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A theoretical study of the transmission performance of the optical orthogonal frequency division multiplexing (OFDM) system was conducted as a function of number of subcarriers. It revealed that small number of subcarriers could improve the transmission performance because the optimum repeater output power of the system was increased. The reason of the improvement could be attributed to the nonlinear impairment reduction through the peak to average power ratio (PAPR) reduction.
©2009 Optical Society of America
1. Introduction
The optical orthogonal frequency division multiplexing (OFDM) is an attractive method to improve the transmission performance of the optical fiber communication system, and there are several reports that demonstrate its superior transmission performance with high bit-rate [1,2] and long distance [3,4]. One technical issue of the optical OFDM transmission system is the nonlinear tolerance. In general, as the optical OFDM signal has a large peak to average power ratio (PAPR), it will cause a significant penalty due to the self phase modulation (SPM). Some methods to compensate the nonlinear distortion have already been proposed [5,6], but they are relatively complicated.
In this paper, simple method to improve the nonlinear tolerance of the optical OFDM system is discussed. The transmission performance of the optical OFDM system is studied with respect to number of subcarriers. The optical waveform of the optical OFDM signal changes as number of subcarriers changes, and the PAPR changes accordingly. The result obtained through the numerical simulations shows that reduction of number of subcarriers can improve the tolerance of the OFDM transmission system against the optical fiber nonlinearity.
2. Simulation model
Figure 1 shows a schematic diagram of the simulation model used in this study. At the transmitting end, at first, a serial binary sequence was generated, and it was 216 De Brujin sequence. Then, the serial binary sequence was converted to a parallel sequence and mapped to the QPSK symbols through a serial to parallel converter and a QPSK mapper. Then, the QPSK mapped parallel sequence was inverse Fourier transformed by an inverse fast Fourier transformer (IFFT), and converted to the serial sequence again by a parallel to serial converter. The real and the imaginary parts of the serial sequence were then upconverted to the intermediate frequency (IF) domain, and they drove a Mach-Zehnder modulator to generate corresponding optical field.
At the receiving end, coherent detection was assumed for the receiver, but the effect of the phase noise of the signal and the local oscillator light sources was ignored. The received optical field was converted to the IF domain first, and then, downconverted to the baseband. After that, the received serial sequence was converted to the parallel sequence through a serial to parallel converter, and fed to a fast Fourier transformer (FFT). Fourier transformed parallel sequence was then demapped by a QPSK demapper, and converted back to the serial sequence by a parallel to serial converter. Finally, an error counter counted bit-errors of the recovered serial sequence.
Number of subcarriers of the optical OFDM signal was determined by a size of the IFFT/FFT. In this study, the size N was chosen to be 512, 256, 128, 64, 32, 16, and 8. In addition, data patterns were occupying half of the IFFT/FFT size, and residual half was occupied by virtual subcarriers for oversampling [7].
The system parameters used for this study referred previously published experimental paper [7]. The signal wavelength was 1550nm, and the bit-rate was 25.8Gb/s. The sampling rate was 12.9GSa/s for the real and the imaginary part independently. The IF was set to 15.1GHz. The signal clipping was not adopted to show the impact of the PAPR difference upon the transmission performance clearly. The transmission line comprised 32 spans of standard single mode fiber (SMF) and 32 erbium-doped fiber amplifiers (EDFA). The SMF had 80km span length, 18.6ps/km/nm chromatic dispersion, 0.06ps/km/nm2 dispersion slope, 72μm2 effective area, 0.2dB/km transmission loss, and 2.6 x 10−20 nonlinear refractive index. The EDFA had 16dB gain and 5dB noise figure. Conventional split-step Fourier method was used to calculate optical signal propagation in the transmission line [8,9]. The cumulative dispersion of the transmission line was fully compensated by the dispersion compensation fiber (DCF) at the receiving end, but the nonlinearity of the DCF was ignored.
The cyclic prefix and the training symbols were not used for this simulation due to the restriction of the FFT/IFFT for the split-step Fourier calculation. The number of sample points should be 2n for the FFT/IFFT used for the split-step Fourier simulation. As the inclusion of the cyclic prefix and the training symbols made the number of sample points to be 2n+α, it was not feasible to include them in the simulation. Then, the chromatic dispersion could not be equalized in the electrical domain, and it was equalized in the optical domain.
In order to evaluate the transmission performance, Monte-Carlo method was used to obtain the bit-error rate (BER). About 3.3 million bits were simulated for each condition, and the BER was calculated from number of errored bits over number of simulated bits.
3. Results and discussions
Transmission performance was simulated under various EDFA output power. Figure 2 shows the results. Calculated BER is shown as a function of EDFA output power and number of subcarriers. Compared to the reference [7], the simulated performance matched qualitatively well to the experimental result when there were 512 subcarriers. As seen in the figure, transmission performance was improved by reducing number of subcarriers. In addition, the optimum EDFA output power was shifted toward higher region by reducing number of subcarriers. These results clearly show that the nonlinear tolerance of the optical OFDM transmission system can be improved by reducing number of subcarriers.
The reason of this phenomenon can be attributed to the reduction of the PAPR. Figure 3 shows the optical intensity waveform of (a) 512 subcarriers and (b) 8 subcarriers. The horizontal axis is the time, and the vertical axis is the intensity of the optical field. The intensity of the optical signal is normalized by the average value, and the peak power in this figure corresponds to the PAPR for each case. As seen in this figure, reduction of the number of subcarriers led to decrease of the PAPR. Figure 4 shows the PAPR as a function of number of subcarriers. The PAPR monotonically increased by increasing number of subcarriers. In addition, the difference of the PAPR in dB scale corresponded roughly to the difference of optimum EDFA output power obtained from Fig. 2. From these results, it can be concluded that the PAPR of the optical OFDM signal limited the optical OFDM system performance through the nonlinear impairment, and the reduction of the PAPR by reducing number of subcarriers improved the nonlinear tolerance of the optical OFDM system.
4. Conclusions
Transmission performance of the optical OFDM system was investigated theoretically, and number of subcarriers was shown to have a significant impact on the nonlinear tolerance of the optical OFDM transmission system. Reduction of number of subcarriers is a simple method to improve the nonlinear tolerance of the optical OFDM transmission system.
Acknowledgments
The author would like to thank Drs. H. Tanaka and I. Morita of KDDI R&D Laboratories Inc. for valuable discussions and support. This work is supported partially by National Science Council 96-2221-E-110-049-MY3, partially by key module technologies for ultra-broad bandwidth optical fiber communication project of Ministry of Economics, Taiwan, R.O.C., and partially by Aim for the Top University Plan of the National Sun Yat-Sen University and Ministry of Education, Taiwan, R.O.C.
References and links
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