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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6984–6995
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Electronic dispersion compensation in a 50 Gb/s optically unamplified direct-detection receiver enabled by vestigial-sideband orthogonal frequency division multiplexing

William A. Ling and Ilya Lyubomirsky  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6984-6995 (2014)
http://dx.doi.org/10.1364/OE.22.006984


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Abstract

We present a novel method for dispersion compensation based on vestigial-sideband transmission of an orthogonal frequency division multiplexed signal through standard signal-mode fiber with a direct-detection receiver. This technique requires simpler optical components and can withstand greater link attenuation and splitting ratios than similar methods previously studied, making the method ideal for optically unamplified receivers, such as those in passive optical networks. We present simulations as well as experimental measurements to demonstrate its practicality.

© 2014 Optical Society of America

1. Introduction

In optical access networks, where cost is a primary concern, chromatic dispersion must be combated without a coherent receiver. Electronic dispersion compensation in a DD receiver can be enabled through single-sideband (SSB) transmission, in which either the upper or lower sideband of the electric field is eliminated. A recent work has also explored the possibility of dispersion compensation for double-sideband (DSB) transmission by block-wise phase switching [3

3. X. Chen, A. Li, D. Che, Q. Hu, Y. Wang, J. He, and W. Shieh, “High-speed fading-free direct detection for double-sideband OFDM signal via block-wise phase switching,” “OFC/NFOEC,” (2013), p. PDP5B.7.

, 4

4. X. Chen, A. Li, Q. Hu, J. He, Y. W. D. Che, and W. Shieh, “Demonstration of direct detected optical OFDM signals via block-wise phase switching,” J. Lightw. Technol. 32, 722–728 (2014). [CrossRef]

]. Previously studied SSB-OFDM systems can be classified into one of two types. The first class of systems transmits the OFDM symbol through a modulated laser intensity, in a manner in which the E-field is SSB [5

5. D. F. Hewitt, “Orthogonal frequency division multiplexing using baseband optical single sideband for simpler adaptive dispersion compensation,” in “Proc. Eur. Conf. Opt. Commun.”, (2007), p. OME7.

8

8. J. L. Wei, X. Q. Jin, and J. M. Tang, “The influence of directly modulated DFB lasers on the transmission performance of carrier-suppressed single-sideband optical OFDM signals over IMDD SMF systems,” J. Lightw. Technol. 27, 2412–2419 (2009). [CrossRef]

]. The second class of systems transmits the OFDM symbol by modulating the complex E-field directly [9

9. 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. Lightw. Technol. 27, 196–203 (2008). [CrossRef]

15

15. D. Y. Qian, N. Cvijetic, J. Q. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightw. Technol. 28, 484–493 (2010). [CrossRef]

]. In this second case, the E-field is made SSB either through SSB modulation with an I-Q modulator or by optically filtering a DSB signal. For both classes of systems, the need for the E-field to be SSB is due to the fact that a DSB signal interacts with dispersion and square-law detection to form nulls in the composite channel [16

16. G. H. Smith, D. Novak, and Z. Ahmed, “Overcoming chromatic-dispersion effects in fiber-wireless systems incorporating external modulators,” IEEE Trans. Microw. Theory Techn. 45, 1410–1415 (1997). [CrossRef]

, 17

17. M. Sieben, J. Conradi, and D. E. Dodds, “Optical single sideband transmission at 10 Gb/s using only electrical dispersion compensation,” J. Lightw. Technol. 17, 1742–1749 (1999). [CrossRef]

]. Although SSB transmission prevents formation of nulls, the first class of systems is inherently nonlinear in the path from the transmitter’s digital OFDM signal to the received electrical OFDM signal. This is due to the fact that transmitted and detected signals are intensities, but dispersion is only a linear operator on the E-field. In contrast, the second class of systems are linear, because the transmitted and detected signals are E-fields. The complex E-field is recovered at the DD receiver through either self-homodyning or self-heterodyning. The linearity of the channel provides improved sensitivity, since equalization is thus nearly perfect. The system described in this paper resembles those of the second class, in that it transmits and receives the E-field rather than intensity, but it differs in that it transmits a vestigial-sideband (VSB) OFDM signal rather than a SSB signal. This VSB signal is produced by partially suppressing one of the sidebands of a DSB E-field. Although this signal is not SSB, its asymmetrical form prevents formation of channel nulls, as will be shown. However, a VSB signal can be produced with a simpler transmitter than a SSB signal.

