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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 9 — Apr. 28, 2008
  • pp: 6209–6215
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Fiber nonlinearity precompensation for long-haul links using direct-detection optical OFDM

Liang B. Y. Du and Arthur J. Lowery  »View Author Affiliations


Optics Express, Vol. 16, Issue 9, pp. 6209-6215 (2008)
http://dx.doi.org/10.1364/OE.16.006209


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Abstract

The use of nonlinearity precompensation in direct-detection optical orthogonal frequency division multiplexed links is investigated by simulation. Because of the presence of a strong optical carrier its performance is poorer than for coherent systems: with compensation the signal quality is found to vary almost periodically across the signal band. We propose and explain the operation of two optical, one electrical and one computational method of removing this periodic variation. Optical filtering of one sideband at the receiver is most effective, but a substantial improvement can be obtained by a simple modification to the precompensation algorithm.

© 2008 Optical Society of America

1. Introduction

Optical OFDM is receiving much attention [1]–[4]

1. A. J. Lowery and J. Armstrong, “Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006). [CrossRef] [PubMed]

because of its ability to electronically compensate for fiber dispersion in long-haul optical communications systems. However, it requires low optical powers along the link, because inter-sub-carrier Four-Wave Mixing (FWM) between the OFDM subcarriers causes significant degradation [5

5. A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007). [CrossRef] [PubMed]

]. This limits the transmission distance for a given optical amplifier spacing, as the signal cannot be allowed to drop below the noise floor before re-amplification. [6

6. A. J. Lowery, L. B. Y. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25, 131–138 (2007). [CrossRef]

]. Recently, we have shown that the effect of fiber nonlinearity can be partially compensated in a Coherent Optical OFDM system (CO-OFDM) [2

2. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006). [CrossRef]

], [4

4. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM Transmission over 4,160-km SSMF Enabled by RF-Pilot Tone Phase Noise Compensation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007- PDP15 [PubMed]

] using nonlinearity precompensation [7

7. A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19, 1556–1558 (2007). [CrossRef]

], or a combination of precompensation and postcompensation [8

8. A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt. Express 15, 12965–12970 (2007). [CrossRef] [PubMed]

]. Shieh, Ma, and Tang [9

9. W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15, 9936–9947 (2007). [CrossRef] [PubMed]

] have demonstrated postcompensation experimentally.

Direct-detection optical OFDM (DDO-OFDM) offers a simpler receiver architecture than CO-OFDM, so could offer cost and space savings, albeit with increased Optical-Signal to Noise Ratio (OSNR) requirements [10

10. A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express 16, 860–865 (2008). [CrossRef] [PubMed]

]. With DDO-OFDM, an optical carrier is transmitted along the fiber with the OFDM subcarriers, so nonlinearity will cause interactions between the carrier and the OFDM sideband, causing the generation of additional optical frequencies. These frequencies could cause some additional nonlinear degradation of the received electrical signal, compared with CO-OFDM. An open question is whether nonlinearity compensation is effective with DDO-OFDM because of these additional mixing products.

In this paper, we demonstrate that nonlinear precompensation is effective for DDO-OFDM systems. However, the nonlinear interactions of the carrier and the OFDM subcarriers have to be considered. Additionally, precompensation causes a periodic variation of signal quality across the signal bandwidth. We propose four methods to mitigate this periodic variation: two using optical filters, one using an electrical filter, and one using a modified calculation of the precompensation waveform. Their performance is compared using numerical simulations.

2. Optical transmitter with precompensation

The principle of operation of optical OFDM is well-known, and the block diagram of a complete system can be found elsewhere [1

1. A. J. Lowery and J. Armstrong, “Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006). [CrossRef] [PubMed]

]. Nonlinear precompensation is discussed in [7

7. A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19, 1556–1558 (2007). [CrossRef]

]. For the purposes of discussion, the transmitter modulator is divided into two parts, shown in Figure 1; however, the function of the two modulators could be combined into a single “complex” modulator (a cascaded triple Mach-Zehnder Interferometer). For coherent OFDM, the first modulator is biased at its null to create a set of optical subcarriers mimicking the electrical OFDM spectrum carried on the waveform VOFDM(t). For direct-detection systems, the modulator can be biased slightly off its null point to give a carrier [3

3. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of 20 Gbit/s direct-detection optical OFDM and 12 Gbit/s with a colorless transmitter,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP18. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP18 [PubMed]

]: a carrier power equal to the power in the sidebands usually results in optimum performance [1

1. A. J. Lowery and J. Armstrong, “Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006). [CrossRef] [PubMed]

]. The carrier is usually offset from the subcarrier band by a gap equal to the bandwidth of the subcarriers [1

1. A. J. Lowery and J. Armstrong, “Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006). [CrossRef] [PubMed]

].

