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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4859–4866
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A hybrid IQ imbalance compensation method for optical OFDM transmission

Abdullah Al Amin, Sander L. Jansen, Hidenori Takahashi, Itsuro Morita, and Hideaki Tanaka  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4859-4866 (2010)
http://dx.doi.org/10.1364/OE.18.004859


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Abstract

Transmitter and receiver IQ imbalance causes image interference that degrades performance in high capacity and high spectral efficiency optical orthogonal frequency division multiplexing (OFDM) schemes. Digital compensation is an attractive method to relax component specifications. In this paper we report the details of a hybrid compensation method for IQ imbalance compensation, comprising of orthogonal training symbol-based method for transmitter-side compensation and an iterative image reduction-based method for receiver-side imbalance compensation. We demonstrate performance improvement using the hybrid method in presence of frequency dependent imbalance by both simulation and back-to-back direct detection optical OFDM experiment. We report on the tolerable limit of transmitter IQ imbalance under presence of carrier frequency offset.

© 2010 OSA

1. Introduction

With the bandwidth consuming internet-based services becoming widely deployed, backbone network speeds in access of 100 Gbps are expected to be needed in the near future. Orthogonal frequency division multiplexing (OFDM) has gained much attention recently for such applications, due to its inherent tolerance to linear impairments such as chromatic dispersion and polarization mode dispersion. Originally developed for wireless communications, OFDM in optical fiber communication has been used to demonstrate high channel capacity transmission of over 100 Gbps or higher [1

1. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2 b/s/Hz spectral efficiency over 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]

,2

2. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]

] using coherent polarization division multiplexed optical OFDM (PDM-OFDM) with no dispersion compensation. Another advantage of OFDM is use of training symbols for channel estimation, which makes it easy to attain high spectral efficiency (SE) by use of high-order modulation, such as 16 QAM. A record SE of 7 b/s/Hz has been achieved using PDM-OFDM with 32QAM modulation at 56 Gbps [3

3. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 bit/s/Hz using 8x65.1-Gbit/s coherent PDM-OFDM,” J. Lightwave Technol. 28, 406–414 (2009). [CrossRef]

]. Recently 100 Gbps-class transmission has also been reported in direct-detection OFDM (DD-OFDM) [4

4. B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “100 Gbit/s transmission using single band direct‐detection optical OFDM,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPC3.

,5

5. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108Gb/s OFDMA‐PON with polarization multiplexing and direct detection,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPD5.

], where the optical carrier is sent along with the OFDM band from the transmitter (Tx), greatly simplifying the receiver (Rx) [6

6. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]

].

From Refs. [1

1. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2 b/s/Hz spectral efficiency over 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]

5

5. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108Gb/s OFDMA‐PON with polarization multiplexing and direct detection,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPD5.

]. we can see that high data rate and/or high SE in OFDM was made possible in two ways, (a) using higher order constellation or (b) using a wider bandwidth for the OFDM band. For (a), a higher electrical signal-noise ratio (SNR) is required at the receiver, meaning tighter requirements of the Tx/Rx components. The later approach (b) is limited by both the sampling rate of state-of-the-art digital-analog/analog-digital converters (DAC/ADC) and by the fact the analog electrical/ optical IQ mixers have increasing amplitude and phase imbalance between I and Q ports the signal bandwidth widens.

It is well known that IQ imbalances cause inter-carrier interference (ICI) from imperfect image rejection in direct conversion-type OFDM receivers [7

7. M. Valkama, M. Renfors, and V. Koivunen, “Advanced methods for I/Q imbalance compensation in communication receivers,” IEEE Trans. Signal Process. 49(10), 2335–2344 (2001). [CrossRef]

,8

8. T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.

]. Even though many IQ imbalance compensation algorithms have been proposed for OFDM wireless transmission [7

7. M. Valkama, M. Renfors, and V. Koivunen, “Advanced methods for I/Q imbalance compensation in communication receivers,” IEEE Trans. Signal Process. 49(10), 2335–2344 (2001). [CrossRef]

,8

8. T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.

], only a few experimental reports exits on their application to optical OFDM transmission [9

9. W. R. Peng, B. Zhang, and X. Wu, K. M. Feng A. E. Willner and S. Chi, “Experimental demonstration of compensating the I/Q imbalance and bias deviation of the Mach-Zehnder modulator for an RF-tone assisted optical OFDM system,” in Proceedings of Europ. Conf. on Opt. Commun. (Amsterdam, 2008), Mo.4.D.3.

11

11. A. Al Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3-Gbit/s direct-detection OFDM transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), OTuO2.