2. Increasing transmission reach in optically unamplified links

Most of the previously studied self-homodyning or self-heterodying OFDM systems have utilized the modulator for generation of the carrier. This was done in one of two ways. The first method is to add a DC offset to the data signal driving the modulator [9

9. 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. Lightw. Technol. 27, 196–203 (2008). [CrossRef]

]. This results in the presence of an unmodulated optical carrier along with the OFDM signal. These two components then mix at the receiving photodiode to perform homodyning. The second method is to apply no DC bias, but instead add a high-frequency RF tone to the OFDM signal. The receiver photodiode then heterodynes this RF tone with the OFDM signal [10

10. W. R. Peng, X. X. Wu, V. R. Arbab, K. M. Feng, B. Shamee, L. C. Christen, J. Y. Yang, A. E. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightw. Technol. 27, 1332–1339 (2009). [CrossRef]

]. Thus, this RF tone is a virtual carrier that is offset from the frequency of the transmitting laser.

Both of these methods of inserting a carrier in the transmitted signal rely on the modulator to add the carrier. This is inherently inefficient for two reasons. The first is that the Mach-Zehnder modulator (MZM) transfer characteristic is a cosine of the input drive signal and is only linear near its null. Adding a DC offset moves the MZM bias into a less linear region; thus the DC offset must be small, which results in a small transmitted carrier. Similarly, adding a large virtual carrier increases the peaks of the composite MZM drive signal (although less severely than a DC offset). The second inefficiency of adding a carrier through the modulator is the modulator insertion loss. A typical commercial Lithium niobate MZM has 6 – 10 dB insertion loss.

Fig. 1 The carrier is added to the data signal through an unmodulated waveguide. This allows for a much larger carrier to mix with the signal at the receiver. Here we depict ideal SSB generation through optical filtering.

3. Vestigial-sideband transmission

Fig. 2 In the proposed system, the carrier is added to the data signal through an unmodulated waveguide and VSB generation is achieved through a waveguide MZI integrated with a single MZM.

Consider the system depicted in Fig. 2. Let the DSB-OFDM signal be given by x(t) and the DC offset added to it be A. Let the impulse responses of the optical filter and fiber be f (t) and g(t), respectively. Let their respective Fourier transforms be F(ω) and G(ω). Then the received E-field is
(A+x(t)*f(t))*g(t),
(2)
where * denotes convolution. Let B = A * g(t) = AG(0), a complex constant. Let h(t) = f (t) * g(t) be the composite channel x(t) traverses. Then the intensity at the receiver is
r(t)=|B+x(t)*h(t)|2=|B|2+|x(t)*h(t)|2+2Re{B*x(t)*h(t)}.
(3)
The first term of (3) is at DC. The second term is intermodulation; it is largest at DC and decreases with increasing frequency. The final term y(t) = 2Re{B*x(t) * h(t)} is the desired signal term. It can be equivalently be expressed as
y(t)=x(t)*heq(t),
(4)
where
heq(t)=B*h(t)+Bh*(t).
(5)
The corresponding transfer function for this system is
Heq(ω)=B*H(ω)+BH*(ω).
(6)
When the real OFDM signal x(t) is chosen such that it occupies the frequency bands (−2ωB, −ωB) and (ωB, 2ωB), the intermodulation term (caused by signal-signal beating) |x(t) * h(t)|2 will occupy the band (−ωB, ωB). Thus after highpass filtering, the received signal becomes y(t), so the system between the transmitted OFDM signal and the received signal is linear. It is apparent that the magnitude of the received signal is proportional to |A|, the magnitude of the transmitted carrier. Thus, adding the carrier through the parallel waveguide results in a much larger received signal than if the carrier (or virtual carrier) were generated through the modulator. If the carrier is sufficiently large compared to the signal, the linear signal term y(t) will become large compared to the intermodulation term |x(t) * h(t)|2, even if x(t) is allowed to occupy the entire band (0, 2ωB) rather than just (ωB, 2ωB). Depending on the relative magnitude of intermodulation compared to receiver thermal and shot noise, it may be advantageous to have a reduced guard band or no guard band at all.

