systems, the penalties due to nonlinear distortion in OFDM systems are comparable to those in links employing electronic predistortion.
©2008 Optical Society of America
Orthogonal frequency division multiplexing (OFDM) is widely used in wireless systems such as GSM and WiMax and has been gaining a great deal of attention in the optical networks area because of its advantages [1-4], which include the reduction in the baud rate, since high-speed serial information is transmitted through multiple lower-speed sub-channels. As a result, the inter-symbol interference is reduced and the equalization at the receiver is easily achieved. Additionally, OFDM allows for the utilization of more advanced modulation formats and thus can achieve higher spectral efficiency. Synchronization can be achieved relatively easily and the implementation of the system is simplified by the use of FFT/IFFT algorithms. However, a major drawback to this technique is the high peak-to-average power ratio (PAPR), although there are many methods such as clipping and pre-coding to mitigate this problem . In optics there are two schemes to achieve OFDM: direct-detection (DD-OFDM) and coherent-detection (CO-OFDM). The former is simpler and cheaper to implement as it only requires a single photodiode and digital signal processing (DSP) at the receiver, albeit with lower spectral efficiency . Coherent detection, on the other hand, has a higher sensitivity and spectral efficiency, but with additional cost and complexity due to the requirement for phase and polarization tracking .
In theory an OFDM signal is resilient to any amount of dispersion, provided a sufficient length of cyclic extension is used. However, in reality the system is limited by noise and/or nonlinearity . In this paper we experimentally demonstrate, to the best of our knowledge, the longest transmission distance and the lowest required OSNR values reported to date for 10-11Gbit/s direct-detection OFDM. We also investigate the effect of self-phase modulation (SPM) on an 11.1 Gb/s 512-subcarrier OFDM transmission system over standard single mode fibre links of distances of 960 and 1600km. We compare the resilience of OFDM to fiber nonlinearity with that of systems using the alternative technique of electronic predistortion at the same bitrate.
2. OFDM transmitter
The digital signal processing (DSP) required to generate and decode the OFDM signals was carried out off-line using Matlab. The OFDM transmitter DSP is shown in Fig. 1. First an 11.1Gbit/s serial data is mapped onto a QAM-4 format then passed to an N=2048 IFFT block. The data is fed to the first 512 input of the IFFT, while zeros occupy the remainder (2 ×oversampled). The block multiplexes the 512 OFDM subcarriers and generates a 0-5.55GHz OFDM band. A cyclic extension is added to each OFDM symbol, then the data is serialized. Following this, an up-conversion stage is necessary where the OFDM band is shifted to the 5.55-11.1GHz band. This is achieved by multiplying the signal by exp(2iπft) where f=5.55GHz. An alternative method to avoid the up-conversion stage is to feed the data to the [N/4+1: N/2] input of the IFFT block . In this case the OFDM subcarriers are directly multiplexed onto the 5.55-11.1GHz band.
The data is then stored in random access memory on the Nortel eDCO transmitter which is described in detail in . The card is utilized as a 22.2Gs/s arbitrary waveform generator (AWG) consisting of a memory, two 6-bit digital-to-analog converters (DACs), a tunable laser and a polar dual-drive Mach-Zehnder modulator (MZM). The OFDM waveform stored in the memory was adjusted to avoid any clipping due to the DACs. In this work the polar MZM is used to generate a double optical sideband and a sideband suppression stage using an optical filter is employed. The power in the carrier was set to equal the power in the sideband. The measured optical spectrum at the output of the OFDM transmitter is depicted in Fig. 1 with 0.01nm resolution (inset). The modulator was biased so that it operated in the linear region and to accommodate the relatively high peak-to-average power (PAPR) ratio. In the worst case, the PAPR can be as high as 10×log(Nsc) where Nsc is the number of subcarrier (512 in this case) .
3. OFDM receiver
Figure 2 shows the direct-detection OFDM receiver model. After the square law detection, the electrical spectrum consists of the transmitted OFDM band (5.55-11.1GHz) and inter-modulation components in the 0-5.55GHz band as shown in the inset in Fig. 2 . The data is then digitized using a real-time sampling scope (Tektronix DPO 72004) and synchronized. Synchronization is realized by sending two subsequent OFDM symbols carrying identically known data (training symbols) at the transmitter . The two symbols are correlated at the receiver and the OFDM symbol boundaries are defined. In addition, the training sequence is utilized to define the rotation angle of each sub-carrier due to chromatic dispersion.
The signal is then down-converted to baseband and passed through a low-pass filter. Following this, the cyclic extensions are removed and the data is fed to a 2048 FFT block. Finally, the zero padding is removed and the data is equalized and then decoded.
4. Loop experiment
The experimental setup used in this work is shown in Fig. 3. An 11.1Gbit/s QAM-4 OFDM signal was generated at 1554.94nm. Because of the memory capacity of the eDCO card, the maximum bit sequence length that could be used was a 214-1 PRBS. The OFDM symbol period was 2048×45ps=92.16ns. The recirculating loop consisted of a span of 80km of standard SMF and no optical dispersion compensation was deployed. Two transmission distances were investigated: 12 and 20 recirculation (for a total of 960 and 1600km respectively). Cyclic extensions of 1.395ns and 2.295ns were added to the OFDM data for 960 and 1600km transmission respectively. The guard interval values were calculated using the equation given in . The signal was noise loaded at the receiver to obtain plots of BER versus received OSNR. An EDFA pre-amplifier followed by a 50GHz wavelength demultiplexer were deployed before the photodiode. The data was captured by the 50Gs/s Tektronix DPO 72004 real-time oscilloscope before being resampled at 22.2Gs/s and processed off-line. 16 PRBS cycles were processed at a time to calculate BER values down to 3.8×10-6.