]. In [9

9. W. R. Peng, B. Zhang, and X. Wu, K. M. Feng A. E. Willner and S. Chi, “Experimental demonstration of compensating the I/Q imbalance and bias deviation of the Mach-Zehnder modulator for an RF-tone assisted optical OFDM system,” in Proceedings of Europ. Conf. on Opt. Commun. (Amsterdam, 2008), Mo.4.D.3.

], a training symbol (TS)-based method was applied to Tx-side IQ imbalance compensation in carrier interleaved OFDM, and IQ imbalance due to bias offset of LN optical IQ modulator is compensated with a relatively large TS overhead. Ref [10

10. Y. Ma, W. Shieh, and Q. Yang, “Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2×2 MIMO OFDM Transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2008), JWA 59.

] demonstrates an Rx side IQ imbalance compensation method, where the imbalance parameter is estimated from ellipticity in the relation between in-phase and quadrature components of the beating tone between a fixed local oscillator (LO) and a cw-laser signal. But in order to have reliable estimation of the imbalance the lasers should have low phase noise. Also the whole process needs to be repeated over different frequencies in the full OFDM band to be able to compensate for frequency dependent IQ imbalance, making the calibration time-consuming.

In the following sections, we explain the influence of IQ imbalance in optical OFDM transmission, the proposed methods for Tx and Rx-side IQ imbalance compensations, the simulation and experimental results determining the effectiveness the hybrid compensation and conclusion, respectively.

2. Compensation method for transmitter/ receiver IQ imbalance

For frequency-dependent IQ imbalance on the Rx side could also be compensated by the orthogonal TS-based method with some additional calculation load [8

8. T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.

]. But this required the assumption that the Tx-side IQ imbalance is rather small. Since a wideband IQ mixer might not meet this assumption and the presence of carrier frequency offset (CFO) will cause deviation of symmetric relationship between the training symbols, in this work we propose to use a digital image rejection filter for Rx IQ imbalance compensation that is independent of the amount of Tx IQ imbalances and CFO. Compared to tone-based orthogonalization [10

10. Y. Ma, W. Shieh, and Q. Yang, “Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2×2 MIMO OFDM Transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2008), JWA 59.

], the proposed method requires only two measurements but no precision tunable oscillators. The compensation filter can be efficiently implemented by finite impulse response (FIR) filters. In order to obtain optimal coefficients of this filter, we generate a pair of dummy OFDM signals, each consisting of only the positive and negative frequency subcarriers, respectively. After separately recording a set of received IQ data for the two test signals, we take fast-Fourier transform (FFT) to calculate the received spectral magnitude, and then quantify the total image intensity on the symmetrically opposite bands of the test signal spectrum in the baseband, as indicated in Fig. 2(b). Then an iterative optimization algorithm is used to estimate the required characteristics of the frequency dependent IQ imbalance compensation filter that jointly minimizes the image power ratio (defined as ratio of the spectral power of the image components to the total input power) from both the measurements. Note that the Tx IQ imbalance or CFO can be present during the adjustment, if the image power measurement range is effectively selected. Due to use of test signal and the required time for the optimization algorithm, the process of estimating the filter characteristics is done offline as part of initial calibration process, after which the OFDM receiver stores the filter coefficients in a look-up table (LUT). In the data receiving mode, this filter corrects the relative imbalance of the I and Q components of the received baseband OFDM signal just after ADCs. Then the CFO is corrected and the baseband samples are synchronized in time using training symbols in the usual manner, followed by channel estimation and equalization employing the above-mentioned orthogonal TS-based method for compensation of any possible Tx IQ imbalance.