To evaluate the effects of dispersion, consider the case where the fiber is a dispersive channel with E-field transfer function
G(ω)=exp(jβ2Lω22),
(7)
where β2 is the group-velocity dispersion parameter, and L is the fiber length. Suppose the optical filter is absent, or equivalently, F(ω) = 1 for all ω. For simplicity of discussion, we will consider B = 1, but this does not affect the results. Then by (6),
Heq(ω)=exp(jβ2Lω22)+exp(jβ2Lω22)=2cos(β2Lω22).
(8)
Such a transfer function has many nulls and thus has low capacity. The origin of the nulls is the even symmetry in H(ω). One can ask whether insertion of an optical filter F(ω) can break this symmetry and prevent formation of nulls. One particular choice of F(ω) which achieves this is
F(ω)={1ifω>00otherwise
(9)
Note that such a choice of F(ω) is equivalent to using SSB modulation with an IQ-MZM and no optical filter present. However, such a sharp filter will be high in order; it would be preferable to use a low-order planar waveguide-based filter which can be integrated with the MZM. In this work, we study the two-branch MZI with a complex-envelope transfer function
F(ω)=12+12ej(ω+ωc)td
(10)
where ωc is the optical carrier frequency (rad/s) and td is the time-delay difference between the two arms of the MZI. The delay td can be tuned through temperature control. Such a filter has a periodic spectrum with period fFSR = 1/td (Hz), the free spectral range (FSR). Figure 3(a) shows a schematic of the MZI and Fig. 3(b) shows a representative transfer function. In this work, we investigate the performance of a system based on such an MZI as the optical filter for preventing formation of nulls in the composite channel transfer function Heq(ω). Since an MZI will not completely suppress one of the sidebands, we call this method of transmission vestigial-sideband (VSB) OFDM.

Fig. 3 (a) The integrated waveguide MZI consists of two waveguides with a propagation delay difference of td. (b) The transfer function of the MZI is periodic in frequency.

Note that according to Eq. (10), the MZI’s transfer function depends on two parameters, ωc and td. The FSR depends only on td, but the frequency offset of the transfer function relative to the carrier depends on the product ωctd. However, to tune the MZI to the desired operating point, one only needs to control td, because minute fractional changes in td will change ωctd by 2π. Thus, the frequency-center of the MZI transfer function can be controlled arbitrarily with negligible impact on the FSR. The FSR is essentially determined only by the fabricated length difference of the two waveguides.

The reason the MZI will eliminate channel nulls, as does a SSB filter, can be seen by examining Eq. (6) with G(ω) being the dispersion transfer function. We can without loss of generality assume B = 1. Then the equivalent channel transfer function is
Heq(ω)=F(ω)exp(jβ2Lω22)+F*(ω)exp(jβ2Lω22).
(11)
When the MZI is placed asymmetrically about the carrier frequency, so that its null is well within one of the sidebands, |F(ω)| ≠ |F(−ω)|. Heq(ω) is the sum of two phasors; Heq(ω) = 0 if and only if these two phasors have the same magnitude and opposite angle. However, since |F(ω)| ≠ |F(−ω)|, these two phasors will have different magnitudes. Thus, the MZI prevents formation of a channel null.

4. Simulations

To illustrate the creation of the VSB-OFDM signal using the MZI, we show a DSB-OFDM optical spectrum (without any low-frequency guard band) in Fig. 4(a), followed by MZI filtering in Fig. 4(b) and then superposition with the carrier in Fig. 4(c).

Fig. 4 (a) Simulated spectrum of DSB-OFDM signal produced by MZM. In this particular example, there is no guard band against signal-signal beating. The resolution in this plot is 2 MHz. (b) Spectrum after filtering by the MZI with FSR of 90 GHz and null centered in the lower sideband. (c) Spectrum after adding the carrier through a parallel waveguide.

