DFTS-OFDM has been proposed recently as an alternative to coherent optical OFDM due to its improved transmission performance. This paper proposes spectral shaping for DFTS-OFDM which reduces the PAPR leading to further improvement in nonlinear tolerance. It is shown that for both SSMF and LEAF, the optimized spectrally shaped DFTS-OFDM outperforms DFTS-OFDM for dispersion managed and unmanaged links by ~10.8% and ~6.8%, respectively. The number of bands and the excess bandwidth parameters are also investigated to optimize the transmission performance.
©2012 Optical Society of America
New landscapes of bandwidth-hungry applications have led to widespread research in recent years for shifting the current 100 Gb/s Ethernet to 400 Gb/s. Coherent receivers in tandem with digital signal processing readily enable the present system to be upgraded to 400 Gb/s system. One of the modulation formats employing them both is coherent optical orthogonal frequency division multiplexing (CO-OFDM). The motivation for CO-OFDM comes from its advantage to easily scale to higher level modulation formats and to realize next generation agile optical networks [1, 2]. However, compared to single carrier counterpart, CO-OFDM exhibits high peak-to-average power ratio (PAPR). A high PAPR necessitates transmitter and receiver components such as modulators and amplifiers to be linear over a wide dynamic range. Moreover, signals with higher PAPR are typically prone to fiber nonlinearities which in turn limit launch power per span and finally the transmission distance. The nonlinear performance of CO-OFDM has been investigated for a variety of dispersion compensated maps [3–6]. In , it is shown that for an OFDM transmission system, a non-dispersion managed (NDM) map has better resilience towards nonlinear effects compared to a periodically dispersion managed (DM) map. For green field deployment NDM map can be used. However, when upgrading a legacy system with a high data rate OFDM channel, the performance will be reduced because of the periodic dispersion compensation. This problem can be mitigated by reducing the PAPR which has been extensively studied .
In addition to PAPR reduction techniques, further investigations have been carried out to improve nonlinear tolerance by employing an electronic pre- and post-compensation scheme [4, 8], RF-pilot, back-propagation or both [9, 10]. In , pre- and post compensation for legacy systems is investigated and it is shown that self-phase modulation (SPM) can be significantly compensated for, resulting in a nonlinear tolerance of OFDM similar to single carrier modulation formats. Similarly back-propagation can be implemented to reduce SPM. However, with electronic pre- and post-compensation or back propagation, the effect of cross-phase modulation (XPM) generated by OFDM cannot be diminished. The XPM generated by CO-OFDM can have detrimental influence on the other neighboring channels especially for periodically DM links . RF-pilot together with back-propagation has been demonstrated to provide both SPM and XPM compensation expanding the transmission reach .
Recently, discrete Fourier transform spread (DFTS)-OFDM, which was initially proposed in 3GPP Long Term Evolution (LTE), has migrated to optical communication [11, 12]. DFT-precoding prior to the conventional OFDM transmitter entails a low PAPR of the OFDM signal resulting in higher nonlinear tolerance. The transmission of 1.63 Tb/s DFT-precoded OFDM over 1010-km NDM standard single-mode fiber (SSMF) link was presented to give a benefit of 20% in reach compared to CO-OFDM . In , spectral shaping of DFTS-OFDM (S-OFDM) was proposed. S-OFDM can be considered as a variant of DFTS-OFDM where spectral shaping is performed on the DFT-precoded signal. Performing spectral shaping decreases spectral efficiency because the spectral width is broadened. However, the PAPR is further reduced than for the DFTS-OFDM signal.