3. Simulation results for transmitter/ receiver IQ imbalance compensation

In order to verify the effectiveness of the Tx IQ imbalance compensation by simulation, for simplicity we assume ideal detection of OFDM signal with no CFO and no phase noise. The employed OFDM signal has the following parameters: FFT size 1024, symbol length 106.4ns, 700 data subcarriers with 16QAM modulation, resulting in a gross data rate of 27.3 Gbps. after considering 3.9% CP and 2% TS overhead becomes 25.7 Gbps pre-FEC, and after 7% FEC overhead, the net data rate is 24 Gbps. As an example of frequency dependent IQ imbalance, we assume linearly varying amplitude imbalance between 0 and 30% and phase imbalance between 0 and 0.37 rad over the sampling frequency range. According to the channel parameters obtained based on the orthogonal TS, we can estimate these imbalance values over the range of OFDM subcarriers. Figure 3(a)
Fig. 3 Simulation results for Tx-side IQ imbalance compensation with ideal receiver. (a) Comparison of actual amplitude and phase imbalance (assumed to be linearly frequency dependent) with estimation results. OSNR is at 20 dB. (b) Received Es/No for each subcarrier in the case of (a), with and without Tx IQ imbalance compensation. Inset shows constellation for all carriers.
shows a comparison of the estimated values of imbalance parameters to their original values at OSNR of 20 dB (at 0.1 nm res.). As can be seen, except for highly attenuated subcarriers, the estimated values closely match actual applied values. Figure 3(b) compares the per-symbol SNR, Es/No for the case of applying and not applying Tx IQ compensation in presence of the imbalance of Fig. 3(a). As we can see, the TS-based IQ compensation almost reaches uniform performance over all subcarriers and the average Es/No improves to 22 dB from 17 dB, when no IQ compensation is applied.

For the Rx optimization, we have parameterized the compensating filter characteristics over the frequency range of OFDM band, and therefore estimating the filter coefficients can be treated as multi-variate optimization problem. We have used a simulated annealing (SA) algorithm [12

12. Numerical Recipes: The Art of Scientific Computing, Available at: http://www.nr.com.

] to minimize the image power ratio. We have applied a single-side band dummy OFDM signal generated by setting the positive or negative subcarriers to zero, and measured the image power ratio over the entire frequency band that is symmetric from the input with respect to the Rx LO frequency. The frequency range of 10 GHz is linearly interpolated by 20 points of amplitude and phase parameters. The joint image minimization converges to a stable value after 1000 steps in the SA algorithm, at which point we store the required filter parameters for applying to measurement data. Figure 4
Fig. 4 Simulated spectrum of LSB (left) and USB (right) OFDM test signal before and after iterative SA-based image minimization for Rx IQ imbalance compensation. Linearly varying amplitude imbalance of 30% (peak) and phase imbalance of 0.37 rad (peak) is assumed.
shows the difference in the received spectra for both LSB and USB, before compensation and after, for an IQ imbalance that is linearly varying over the OFDM frequency range, with same value as in Fig. 3(a) The corresponding Es/No are same to the case of Tx IQ imbalance, shown in Fig. 3(b), because in the back-to-back case with perfect frequency synchronization, the Rx and Tx IQ imbalances act identically.

4. Experimental results

Figure 5
Fig. 5 Experimental setup for single-band, 27.3Gbit/s 16QAM DD-OFDM transmission for demonstration of the hybrid IQ imbalance compensation method.
shows the Tx/Rx setup used to experimentally verify the simulation results. An arbitrary waveform generator sends out real and imaginary components of a baseband OFDM signal, which are upconverted to achieve a band pass OFDM signal by an electrical IQ mixer and the resulting OFDM signal is applied to a Mach-Zehnder modulator (MZM). After modulation, the LSB of the optical signal is filtered by optical band pass filter (a 50 GHz interleaver was used) and only the carrier and USB are transmitted down transmission fiber. The receiver consists of an EDFA preamplifier, a 0.25-nm band-pass filter (BPF) and a 50-GHz pin-PD. The received signal is boosted and down converted to the baseband by the same type of IQ mixer as used in the Tx. The signals are captured by a real time oscilloscope. For this experiment, the LO frequency and sampling rates were 20 GHz and 20 GSa/s, respectively and the OFDM parameters are similar to simulations in Sec.3. After every 100 OFDM symbols, a pair of orthogonal TS are inserted. At the Rx, TS synchronization, cyclic prefix (CP) removal, FFT and demapping are done by Matlab offline. Two bad carriers at fixed frequencies due to electrical interference from the AWG were removed. For comparison, the received signals were analyzed both with IQ compensation method and without. The BER were measured on 2.2 Mbits.