Fig. 1. Block diagram for an optical OFDM transmitter with nonlinear precompensation.

The phase modulator implements the nonlinearity precompensation [7

7. A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19, 1556–1558 (2007). [CrossRef]

], and is usually driven by to give a phase shift, φ(t), linearly proportional to the instantaneous optical power, P(t) at the input to the first fiber span. This phase shift is intended to compensate for the nonlinear phase shift within the fiber itself. The constant of proportionality is defined here using: effective length per fiber span, Leff; number of spans, s; nonlinear coefficient n 2; effective cross-sectional area of the fiber, Aeff; centre wavelength, λ 0:

ϕ(t)=2πn2sLeffP(t)(λ0Aeff)
(1)

The electrical bandwidth of the phase modulator drive will depend on whether there is an optical carrier or not. For example, in a coherent system, the drive will be a result of the superposition of all of the subcarrier fields, and will have a bandwidth equal to the bandwidth of the subcarriers (5 GHz for a 10-Gbit/s 4-QAM system). In a direct-detection system, the drive will include the contribution of the offset optical carrier, so will have strong components in the 5–10 GHz band due to the mixing of the carrier and each subcarrier, and also components from 0 to 5-GHz due to intermixing of the subcarriers with one-another.

The phase modulation (PM) of the optical OFDM signal creates distortion tones that considerably broaden the optical spectrum: Fig. 1 (inset) shows a simulated spectrum (top). These tones can be classified according to their origins, as shown in the lower spectrum of Fig. 1. Distortion A is caused by phase modulation of the subcarriers by the instantaneous power corresponding to the mixing of subcarriers with other subcarriers within the subcarrier band. There are many possible contributions to the instantaneous power, especially for pairs of subcarriers with a small frequency difference, but the maximum modulation frequency is equal to the bandwidth of the subcarrier band. Distortion A is the only component in a coherent system. For direct-detection systems, there are additional tones: Distortion B is caused by phase modulation of the optical carrier by the difference frequencies of the carrier and each subcarrier; Distortion C is caused by the subcarriers being modulated by these same difference frequencies. As shown in Section 5, bandlimiting the electrical drive affects which of the distortion products are produced, hence which nonlinear products are compensated.

3. Comparison of CO-OFDM and DD-OFDM systems without precompensation

Figure 2 plots the signal quality versus subcarrier for direct-detection and coherent systems, both operating with -6 dBm fiber-input power in the sidebands to give similar error rates in the absence of nonlinearity. This is at least 3-dB higher than the power where Q is noise limited. A 17-point (17-subcarriers) moving average was used to smooth across the x-axis. The coherent results are shown as dashed lines. These are symmetrical versus subcarrier index, with the poorest performance in the centre as more FWM products fall on the central subcarriers [5

5. A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007). [CrossRef] [PubMed]

]. In the direct-detection systems, the Q is further degraded because of the nonlinear interaction between the optical carrier and the subcarrier band. This creates an image (Distortion B) of the sideband that falls on the opposite side of the carrier. In short systems and for subcarriers close to the carrier, this image is the conjugate of the subcarrier band, and will actually cancel nonlinearity: a small improvement in Q can be seen for the lowest-frequency carriers in the 400-km case. For longer systems resonance effects can occur, so the lower-frequency subcarriers can become worse than the higher-frequency subcarriers. It is clear that the simple theory [5

5. A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007). [CrossRef] [PubMed]

] for the signal quality versus subcarrier for coherent systems cannot be used for direct detection systems.

Fig. 2. Signal quality versus subcarrier for coherent (C) and direct-detection (DD) systems without precompensation.

4. Performance of DD-OFDM systems using nonlinearity precompensation

Fig. 3. Dependence on Q on subcarrier frequency for various effective lengths of precompensation.