This paper is an extension of , where the nonlinear tolerance of S-OFDM is analyzed and compared to DFTS-OFDM for both NDM and DM maps implemented for SSMF and large effective area fiber (LEAF) fiber links. In , it has been illustrated that the transmission performance of DFTS-OFDM depends on the number of DFT-precoded bands. A similar study is performed for S-OFDM and it is demonstrated that the optimum number of bands for NDM and DM links for S-OFDM resembles the one for DFTS-OFDM. Additionally, the performance of S-OFDM surpasses DFTS-OFDM by ~6.8% and ~10.8% for NDM and DM links, respectively. Furthermore, in this paper, the process of evaluation of maximum reach is explained. Additionally, the performance of S-OFDM while changing the excess bandwidth factor is discussed and is found that the performance is best when it is within 5%- 10%. We demonstrate an increase in maximum reach for NDM links by 13.6% and 17.6% for SSMF and LEAF, respectively and for DM links by 31% and 32.6% for SSMF and LEAF, respectively, when compared to CO-OFDM. Clearly, the effectiveness of S-OFDM is higher for DM links
2. Spectrally shaped DFTS-OFDM
Figure 1 illustrates the method with which spectral shaping on DFTS-OFDM is realized. At the transmitter, the mapped data (d) is grouped into K bands with m subcarriers per band. Similar to DFTS-OFDM, each group of subcarriers undergoes m-point DFT. The NZ subcarriers are then padded with zeros as indicated in Inset (a) of Fig. 1. Performing N-point IFFT on the signal after zero padding generates DFTS-OFDM signal such that N = MT + NZ is the IFFT size and MT = m.K is the total number of modulated subcarriers. For S-OFDM, before performing the IFFT, the spectrum is artificially broadened by spreading the information over ΔMT subcarriers to smooth the spectral shape of DFTS-OFDM . The new ΔMT derived subcarriers are the cyclic extension of original DFTS data subcarrier. The outer ΔMT/2 subcarriers on the right and left hand of the DFTS-OFDM spectrum are reduced in power by a factor alpha (α). Subsequently, these subcarriers are added on the opposite side of the spectrum with the same power factor (Refer to Fig. 1 Inset (b)). Consequently, the signal power of the paired subcarriers adds up to the original subcarrier power . The excess bandwidth of the S-OFDM signal is proportional to the excess bandwidth factor β ( = ΔMT / MT, measured in percentage), leading to lower feasible spectral efficiency.
3. Simulation setup
For simulations, 9 co-propagating channels at 50-GHz channel spacing are generated. Each of the WDM signals carries a dual polarized 200-Gb/s OFDM signal (net datarate) with 4.7% cyclic prefix overhead, 5% training overhead and 20% FEC overhead. The FFT size is 1024 of which 684 subcarriers are modulated with 16-QAM. When generating DFTS-OFDM signal, these 684 subcarriers are divided into K number of bands. On each of the bands, (684/K)-point DFT is then performed, the output of which is then zero padded to eventually perform IFFT. For S-OFDM, α and β are set to 0.4 and 10%, respectively resulting in 10% increase in bandwidth of the signal. The transmit spectrums of CO-OFDM, DFTS-OFDM and S-OFDM are portrayed in Fig. 2 . For DFTS-OFDM depicted in Fig. 2(b), two 342-DFT blocks are implemented. In Fig. 2(c), the spectrum of S-OFDM with β = 30% is shown, to make the ladder like structure more visible. Here as well two 342-DFT blocks are employed. At the receiver DSP, after IFFT on the received OFDM signal, the inverse of shaping is performed for the S-OFDM signals, which is putting back the subcarriers to the right allocated frequency. For DFTS-OFDM, the signal is directly fed to the K IDFT blocks. By the implementation of S-OFDM with β = 10%, the PAPR is reduced to 7.9 dB from 10.9 dB (CO-OFDM) and 8.8 dB (DFTS-OFDM) when two bands are employed.
The transmission link consists of several spans of 95 km of fiber, either SSMF or LEAF and Erbium Doped Fiber Amplifier (EDFA) with 5 dB of noise figure (NF). Fully inline DM with inline compensation of 1596 ps/nm and 399 ps/nm for SSMF and LEAF respectively and NDM links are considered. The fiber specifications are depicted in Table 1 .
4. Simulation Results
The system nonlinearity tolerance is assessed by evaluating the maximum reach with FEC limit at BER = 10−2. The maximum reach for each launch power is the intersection between the required signal-to-noise ratio (Eb/N0) for BER = 10−2 and the available Eb/N0. The available Eb/N0 can be calculated as Figure 3 depicts the transmission performance for CO-OFDM signal for SSMF with NDM links. The maximum reach has been pointed with an arrow.