Figures 6(a)
Fig. 6 Effect of the varying Tx IQ imbalances on the back-to-back DD-OFDM transmission at OSNR of 34 dB for cases of frequency dependent IQ imbalance compensation (Tx/Rx comp) and no IQ compensation (No Tx/Rx comp). Also the case of frequency independent (F.I.) Tx IQ compensation (method of Ref [8].) is demonstrated for comparison. (a) with added amplitude imbalance (phase imbalance minimum). (b) with added phase imbalance (amplitude imbalance minimum). Imbalance values are nominal offset from initial coarse setting. Here each ps of delay corresponds to 0.02 rad phase difference at the highest frequency subcarriers.
and 6(b) shows the Q values measured from BER with respect to amplitude and phase imbalances, respectively. Here, bit error ratio = ½ erfc(Q/√2), assuming Gaussian noise. The received OSNR was set at 34 dB (0.1 nm). As the figures show, the frequency dependent Tx and Rx IQ compensation method shows a better performance than applying no IQ compensation at Tx or Rx. Here we do not assume gain balance by auto-gain control feature after the Rx IQ mixer, which had a fixed amount of inherent IQ imbalance. This results in large improvement due to Rx IQ compensation even though the no intentional imbalance was added to the Rx IQ mixer. Noticeably, application of the Tx IQ imbalance compensation only cannot sufficiently reduce the image interference, which confirms the importance of the hybrid compensation of both Rx and Tx IQ imbalance. Note that the x-axis imbalance values in Figs. 6(a) and 6(b) are nominal values from the DAC settings, and the 0 values of imbalance in both figures refers to a point of coarse adjustment. Therefore, the peak performance is observed at an offset from nominal 0 value of amplitude (about −5%) and phase imbalances (about + 1.5 ps). Furthermore, because overall Q depends on image interference, which in turn is affected by residual frequency dependent imbalances, we can see an asymmetry in Q-vs-imbalance curves. This explains the best performance being achieved at slightly different amount of nominal imbalance values between the cases of applying and not applying the Tx-side IQ compensation.

From Figs. 6(a) and 6(b), the amplitude imbalance seems to be causing greater variation in performance compared to phase imbalance, which is also reflected in simulation [11

11. A. Al Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3-Gbit/s direct-detection OFDM transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), OTuO2.

]. When both Tx and Rx IQ compensations were applied, assuming 1 dB Q penalty to be allowable, the amplitude imbalance tolerable range was more than ± 10%, and phase skew range was more than ± 4 ps, which corresponds to phase imbalance of ± 0.085 rad for the highest frequency subcarriers. When only the Rx IQ compensation is applied, the amplitude imbalance tolerances quantified to be ± 6%, but the absolute performance itself is degraded due to frequency dependent imbalances. Note that the absolute amount of improvement for Q value and imbalance tolerance is dependent on the shape of frequency dependence of each mixer’s IQ imbalance. As this shape may be vary among different broadband IQ mixers, the improvements achieved in Figs. 6(a) and 6(b) should be only interpreted as a qualitative proof of the effectiveness of the proposed Tx side imbalance compensation method. From the figures it is also confirmed that, when we apply frequency independent IQ imbalance compensation by averaging over the derived imbalance coefficients α( ± k) and β( ± k) as in Ref [8

8. T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.

], the absolute Q performance is still worse than the case of frequency dependent IQ imbalance compensation. This is due to the fact that the IQ imbalance of the broadband IQ mixers is typically frequency dependent, and this fact also underscores the usefulness of the proposed frequency dependent IQ imbalance compensation.

Note that due to practical limitations in controlling the imbalance in the IC-packaged IQ mixer at the Rx, we did not experimentally confirm the imbalance tolerance range of the Rx IQ mixer. However with sufficient optimization by the proposed SA algorithm, the Rx compensation filter can be designed to offset the effects of quite large IQ imbalance, as demonstrated in the simulation results in Fig. 4. Therefore, we can conclude that the proposed hybrid IQ compensation method is useful for a wide range of IQ imbalances. The performance improvement comes at only a small increase of digital processing complexity for the Tx-side imbalance. For the Rx-side compensation, only an added step of initial calibration is required, which requires only two measurements steps and does not require sophisticated tools other than the OFDM Tx, which is usually on the same line card as the Rx. The relaxed specifications for DAC/ADC characteristics and broadband IQ mixer/ optical hybrids may well justify any added cost of applying the proposed hybrid IQ imbalance compensation method.

5. Conclusion

We have investigated a hybrid method for independent Tx and Rx-side frequency dependent IQ imbalance compensation for use in high spectral efficiency optical OFDM transmissions. The hybrid method comprises of two simple algorithms: an orthogonal TS-based method for Tx IQ imbalance compensation and an iterative image minimization-based method for Rx IQ imbalance compensation. The proposed method provides a larger performance improvement compared to individual compensation of Tx or Rx IQ imbalance. Both simulation and experimental results showed performance improvement in a back-to-back, 27.3-Gbps, 16QAM OFDM setup under presence of small amount of CFO. The proposed method was found to be effective under a wide range of frequency dependent IQ imbalances, with more than ± 10% amplitude imbalance and up to ± 0.085 rad phase imbalance for 1 dB of Q penalty. Although the experiments in this work are based on DD-OFDM, the proposed method is expected to be also useful for coherent optical OFDM as well, and can help to lower the required specifications for the high-speed optical and electronic devices in the front-end, thereby reducing the system cost.