A frequency-dependent ripple occurs when precompensation is used, suggesting that the phase modulation required for compensation is responsible for this ripple. An explanation for the ripple is that the phase modulation, φ(t), is converted to intensity noise along the dispersive fiber, in a similar manner to laser phase noise being converted to intensity noise [11

11. S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, “Analysis of laser phase noise to intensity noise conversion by chromatic dispersion in intensity modulation and direct detection optical-fiber transmission,” J. Lightwave Technol. 8, 1716–1722 (1990). [CrossRef]

]. This intensity noise is frequency-dependent because PM creates upper and lower sidebands for Distortion B, which undergo opposite frequency-dependent phase shifts relative to the carrier due to dispersion. Upon detection each sideband mixes with the carrier to produce two electrical components that will interfere with one another. Constructive interference produces a large intensity noise, hence a degraded signal quality. Simulation confirmed that the spacing of the ripples depends solely on the dispersion-length product of the system, and this spacing agrees with [11

11. S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, “Analysis of laser phase noise to intensity noise conversion by chromatic dispersion in intensity modulation and direct detection optical-fiber transmission,” J. Lightwave Technol. 8, 1716–1722 (1990). [CrossRef]

]. Stronger precompensation using strong phase modulation leads to stronger ripples. Thus the optimum effective length will be a compromise between how much nonlinearity is compensated and how much noise is generated by the precompensating phase modulation.

5. Strategies for removing the frequency dependence of Q

If one of the compensation sidebands of Distortion B can be removed, then interference should not occur upon photodetection, removing the ripples in signal quality. Sideband removal could be achieved optically either at the transmitter (which will eliminate the strong ripples due to phase modulation at the transmitter, but not ripples caused by the phase modulation in each span), or at the receiver (which should remove all ripples). The extent of the sidebands can also be limited electrically, by bandlimiting the phase modulator drive.

Fig. 4. Performance of the precompensation systems versus subcarrier frequency.

Figure 4 compares optical (transmitter or receiver) filtering with electrical filtering, no filtering, and no precompensation. The effective length was 8 km. No precompensation produces the direct-detection result of Fig. 2. No filtering reproduces the 8-km precompensation result of Fig. 3, with its associated ripples. Transmitter optical filtering, using a filter removing all tones more than 1 GHz below the carrier, produces a minimum Q improvement of around 3 dB, compared with 2 dB without the filter. The average Q value across the bands is not improved significantly. Filtering at the receiver, using a filter extending 1-GHz below the carrier to 1-GHz above the sideband, produces the best average improvement (>4.5 dB minimum improvement). Electrical bandlimiting of the phase modulation waveform produces a similar result to optical filtering at the transmitter, with the advantage that a narrow-band electrical filter is far easier to implement than a narrowband optical filter.

The bandwidth of the phase modulation can also be reduced by modifying the calculation of the power waveform in Eq. (1). For example, removing the carrier from the calculation means that no components exist above 5 GHz. Additional simulations showed that this is equivalent to a 5-GHz brickwall electrical filter. Obviously this calculation is easy to implement using digital signal processing, and is identical to the calculation used to precompensate coherent systems.

6. Discussion

Electrical filtering of the precompensation phase waveform for frequencies above 5 GHz, removes both the upper and lower phase modulated sidebands at greater than 5 GHz away from the carrier and subcarriers. Unfortunately, Distortion B in the fiber is not precompensated. Histograms of Q (Figure 5) show that electrical filtering will increase the average performance of each subcarrier more than a transmitter optical filter, but both systems have similar worst-case performances. Coding over all subcarriers would obviously be beneficial.

Fig. 5. Histograms of Q(dB) for the individual subcarriers. Top - optical filtering at the transmitter; Bottom - electrical filtering at the transmitter.

7. Conclusions

This paper shows that nonlinearity precompensation benefits DDO-OFDM. If the CO-OFDM precompensation scheme [7

7. A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19, 1556–1558 (2007). [CrossRef]

], [8

8. A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt. Express 15, 12965–12970 (2007). [CrossRef] [PubMed]

] is implemented without modification, an image band is transmitted which induces variations in the received signal quality across the subcarrier band. The ripples can be suppressed by optically filtering to remove the image band at the transmitter or preferably the receiver. Since very sharp optical filters are required, this is difficult to achieve. Alternatively, the precompensation input can be electrically band limited to prevent the creation of the image band. This produces similar results to a transmitter optical filter. Alternatively, the phase modulation calculation should exclude the carrier.

