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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 6115–6130
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Nonlinear performance of multi-granularity orthogonal transmission systems with frequency division multiplexing

Fan Zhang, Chuanchuan Yang, Xi Fang, Tingting Zhang, and Zhangyuan Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 6115-6130 (2013)
http://dx.doi.org/10.1364/OE.21.006115


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Abstract

Orthogonal transmission with frequency division multiplexing technique is investigated for next generation optical communication systems. Coherent optical orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiplexing (SCFDM) schemes are compared in combination with polarization-division multiplexing quadrature phase shift keying (QPSK) or 16-QAM (quadrature amplitude modulation) formats. Multi-granularity transmission with flexible bandwidth can be realized through ultra-dense wavelength division multiplexing (UDWDM) based on the orthogonal technique. The system performance is numerically studied with special emphasis on transmission degradations due to fiber Kerr nonlinearity. The maximum reach and fiber capacity for different spectral efficiencies are investigated for systems with nonlinear propagation over uncompensated standard single-mode fiber (SSMF) links with lumped amplification.

© 2013 OSA

1. Introduction

The continuously increasing growth of traffic in backbone networks pushes the demand for a more effective exploitation of the optical fiber capacity. Coherent detection obtains the full information of the optical field in both polarizations, enabling digital signal processing (DSP) techniques to compensate for transmission distortions, which could pave the way for approaching the fundamental Shannon limit of information capacity.

Orthogonal frequency division multiplexing (OFDM) is a well-established multi-carrier (MC) transmission scheme in the field of wireless communications [1

1. 3rd Generation Partnership Project, “Physical layer aspects for evolved universal terrestrial Radio access (UTRA),” http://www.3gpp.org/ftp/Specs/html-info/25814.htm.

], which stands out as a standard for many applications such as the Long Term Evolution (LTE) of cellular systems by the Third Generation Partnership Project (3GPP), Mobile Worldwide Interoperability for Microwave Access (WiMax), wireless local area network (LAN), etc. Coherent optical OFDM (CO-OFDM) has been recently extensively studied as a strong candidate for long-haul optical transmission. Terabit per channel transmission based on CO-OFDM technique has been reported by the research groups worldwide [2

2. R. Dischler and F. Buchali, “Transmission of 1.2 Tb/s continuous waveband PDM-OFDM-FDM signal with spectral efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” in Proc. Optical Fiber Communication Conference 2009, Paper PDPC2.

6

6. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckha, “Transmission of a 1.2-Tb/s 24-Carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proc. 35 th European Conference on Optical Communication, 2009, Paper PD2.6.

]. One of the main advantages of CO-OFDM is its resilience to the linear channel impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD). Moreover, OFDM has a rectangular-like spectrum, which provides the possibility of high spectral efficiency (SE). One can aggregate tightly spaced optical subcarriers to form a super-channel conveying ultra-high speed signals. Both Terabit transmission and ultra-dense wavelength division multiplexing (UDWDM) systems can be constructed based on the orthogonal technique.

Terabit per second super-channel transmission of polarization-division-multiplexing (PDM) CO-SCFDM signals has been experimentally demonstrated [11

11. C. Zhao, Y. Chen, S. Zhang, J. Li, F. Zhang, L. Zhu, and Z. Chen, “Experimental demonstration of 1.08 Tb/s PDM CO-SCFDM transmission over 3170 km SSMF,” Opt. Express 20(2), 787–793 (2012). [CrossRef] [PubMed]

, 12

12. Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-Spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012). [CrossRef] [PubMed]

]. In [11

11. C. Zhao, Y. Chen, S. Zhang, J. Li, F. Zhang, L. Zhu, and Z. Chen, “Experimental demonstration of 1.08 Tb/s PDM CO-SCFDM transmission over 3170 km SSMF,” Opt. Express 20(2), 787–793 (2012). [CrossRef] [PubMed]