5. Results and discussion
Figure 4 shows the BER versus OSNR after 960km for launch power values ranging from -10 to 0dBm plotted with 2dB resolution. Monte Carlo simulations lead to a value of the required OSNR for a BER=10-3, using our setup and a perfect demultiplexer (a brick wall 50GHz filter) at the receiver, of ~10dB (using 0.1nm resolution bandwidth). However, we observed a 1.5dB penalty when using a second-order Gaussian filter (OSNR becomes 11.5dB). In the back-to-back experimental results it can be observed that the OSNR value increases to 12.2dB. This penalty is due to the imperfect nature of the optical filter at the receiver (demux) and also to the fact that the frequency response of the transmitter is not flat over the 5.55-11.1GHz band (it exhibits amplitude and phase distortion). With launch power of -10dBm, we observed an OSNR penalty of ~1.5dB compared with back-to-back, the OSNR sensitivity increasing to 13.8dB. The required OSNR increases gradually with increasing launch power to reach 14.4dB at -2dBm. However at 0dBm, where the SPM effect is the strongest, a significant increase to 16.3dB occurred. We detected all transmitted bits without error for launch powers -6, -4 and -2dBm at 19, 20.5 and 21dB OSNR respectively.
Figure 5 shows the BER versus received OSNR curves for the same power values after 1600km. It can be observed that the required OSNR for levels less than -10dBm is 13.8dB. This is the same as 960km and shows that there are negligible additional penalties when extending the transmission distance. This demonstrates that OFDM is only noise limited, for low launch powers, albeit with extra overheads. The required OSNR increased gradually up to a launch power of -6dBm where it reaches 14.1dB and significantly increases for higher values, reaching 16.5dB at -2dBm. We could not achieve a BER=10-3 at 0dBm even at a maximum OSNR of 23dB. Figures 4 and 5 demonstrate how the effects of nonlinearity increase with increasing distance. Moreover, the optimum launch power (that achieves the highest OSNR margin) in the 960km transmission distance is about -2dBm (<1dB penalty wrt -10dBm curve) whereas it reduces to approximately -4dBm for 1600km (~1.6dB penalty).
Finally it is of interest to compare the impact of SPM on OFDM and electronic pre-distortion (EPD). Figure 6 shows the required OSNR penalty to achieve a BER=10-3 for different launch power levels after 1600km at 11.1Gbit/s. The OFDM curve is taken from the results shown in Fig. 5 whereas the EPD curve is taken from our previous work  where an IMDD NRZ signal carrying a 215 PRBS was transmitted over 1600km at the same bitrate. The required OSNR in the back-to-back configuration for this system was just under 10dB. It can be observed that nonlinear effects become noticeable at -7dBm for OFDM and -5dBm for EPD. At -6dBm, OFDM is only 0.5dB worse than EPD and increases to ~1dB at -2dBm. Above this value, the OFDM curve becomes steeper than that of EPD and the difference is approximately 5dB at 0dBm. Note that the OSNR value for OFDM at 0dBm was obtained by extrapolating the curve in Fig. 5. The performance of OFDM is comparable to that of EPD, both suffering from the high peak-to-average power ratio (although the latter is slightly more tolerant). In the case of coherent OFDM systems, it was shown in  that the nonlinear limit is independent of the number of subcarriers and therefore the sensitivity to fiber nonlinearity of coherent OFDM should be very similar to EPD. In direct-detection systems however, in addition to the four-wave mixing (FWM) that affects all OFDM systems, the signal is further degraded by the nonlinear interaction between the optical carrier and the subcarrier band which may explain the higher penalty in this type of systems . In addition, while the PAPR in OFDM systems remains relatively constant along the transmission path, it gets lower in EPD systems as the signal approaches the receiver (especially in the last 10% of the link). Further analysis is required to explain the difference in performance between DD-OFDM and EPD signals.
In this work we realized an 11.1Gbit/s single-sideband direct-detection OFDM system using an optical filter at the transmitter. The back-to-back required OSNR for a BER=10-3 was 12dB, and 13.8dB after transmission over 960km and 1600km of standard SMF. The launch power was incrementally increased from -10 to 0dBm to investigate the effects of SPM. For the 960km transmission distance, the optimum power was -2dBm with less than 1dB penalty due to nonlinearity. In the 1600km case, the optimum launch power was around -4dBm with less than 1.5dB penalty. Finally we compared the impact of SPM on OFDM and EPD and we found comparable performance between the two techniques.
The authors would like to thank Kim Roberts and Doug McGhan of Nortel, for donating the eDCO card and for the useful discussions. We also wish to thank David Krauss (Nortel) for assistance with the eDCO card. We acknowledge Prof. Polina Bayvel for useful discussions and feedback. Funding support from EPSRC is gratefully acknowledged.
References and links
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