In Fig. 4(a) , the maximum attainable reach for increasing values of launch power is depicted. The maximum attainable reach for CO-OFDM () is observed to be 1800 km with an optimum launch power at −1 dBm for NDM SSMF links. DFTS-OFDM () and S-OFDM () demonstrate a slight improvement over CO-OFDM with optimum launch powers located at −2 dBm and −1 dBm, respectively. Figure 4(b) depicts the performance of these systems for DM fiber links. The maximum reach for CO-OFDM, as anticipated, is reduced to 570 km with optimum launch power also lowered to −3 dBm. For DFTS-OFDM, the maximum transmission reach is 700 km, showing 170 km increase with the same optimum launch power as for CO-OFDM. Interestingly for DM case, S-OFDM shows increment in optimum launch power to −2 dBm with ~50 km increase in reach compared to DFTS-OFDM. Clearly, S-OFDM improves the transmission reach by 31% and 7% when compared to CO-OFDM and DFTS-OFDM, respectively. For fully dispersion compensated maps, optical nonlinear effects are generally discussed amongst the most challenging problems faced by CO-OFDM [3, 6]. Nevertheless in DM links, the DFTS-OFDM and S-OFDM signals in the dispersion compensated region have low PAPR, similar to single carrier formats. Thus, we see a significant improvement when compared to CO-OFDM. Furthermore, from , it can be seen that S-OFDM has similar transmission reach as 200 Gb/s 16-QAM single carrier transmission. Thereby, we conjecture that S-OFDM is a novel technique that can push OFDM to higher distances, when dispersion managed links are considered.
In the above results, the DFT bands are set to 2. At the respective optimum launch powers from Fig. 4, the optimum number of bands is investigated. The number of bands, K, is varied from 1 to 128 and the percent increment in the transmission reach is evaluated with respect to CO-OFDM transmission reach and depicted in Fig. 5(a) for SSMF. Figure 5(b) depicts the percent increase in reach at the optimum powers for LEAF transmission while varying K. From both Fig. 5(a) and Fig. 5(b), it is evident that the optimum number of bands for S-OFDM () is identical to the one for DFTS-OFDM () for all the cases. The optimum bands for NDM and DM links are 8 and 2 for SSMF; and 4 and 2 for LEAF, respectively.
As discussed in [11, 20], the PAPR monotonically increases as K is increased. When K = 1, it resembles a single carrier case with the least PAPR. Whereas when K is increased, the PAPR approaches that of CO-OFDM. From Fig. 5(a) and Fig. 5(b), it is evident that the nonlinear tolerance however does not monotonically decrease with the number of bands. Instead there is an optimum point where the performance is the best, disclosing PAPR to be an insufficient measure for determining nonlinear tolerance of a system. As explained in , the PAPR transforms along the fiber due to its dispersive characteristic. For the DM case, the signal waveform returns to the low PAPR value after each dispersion compensation module, thus entering the fiber with least PAPR. This is why the optimum number of bands is lower for DM links in comparison to NDM links. In addition, the performance improvement is identical for K = 1 and K = 2 for DM links. At the optimum points, the performance of S-OFDM surpasses by approximately 6.8% and 10.8% (averaged over two fibers) for NDM and DM links, respectively with respect to DFTS-OFDM.
Finally, the transmission performance of S-OFDM is analyzed by changing β which relates to the spectral bandwidth. Subsequently, changing β changes the PAPR of the signal. Thus, β defines the trade-off between overhead and PAPR. In Fig. 6 , the change in PAPR while varying β is depicted. Increasing β decreases the PAPR of the signal however increasing the bandwidth of the signal. At β□ = 0%, the signal results in a DFTS-OFDM signal with the highest PAPR and without any spectral broadening. In Fig. 7(a) and Fig. 7(b), the maximum reach attained by changing β for SSMF and LEAF with NDM () and DM () links are displayed respectively. The number of bands is set to the optimum value for both the NDM and DM links as evaluated in Fig. 5. An initial improvement in maximum transmission reach is seen while increasing β, which is because of the reduced PAPR. After an optimal point, however, the performance starts to degrade drastically though the PAPR is still getting lower. As the β increases, the number of data subcarriers being attenuated by α increase, thus limiting the performance by ASE noise. It can be observed that the optimum for SSMF case is 10% for both DM and NDM links while for LEAF the optimum is 5% for NDM and 10% for DM links. In summary it can be said that the optimum is between 5% and 10% for all cases.
In this paper, spectrally shaped DFTS-OFDM has been presented to mitigate the fiber nonlinearity. It is shown that for S-OFDM, the optimum number of bands is similar to the one for DFTS-OFDM and the maximum reach of S-OFDM surpasses DFTS-OFDM by ~6.8% and ~10.8% for NDM and DM links, respectively for both SSMF and LEAF transmission. It is also shown that the excess bandwidth parameter of around 5% to 10% provides better nonlinear tolerance. In summary, S-OFDM is an interesting approach that benefits from the advantages of CO-OFDM along with lower PAPR and can be used for long haul transmission.
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