], 40 optical subcarriers tightly spaced at 9.375 GHz carry 1.08 Tb/s OFDM or SCFDM signals, transmitting over 2536 km or 3170 km standard single-mode fiber (SSMF), respectively. Compared with CO-OFDM, CO-SCFDM has about 1.0 dB more nonlinear tolerance, thus achieves a larger maximum transmission reach in the experiment [11

11. C. Zhao, Y. Chen, S. Zhang, J. Li, F. Zhang, L. Zhu, and Z. Chen, “Experimental demonstration of 1.08 Tb/s PDM CO-SCFDM transmission over 3170 km SSMF,” Opt. Express 20(2), 787–793 (2012). [CrossRef] [PubMed]

]. In [12

12. Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-Spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012). [CrossRef] [PubMed]

], 87 optical subcarriers spaced at 5.15625 GHz carry 1.45 Tb/s DFT-S-OFDM signals, transmitting over 480 km SSMF.

UDWDM is highly desired for high spectral efficiency transmission. Meanwhile, flexible bit-rate and/or bandwidth transmission can be achieved by controlling the amount or the granularity of the optical subcarrier in an OFDM/SCFDM super-channel. Grid-less UDWDM system would provide transport service from Gigabit to Terabit per second through tightly spaced super-channels. The super-channel can be transmitted or routed as a single entity. Each optical subcarrier within the super-channel can also be added or dropped to realize sub-wavelength allocation [13

13. Y. Chen, J. Li, C. Zhao, L. Zhu, F. Zhang, Y. He, and Z. Chen, “Experimental demonstration of ROADM Functionality on an optical SCFDM Superchannel,” IEEE Photon. Technol. Lett. 24(3), 215–217 (2012). [CrossRef]

]. Limits of spectral efficiency and transmission reach are analyzed for grid-less OFDM super-channels [14

14. A. Klekamp, R. Dischler, and F. Buchali, “Limits of spectral efficiency and transmission reach of optical-OFDM Superchannels for adaptive Networks,” IEEE Photon. Technol. Lett. 23(20), 1526–1528 (2011). [CrossRef]

]. In [14

14. A. Klekamp, R. Dischler, and F. Buchali, “Limits of spectral efficiency and transmission reach of optical-OFDM Superchannels for adaptive Networks,” IEEE Photon. Technol. Lett. 23(20), 1526–1528 (2011). [CrossRef]

], adaptive WDM system is simulated through 5 channels with variable modulation format, symbol rate or channel spacing, while the OFDM signal always has a constant number of 120 data subcarriers.

The paper is outlined as follows. In Section 2, we present a general theoretical treatment of PDM-CO-OFDM and PDM-CO-SCFDM systems. In Section 3, we provide a uniform frame design of OFDM/SCFDM for different granularities. Section 4 compares the basic performance of CO-OFDM/SCFDM systems at back to back (BTB) scenario. The PAPR character is also discussed in both BTB case and dispersive channels. Section 5 shows nonlinear transmission performance of UDWDM systems based on OFDM/SCFDM techniques. The fiber capacity and the maximum transmission reach are studied in terms of various modulation formats, granularities and guard bands. Cross phase modulation (XPM) induced performance distortions are also specified. Finally, in Section 6, we comment on our results and draw the conclusions.

2. Basic theory

PDM system can be modeled with a 2 × 2 multiple-input multiple-output (MIMO) technique. hxx, hyx, hxyand hyy are time domain channel impulse response (CIR) vectors of the four equivalent MIMO channels with a memory length of l1.
hxx=[hxx(0)hxx(1)hxx(l1)],hyx=[hyx(0)hyx(1)hyx(l1)],hxy=[hxy(0)hxy(1)hxy(l1)],hyy=[hyy(0)hyy(1)hyy(l1)].
(3)
F=[f0f1fN1]Hdenotes DFT transformation whose element fm is described as

fm=1N[1ej2πNmej2π(N1)Nm]T.
(4)

Here the superscript H and T stand for Hermitian transpose and transpose, respectively. wiof size 2N×1 denotes additive white Gaussian noise (AWGN).