Acknowledgments

This work was partly supported by a project of the National Institute of Information and Communications Technology of Japan. The authors would like to acknowledge Dr. S. Akiba and Dr. M. Suzuki of KDDI R&D Laboratories Inc for their support and encouragement.

References and links

1.

S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2 b/s/Hz spectral efficiency over 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]

2.

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]

3.

H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 bit/s/Hz using 8x65.1-Gbit/s coherent PDM-OFDM,” J. Lightwave Technol. 28, 406–414 (2009). [CrossRef]

4.

B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “100 Gbit/s transmission using single band direct‐detection optical OFDM,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPC3.

5.

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108Gb/s OFDMA‐PON with polarization multiplexing and direct detection,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPD5.

6.

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]

7.

M. Valkama, M. Renfors, and V. Koivunen, “Advanced methods for I/Q imbalance compensation in communication receivers,” IEEE Trans. Signal Process. 49(10), 2335–2344 (2001). [CrossRef]

8.

T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.

9.

W. R. Peng, B. Zhang, and X. Wu, K. M. Feng A. E. Willner and S. Chi, “Experimental demonstration of compensating the I/Q imbalance and bias deviation of the Mach-Zehnder modulator for an RF-tone assisted optical OFDM system,” in Proceedings of Europ. Conf. on Opt. Commun. (Amsterdam, 2008), Mo.4.D.3.

10.

Y. Ma, W. Shieh, and Q. Yang, “Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2×2 MIMO OFDM Transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2008), JWA 59.

11.

A. Al Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3-Gbit/s direct-detection OFDM transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), OTuO2.

12.

Numerical Recipes: The Art of Scientific Computing, Available at: http://www.nr.com.

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 24, 2009
Revised Manuscript: January 26, 2010
Manuscript Accepted: February 10, 2010
Published: February 24, 2010

Citation
Abdullah Al Amin, Sander L. Jansen, Hidenori Takahashi, Itsuro Morita, and Hideaki Tanaka, "A hybrid IQ imbalance compensation method for optical OFDM transmission," Opt. Express 18, 4859-4866 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4859


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References

  1. S. L. Jansen, I. Morita, T. C. W. Schenk, and H. Tanaka, “121.9-Gb/s PDM-OFDM transmission with 2 b/s/Hz spectral efficiency over 1,000 km of SSMF,” J. Lightwave Technol. 27(3), 177–188 (2009). [CrossRef]
  2. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]
  3. H. Takahashi, A. Al Amin, S. L. Jansen, I. Morita, and H. Tanaka, “Highly spectrally efficient DWDM transmission at 7.0 bit/s/Hz using 8x65.1-Gbit/s coherent PDM-OFDM,” J. Lightwave Technol. 28, 406–414 (2009). [CrossRef]
  4. B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “100 Gbit/s transmission using single band direct‐detection optical OFDM,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPC3.
  5. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108Gb/s OFDMA‐PON with polarization multiplexing and direct detection,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), PDPD5.
  6. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26(1), 196–203 (2008). [CrossRef]
  7. M. Valkama, M. Renfors, and V. Koivunen, “Advanced methods for I/Q imbalance compensation in communication receivers,” IEEE Trans. Signal Process. 49(10), 2335–2344 (2001). [CrossRef]
  8. T. C. W. Schenk, RF Imperfections in High-rate Wireless Systems, (Springer, 2008), Chapter 5.
  9. W. R. Peng, B. Zhang, and X. Wu, K. M. Feng A. E. Willner and S. Chi, “Experimental demonstration of compensating the I/Q imbalance and bias deviation of the Mach-Zehnder modulator for an RF-tone assisted optical OFDM system,” in Proceedings of Europ. Conf. on Opt. Commun. (Amsterdam, 2008), Mo.4.D.3.
  10. Y. Ma, W. Shieh, and Q. Yang, “Bandwidth-Efficient 21.4 Gb/s Coherent Optical 2×2 MIMO OFDM Transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2008), JWA 59.
  11. A. Al Amin, H. Takahashi, S. L. Jansen, I. Morita, and H. Tanaka, “Effect of hybrid IQ imbalance compensation in 27.3-Gbit/s direct-detection OFDM transmission,” in Proceedings of Optical Fiber Commun. Conf., (San Diego, 2009), OTuO2.
  12. Numerical Recipes: The Art of Scientific Computing, Available at: http://www.nr.com .

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