One of the unique advantages of OFDM is the ability to optimally allocate power and information among the subcarriers, according to the modified channel capacity formula
bi=log2(1+SNRiΓ),
(12)
where bi is the number of bits/symbol transmitted by the ith subcarrier, SNRi is the signal-to-noise ratio (SNR) of the ith subchannel, and Γ is the gap constant determined by the desired BER [21

21. J. M. Cioffi, G. P. Dudevoir, M. V. Eyuboglu, and G. D. Forney, “MMSE decision-feedback equalizers and coding-part II: Coding results,” IEEE Trans. Commun. 43, 2595–2604 (1995). [CrossRef]

]. In our simulations, we chose a BER of 10−3. To optimize the power and bit allocation among the subcarriers, we employed Campello’s bit-loading algorithm, which is the optimal discrete-bit-allocation algorithm [22

22. J. Campello, “Practical bit loading for DMT,” in “Proc. Global Telecommun. Conf. (GLOBECOM ’99),” (Vancouver, Canada, 1999), pp. 801–805.

]. The performance gained by bit loading is the result of the non-uniform SNR over frequency. A frequency-varying SNR is also present in systems with multi-mode dispersion, resulting in significant gains through bit loading [23

23. S. Lee, F. Breyer, S. Randel, M. Schuster, J. Zeng, F. Huijskens, H. van den Boom, A. Koonen, and N. Hanik, “24-Gb/s transmission over 730 m of multimode fiber by direct modulation of an 850-nm VCSEL using discrete multi-tone modulation,” “OFC/NFOEC,” (2007), p. PDP6.

].

Due to the large carrier-to-signal ratio, the intermodulation from signal-signal beating was small compared to the receiver’s combined thermal and shot noise after 50 km of fiber. Thus, we eliminated the low-frequency guard band and allowed the bit-loading algorithm to determine optimal use of the entire 0–28 GHz band. In this case, the “noise” caused by signal-signal beating was a signal-dependent noise. Thus, we allocated the bits and power among the sub-carriers iteratively. After the first bit-loading iteration, the signal spectrum changed, which thus changed the signal-signal beating distribution and thus changed the SNR. This changed the optimal bit and power allocation among subcarriers, so the bit-loading process was re-iterated. This process was repeated and converged within a few iterations.

We first show the back-to-back sensitivity performance of VSB-OFDM for fixed bit rates of 56 Gb/s and 112 Gb/s in Fig. 5(a). For a comparison of techniques, we varied the transmission distance and compared the achievable bit rates of VSB and ideal SSB transmission, with the SSB signal generated by an ideal SSB filter with no insertion loss. To take into account the potential drift of the MZI relative to the carrier, the VSB simulations were also conducted for ±3 GHz offsets of the MZI relative to the carrier, as shown in shown in Fig. 5(b). Although an ideal SSB filter provides improved performance, it is only realizable with high insertion loss (or an IQ modulator with two identical MZMs driven by two identical DACs). We see that an MZI drift of ±3 GHz relative to the carrier has little impact on performance. We also compare VSB-OFDM to the straightforward approach of DSB transmission (which will suffer from channel fading) along with bit loading to prevent allocation of data to the nulled frequencies [24

24. D. J. F. Barros and J. M. Kahn, “Comparison of orthogonal frequency-division multiplexing and on-off keying in amplified direct-detection single-mode fiber systems,” J. Lightw. Technol. 28, 1811–1820 (2010). [CrossRef]

].

Fig. 5 (a) Simulation of the back-to-back performance of VSB-OFDM for 56 Gb/s and 112 Gb/s. (b) Simulation of optically unamplified link to compare VSB with SSB and DSB transmission, including the effect of MZI offsets. The BER in all cases was 10−3.