For CO-OFDM, a few (Nvirtual) side subcarriers are usually turned off to spectrally separate the aliasing products generated by DAC processing. For PDM-CO-SCFDM transmission, the mapped information sequence at the transmitter is first grouped into data blocks of length M(MN). The elements of the ith data block ai for two polarizations are aix=[aix(0)aix(1)aix(M1)]T and aiy=[aiy(0)aiy(1)aiy(M1)]T. aix and aiy are transformed into frequency domain by M-point DFT, respectively. Then the M-point DFT outputs are mapped to N orthogonal subcarriers by allocating virtual subcarriers at both sides of the band. After the N-point IDFT which transforms the signal to time domain, cyclic extension is inserted for each block before the data sequence is transmitted. Therefore, for PDM-CO-SCFDM transmission, the received signal ri is
ri=[F00F][CxxCyxCxyCyy][FH00FH][TF˜00TF˜]ai+wi.
(5)
Here the DFT transformation matrixF˜=[f0f1fM1]H. For the widely-used localization mapping in CO-SCFDM transmission, the mapping matrix T can be described as
T=[0lT×MIM×M0(N-M-lT)×M].
(6)
Here lT and M determine which part of the whole spectrum is used for transmission. In order to realize a fair comparison between OFDM and SCFDM in terms of SE, the same virtual carriers with length of Nvirtual/2 are allocated at both sides of OFDM/SCFDM frequency band by setting Nvirtual=NM and lT=Nvirtual/2. Virtual subcarriers provide an oversampling to separate the aliasing products with an electrical low-pass filter (LPF).

Intra-symbol frequency-domain averaging (ISFA) [15

15. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

, 16

16. X. Liu and F. Buchali, “A novel channel estimation method for PDM-OFDM enabling improved tolerance to WDM nonlinearity,” in Proc. Optical Fiber Communication Conference 2009, Paper OWW5.

] based channel estimation and equalization is considered in this paper. At the transmitter, the training sequences Px and Py for the two polarization branches are inserted, respectively, which consist of a pair of correlated dual-polarization (CDP) training symbols as
Px=[pxpx],Py=[pypy].
(7)
Herepx=[px(0)px(1)px(N1)] and py=[py(0)py(1)py(N1)]. Based on Eq. (1) and Eq. (5), one can obtain the channel frequency domain transformation matrix

H=[HxxHyxHxyHyy]=[F00F][CxxCyxCxyCyy][FH00FH].
(8)

The estimation of H is denoted by H^, which can be derived with the ISFA method as
[H^xx(k)H^yx(k)H^xy(k)H^yy(k)]=12m+1k=kmk+m12[r1x(k)+r2x(k)px(k)r1x(k)r2x(k)py(k)r1y(k)+r2y(k)px(k)r1y(k)r2y(k)py(k)].
(9)
Herek=1,2,,N,rix=[rix(1)rix(2)rix(N)] and riy=[riy(1)riy(2)riy(N)]. The averaging is performed over subcarrier k and its m left and mright neighbors. The averaging window includes totally 2m+1 adjacent subcarriers. Near the two edges of OFDM/SCFDM band, the window size has to be narrowed to keep only the data subcarriers as well as a symmetrical averaging with the center of subcarrier k. To obtain more accurate H^, the preamble consisting of multi-pair of training symbols can be inserted for each polarization branch. The estimated channel frequency domain transformation matrices, which correspond to each pair of CDP training symbols, can be averaged to obtain the final H^. Thus the equalized PDM-CO-OFDM signal can be obtained by
a^i=H^1ri.
(10)
While for PDM-CO-SCFDM, the estimation of the transmitted data aican be derived by

a^i=[F˜HTT00F˜HTT]H^1ri.
(11)

3. Multi-granularity design principle

The virtual subcarriers for oversampling provide a guard band in the frequency domain to reduce the out-of band radiation. The optical subcarrier within one super-channel may pass a reconfigurable optical add–drop multiplexer (ROADM). The guard band between optical subcarriers should also account for optical filtering effect. Moreover, in practice, a frequency drift may exist when optical subcarriers come from different sources, a guard band can increase the tolerance to this kind of orthogonal misalignment. Therefore, an oversampling ratio of about 120% is adopted in this work.