Acknowledgments

We would like to thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMaker™WDM V7.1. This work is supported under the Australian Research Council’s Discovery funding scheme (DP 0772937).

References and links

1.

A. J. Lowery and J. Armstrong, “Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14, 2079–2084 (2006). [CrossRef] [PubMed]

2.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42, 587–589 (2006). [CrossRef]

3.

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of 20 Gbit/s direct-detection optical OFDM and 12 Gbit/s with a colorless transmitter,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP18. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP18 [PubMed]

4.

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM Transmission over 4,160-km SSMF Enabled by RF-Pilot Tone Phase Noise Compensation,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007- PDP15 [PubMed]

5.

A. J. Lowery, S. Wang, and M. Premaratne, “Calculation of power limit due to fiber nonlinearity in optical OFDM systems,” Opt. Express 15, 13282–13287 (2007). [CrossRef] [PubMed]

6.

A. J. Lowery, L. B. Y. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25, 131–138 (2007). [CrossRef]

7.

A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19, 1556–1558 (2007). [CrossRef]

8.

A. J. Lowery, “Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM,” Opt. Express 15, 12965–12970 (2007). [CrossRef] [PubMed]

9.

W. Shieh, X. Yi, Y. Ma, and Y. Tang, “Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems,” Opt. Express 15, 9936–9947 (2007). [CrossRef] [PubMed]

10.

A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express 16, 860–865 (2008). [CrossRef] [PubMed]

11.

S. Yamamoto, N. Edagawa, H. Taga, Y. Yoshida, and H. Wakabayashi, “Analysis of laser phase noise to intensity noise conversion by chromatic dispersion in intensity modulation and direct detection optical-fiber transmission,” J. Lightwave Technol. 8, 1716–1722 (1990). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4080) Fiber optics and optical communications : Modulation

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 22, 2008
Revised Manuscript: April 7, 2008
Manuscript Accepted: April 14, 2008
Published: April 18, 2008

Citation
Liang B. Y. Du and Arthur J. Lowery, "Fiber nonlinearity precompensation for long-haul links using direct-detection optical OFDM," Opt. Express 16, 6209-6215 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6209


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References

  1. A. J. Lowery and J. Armstrong, "Orthogonal frequency division multiplexing for dispersion compensation of long-haul optical systems," Opt. Express 14, 2079-2084 (2006). [CrossRef] [PubMed]
  2. W.  Shieh and C.  Athaudage, "Coherent optical orthogonal frequency division multiplexing," Electron. Lett.  42, 587-589 (2006). [CrossRef]
  3. B. J. C. Schmidt, A. J. Lowery and J. Armstrong, "Experimental demonstrations of 20 Gbit/s direct-detection optical OFDM and 12 Gbit/s with a colorless transmitter," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP18. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP18 [PubMed]
  4. S. L.  Jansen, I.  Morita, N.  Takeda, and H.  Tanaka, "20-Gb/s OFDM Transmission over 4,160-km SSMF Enabled by RF-Pilot Tone Phase Noise Compensation," in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15. http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-PDP15 [PubMed]
  5. A. J. Lowery, S. Wang, and M. Premaratne, "Calculation of power limit due to fiber nonlinearity in optical OFDM systems," Opt. Express 15, 13282-13287 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-20-13282 [CrossRef] [PubMed]
  6. A. J.  Lowery, L. B. Y.  Du, and J.  Armstrong, "Performance of optical OFDM in ultralong-haul WDM lightwave systems," J. Lightwave Technol.  25, 131-138 (2007). [CrossRef]
  7. A. J. Lowery, "Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation," IEEE Photon. Technol. Lett. 19,1556-1558 (2007). [CrossRef]
  8. A. J. Lowery, "Fiber nonlinearity pre- and post-compensation for long-haul optical links using OFDM," Opt. Express 15, 12965-12970 (2007). [CrossRef] [PubMed]
  9. W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007). [CrossRef] [PubMed]
  10. A. J. Lowery, "Amplified-spontaneous noise limit of optical OFDM lightwave systems," Opt. Express 16, 860-865 (2008). [CrossRef] [PubMed]
  11. S. Yamamoto, N, Edagawa, H. Taga, Y, Yoshida, and H. Wakabayashi, "Analysis of laser phase noise to intensity noise conversion by chromatic dispersion in intensity modulation and direct detection optical-fiber transmission," J. Lightwave Technol.  8, 1716-1722 (1990). [CrossRef]

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