Table 1

Table 1. OFDM/SCFDM parameters

table-icon
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gives a list of OFDM/SCFDM parameters. Note that a fast Fourier transform (FFT) or inverse fast Fourier transform (IFFT) is an efficient algorithm to compute DFT and its inverse. An FFT size of 4096 is chosen for 100G operation with a sampling rate of 37 GS/s. The symbol duration is 117.1 ns and the cyclic overhead is 5.86%. The effective symbol duration Teff without cyclic extension is 110.6 ns. If a preamble ratio is set as 2.44%, a total of 8.3% overhead are obtained. For multiple optical granularities operation, FFT simply scales to different sizes, while electrical subcarrier spacing Δf remains the same value of 9.04 MHz. Therefore both the symbol duration and cyclic overhead keep unchanged for multi-granularity optical carriers. An FFT size of 1024, 2048 and 4096 corresponds to a respective sampling rate Sp of 9.25, 18.5 and 37 GS/s. The above scenarios can be referred as fine, medium and coarse granularities, which have effective bandwidths Beff of 7.75, 15.5 and 31 GHz, respectively. Grid-less UDWDM systems can be constructed on the basis of such tightly spaced optical carriers. As cyclic overhead is the same for different granularities, cyclic supported transmission reach should be doubled when the granularity downs to half size.

4. Basic comparison of OFDM and SCFDM

Figures 2
Fig. 2 Constellation diagrams of PDM CO-OFDM and CO-SCFDM with QPSK mapped. (a) OFDM before equalization; (b) SCFDM before equalization; (c) OFDM after equalization; (d) SCFDM after equalization. FFT granularity is 1024. The OSNR is set as 25 dB.
and 3
Fig. 3 Constellation diagrams of PDM CO-OFDM and CO-SCFDM with 16-QAM mapped. (a) OFDM before equalization; (b) SCFDM before equalization; (c) OFDM after equalization; (d) SCFDM after equalization. FFT granularity is 1024. The OSNR is set as 25 dB.
show constellation diagrams of PDM CO-OFDM/SCFDM systems at BTB scenario for QPSK and 16-QAM signals mapped, respectively. The optical signal to noise ratio (OSNR) is set as 25 dB at a resolution of 0.1 nm. Before equalization, the constellation diagrams will be influenced by optical and electrical filtering at both the transmitter and the receiver sides. After equalization, the signal can be recovered with only the degradation from amplified spontaneous emission (ASE) noise remains. Note that before equalization, two polarizations will superimpose on each other and virtual subcarriers remain around the constellation origins. The constellations of OFDM and SCFDM are different before equalization due to the extra FFT and IFFT processing in SCFDM systems. After equalization, similar performances are observed for both OFDM and SCFDM systems. The back-to-back performance of OFDM/SCFDM-PDM-QPSK signals, in terms of OSNR needed to achieve a bit error rate (BER) of 10−3 is 7.9, 10.9, and 13.9 dB for the granularities of 7.75, 15.5 and 31 GHz, respectively. For PDM-16-QAM signals, the corresponding required OSNRs are 14.7, 17.7, and 20.7 dB, respectively.

For linear transmission, we evaluate the PAPR distribution with complementary cumulative distribution function (CCDF), which gives the probability of the PAPR higher than a certain threshold. Figure 4
Fig. 4 CCDF curves of PAPR of OFDM and SCFDM systems. The granularity of 7.75 GHz with (a) QPSK and (b) 16-QAM formats is considered.
shows the CCDF curves of the PAPR for OFDM and SCFDM systems. The fine granularity with QPSK and 16-QAM encoded is chosen as an example. 12800 OFDM/SCFDM symbols are transmitted to calculate the PAPR samples. SCFDM demonstrates much lower PAPR at BTB scenario. After transmission, the PAPR of SCFDM increases with accumulated dispersion. In contrast, the PAPR distribution of OFDM keeps almost unchanged with transmission. After thousands of kilometers SSMF propagation, SCFDM demonstrates similar PAPR distribution as OFDM. This confirms that SCFDM has the single carrier character, which has been observed in single carrier frequency domain equalization (SCFDE) systems [21

21. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009). [CrossRef]

]. Due to the low PAPR, SCFDM has superior nonlinear performance compared to OFDM, which is shown in Section 5. It is interesting to note that for OFDM system, similar PAPR distribution is observed for both QPSK and 16-QAM signals regardless of propagation distance. In contrast, for SCFDM, 16-QAM yields larger PAPR than QPSK, although the difference becomes trivial after longer propagation.

5. Nonlinear performance

Each UDWDM channel is polarization-multiplexed and encoded with different and uncorrelated pseudo-random binary sequence (PRBS). A time window of 64 Teff is chosen to perform simulation. We first study UDWDM systems with optical carrier spacing of Sp. The corresponding guard bandwidth is GB=NvirtualΔf. Then we change the guard bandwidth to see how it influences the performance of UDWDM systems.

5.1 Time and frequency domain averaging

Ntraining training symbols are implemented in the center channel for channel estimation. Both the time domain averaging based on multiple training symbols and the frequency domain averaging ISFA method based on subcarriers are employed to obtain a more accurate estimation of channel matrix.

Note that the number of averaged subcarriers of ISFA processing is ultimately limited by phase variation induced by large amount of residual dispersion [15

15. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

]. For less than about 1 rad phase difference between the center subcarrier and the farthest subcarrier in the averaging process of the ISFA, the criterion is deduced in [15

15. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

] and we rewrite it again with the parameters defined in our paper.

|DISFA(ps/nm)|<1068πBeff(GHz)mΔf(GHz).
(12)

DISFA is the residual dispersion prior to the ISFA. Beff is the effective bandwidth of OFDM/SCFDM signals. As 2m+1 is the averaging subcarrier number of the ISFA window, mΔfis the optical frequency difference between the center subcarrier and the farthest subcarrier in the ISFA averaging process. For instance, after 50 spans transmission in Fig. 5, the residual dispersion is 68000 ps/nm, which yields the dispersion limited ISFA window with less than 17 subcarriers (m<8.3). We test the ISFA window with the averaging subcarrier number larger than 17, the system performance will degrade due to the criterion of Eq. (12).

The residual dispersionDISFAis less than the cyclic supported values, which is inversely proportional to the effective bandwidth Beff. Therefore, the averaging ISFA window should be approximately the same for different granularities.

More training symbols and ISFA subcarriers would also increase preamble overhead and DSP complexity. For a trade-off, we choose Ntraining=4 pairs for time domain averaging and 11 subcarriers for frequency domain averaging in the following studies, which provide sufficient channel estimation accuracy and fulfill the criterion of Eq. (12).

5.2 Simulation bandwidth choice

The nonlinear penalty increases with the bandwidth expanding of UDWDM system and tends to saturate when UDWDM system assembles more and more channels. For instance, a 27-channel OFDM-QPSK system with fine granularity suffers a QBERdegradation of 1.61dB compared to the single channel transmission, while a further increase of 12 channels only brings 0.1dB additional nonlinear penalty. Similar results are observed in both QPSK and 16-QAM systems with different granularities. Therefore we choose the number of simulated tightly aggregated optical carriers as 28, 14, and 7 at the granularities of 7.75, 15.5 and 31 GHz, respectively. With an optical channel spacing of Sp, the same bandwidth occupancy of 259 GHz is obtained for all three configurations, which ensures a fair comparison between different granularities. It is worthy to note that 259 GHz bandwidth is appropriate to evaluate nonlinear degradation of UDWDM systems. Further increase of simulation bandwidth will observe slightly difference of nonlinear penalty, while result in unrealistic computer time. When extrapolating the results to the entire C-band, we implicitly assume that the nonlinear distortions of optical carriers can be well approximated by such UDWDM systems.

5.3 Maximum reach and fiber capacity

For OFDM and SCFDM systems with different granularities, we assess the maximum transmission distance still ensuring a BER below the FEC threshold of BER = 4 × 10−3. The transmission reach for BER≤4 × 10−3 is shown in Fig. 8 for QPSK and 16-QAM formats, as a function of optical launch power. For UDWDM operation, optical channel spacing is set as Sp. We can draw the following observations from Fig. 8. SCFDM has a larger maximum transmission reach in both QPSK and 16-QAM systems with various granularities for both single channel and UDWDM scenarios. In the left column of Fig. 8, with QPSK mapped, although suffers the most serious XPM degradation, the fine granularity still has the longest maximum reach, compared to the medium and the coarse granularities. For the coarse granularity, the maximum reach decreases slightly at UDWDM systems compared with the single channel scenario, indicating that the nonlinear distortions mainly result from intra-channel effect instead of inter-channel ones. The right column of Fig. 8 demonstrates the transmission reach for OFDM and SCFDM systems with 16-QAM mapped. For single channel operation, the transmission reach decreases at the larger granularity, this is the same as the QPSK cases. For 16-QAM format, the inter-channel nonlinearities strongly degrade the system performance, especially in the smaller granularities. Therefore, for UDWDM systems, it is interesting almost the same maximum reach is observed for different granularities.

The above discussions assume UDWDM systems with optical channel spacing of Sp. In the following paragraphs, we study UDWDM performance as a function of guard bandwidth. In order to compare the different granularities in a general frame, we define the normalized guard band with regard to the effective bandwidthGBnormal=GB/Beff.

Figures 9
Fig. 9 Maximum reach at the threshold of BER = 4 × 10−3 versus fiber capacity in the C-band (top axis) and spectral efficiency (bottom axis) for OFDM-QPSK (squares) and SCFDM-QPSK (circles).
and 10
Fig. 10 Maximum reach at the threshold of BER = 4 × 10−3 versus fiber capacity in the C-band (top axis) and spectral efficiency (bottom axis) for OFDM-16-QAM (squares) and SCFDM-16-QAM (circles).
show the maximum reach Lmax in terms of fiber capacity and spectral efficiency for PDM-OFDM/SCFDM systems with QPSK and 16-QAM formats, respectively. The spectral efficiency varies from 1.48 to 3.15 bit/s/Hz for QPSK, and from 2.96 to 6.30 bit/s/Hz for 16-QAM. The corresponding normalized guard band varies from 1.178 to 0.026. For QPSK, the maximum reach decreases significantly with the increase of SE at the fine and medium granularities. For the coarse granularity, it is interesting to see that the maximum reach changes slightly with different SE, indicating that XPM distortion is not serious for this scenario. For 16-QAM, the maximum reach is much less than that of QPSK due to both the high OSNR requirement and large nonlinear distortions. Figure 10 shows the maximum reach increases moderately with the SE decreases for all granularities we considered.

As shown in Figs. 9 and 10, we can see that the high SE, or equivalently, large fiber capacity usually corresponds to short transmission distance. We thus use the widely known SE-distance product to measure the performance of UDWDM systems. Figures 11
Fig. 11 Maximum SE-distance product at the threshold of BER = 4 × 10−3 as a function of the normalized guard band for OFDM-QPSK (squares) and SCFDM-QPSK (circles).
and 12
Fig. 12 Maximum SE-distance product at the threshold of BER = 4 × 10−3 as a function of the normalized guard band for OFDM-16-QAM (squares) and SCFDM-16-QAM (circles).
, which are derived from the data of Figs. 9 and 10, plot the values of SE×Lmax achievable with both QPSK and 16-QAM PDM-OFDM/SCFDM signals over SSMF as a function of the normalized guard band.

For QPSK, the SE-Lmaxproduct is similar for the fine and the medium granularities, but significantly degrades for the coarse granularity. For 16-QAM, the SE-Lmax product is similar for all the three granularities considered, indicating that multi-level formats such as 16-QAM or above can only increase system capacity with a limited transmission reach. For orthogonal transmission with OFDM/SCFDM, the maximum value of SE-distance product is usually achieved at the small guard band.

6. Conclusion

In this paper, we numerically investigate orthogonal UDWDM transmission based on PDM CO-OFDM and CO-SCFDM techniques at various granularities. Compared to OFDM, SCFDM shows better nonlinear performance over uncompensated SSMF transmission with EDFA amplification. If PDM-QPSK mapped, both the fine and the medium granularities demonstrate significantly larger SE-distance product than the coarse granularity. For instance, PDM-QPSK can achieve a capacity of 12.6 Tb/s with a maximum reach of 5120 km for SCFDM and 4400 km for OFDM at the fine granularity. However, if 16-QAM mapped, the maximum reach becomes much smaller compared to QPSK scenario. The SE-distance product is slightly different for these three granularities. For instance, PDM-16-QAM can achieve a capacity of 25.2 Tb/s with a maximum reach of 1120 km for SCFDM and 1024 km for OFDM at the fine granularity. For UDWDM system with orthogonal transmission, tightly spaced optical carriers usually show better performance in terms of SE-distance product.

Acknowledgment

This work is supported by Natural Science Foundation of China (No. 61077053, 60932004 and 61275005), National Hi-tech Research and Development Program of China (No.2012AA011302), National Basic Research Program of China (No. 2010CB328201) and Program for New Century Excellent Talents in University.

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2.

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14.

A. Klekamp, R. Dischler, and F. Buchali, “Limits of spectral efficiency and transmission reach of optical-OFDM Superchannels for adaptive Networks,” IEEE Photon. Technol. Lett. 23(20), 1526–1528 (2011). [CrossRef]

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17.

F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag. 48(3), S48–S55 (2010). [CrossRef]

18.

D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory 18(4), 531–532 (1972). [CrossRef]

19.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]

20.

I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010). [CrossRef]

21.

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 15, 2013
Manuscript Accepted: February 19, 2013
Published: March 4, 2013

Citation
Fan Zhang, Chuanchuan Yang, Xi Fang, Tingting Zhang, and Zhangyuan Chen, "Nonlinear performance of multi-granularity orthogonal transmission systems with frequency division multiplexing," Opt. Express 21, 6115-6130 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-6115


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References

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  11. C. Zhao, Y. Chen, S. Zhang, J. Li, F. Zhang, L. Zhu, and Z. Chen, “Experimental demonstration of 1.08 Tb/s PDM CO-SCFDM transmission over 3170 km SSMF,” Opt. Express20(2), 787–793 (2012). [CrossRef] [PubMed]
  12. Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-Spread OFDM transmission using orthogonal band multiplexing,” Opt. Express20(3), 2379–2385 (2012). [CrossRef] [PubMed]
  13. Y. Chen, J. Li, C. Zhao, L. Zhu, F. Zhang, Y. He, and Z. Chen, “Experimental demonstration of ROADM Functionality on an optical SCFDM Superchannel,” IEEE Photon. Technol. Lett.24(3), 215–217 (2012). [CrossRef]
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  15. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express16(26), 21944–21957 (2008). [CrossRef] [PubMed]
  16. X. Liu and F. Buchali, “A novel channel estimation method for PDM-OFDM enabling improved tolerance to WDM nonlinearity,” in Proc. Optical Fiber Communication Conference 2009, Paper OWW5.
  17. F. Chang, K. Onohara, and T. Mizuochi, “Forward error correction for 100 G transport networks,” IEEE Commun. Mag.48(3), S48–S55 (2010). [CrossRef]
  18. D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory18(4), 531–532 (1972). [CrossRef]
  19. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983). [CrossRef]
  20. I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett.22(9), 631–633 (2010). [CrossRef]
  21. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun.E92-B(12), 3736–3743 (2009). [CrossRef]

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