5. Experimental measurements

To experimentally demonstrate the feasibility of high bit rate VSB transmission using existing commercial components, we constructed the VSB transmitter depicted in Fig. 6. Note that this differed from the original VSB transmitter shown in Fig. 2 in that the optical filter was previously placed before the Y-junction. The only difference between the performance of these two configurations is that the modified system of Fig. 6 slightly attenuates the carrier component. We used this configuration in our experiments because it was simpler to construct: the MZM in parallel with a waveguide was implemented in our experiments using an I-Q modulator, with the I-MZM modulated with the DSB-OFDM signal and the Q-MZM unmodulated and biased away from the null. The Q-MZM thus operated as an unmodulated waveguide transporting the carrier. This thus required the MZI to be implemented as an external filter placed after the Y-junction between the MZM and carrier waveguide. The transmitted DSB-OFDM signal consisting of 512 subcarriers was produced offline using MATLAB and loaded into the memory of the Fujitsu LEIA DAC, operated at a sampling rate of 56 Gsample/s. The cyclic prefix length was 16 samples. Due to bandwidth and high-frequency SNR limitations of the DAC, the OFDM signal band was chosen to be the 0 to 19.6 GHz band rather than the 0 to 28 GHz band. Thus, the last 30% of the subcarriers were zeroed. In principle, the system could be implemented with only a 40 Gsample/s DAC if the OFDM signal band is from 0 to 19.6 GHz, but the clocking circuitry of our DAC required a minimum sampling rate of 56 Gsample/s. The modulator was a Sumitomo I-Q modulator with 20-GHz bandwidth, with the I-MZM modulated by the DAC. The MZI was implemented using the Finisar Waveshaper, an arbitrarily programmable optical filter. The MZI emulation had an FSR of 63 GHz, since 70% of 90 GHz (the simulation FSR) is 63 GHz. Its null was placed 13 GHz below the carrier frequency. The fiber channel consisted of 80 km of S-SMF, with a loss of 0.2 dB/km and dispersion of 18 ps/nm/km. The receiver consisted of a Newport InGaAs photoreceiver with 35 GHz bandwidth and an Agilent 80 Gsample/s, 33-GHz bandwidth real-time oscilloscope.

Fig. 6 This modified transmitter configuration was used in the experiments for convenience of implementation. Its operation is essentially equivalent to that of the original transmitter configuration of Fig. 2.

For these experiments, an Amonics Erbium-doped fiber amplifier was used to compensate for the following limitations in the experimental setup: (1) The waveguide for producing the carrier was part of a modulator and thus had insertion loss. (2) The programmable optical filter emulating the MZI had a 5 dB insertion loss. (3) The input-referred thermal noise of the receiver (consisting of a photoreceiver and oscilloscope) was many times higher than the value used in our simulations. The thermal noise value used in the simulations was based on specifications of integrated receivers used in existing commercial 100G transceivers. However, the purpose of these experiments was to demonstrate the practicality of the approach in combating dispersion, including the effects of MZI drift.

As seen in Fig. 7(a), the system is capable of transmitting 72 Gb/s at a BER of 10−3. This provides ample margin for meeting the standard rate of 50 Gb/s/wavelength. Additionally, its performance is insensitive to ±3 GHz drift of the MZI relative to the carrier frequency, as shown in Fig. 7(b). In Fig. 8(a), we show the SNR of the composite channel from the transmitter’s digital output to the receiver’s digital output. In Fig. 8(b), we show the corresponding optimal bit allocation for the case of 72 Gb/s transmission. The 256th subcarrier was zeroed due to strong DAC nonlinearity at that frequency.

Fig. 7 Measured BER after 80 km of S-SMF. (a) Measured BER as a function of bit rate. (b) Measured BER as a function of MZI offset relative to the carrier at 65 Gb/s.
Fig. 8 (a) Channel SNR for 80-km link. (b) Optimal bit allocation for 72 Gb/s transmission across 80 km S-SMF. The 256th subcarrier was zeroed due to strong DAC nonlinearity at that frequency.

6. Conclusions

7. Appendix

Here we compare the received electrical signal strength for the case of virtual carrier transmission and the case where the carrier is added by a separate waveguide. For simplicity, we consider the transmitted optical signal to be SSB in both cases. For the VSB case, this analysis is still approximately correct.

Let Acw be the amplitude of the CW source of the modulator. Since this source is split evenly between the I-MZM and Q-MZM, the output of the modulator, after summing I and Q branches, is
e1(t)=Acw2am(x+jx^+2CejωBt)=Acwam(x++CejωBt).
(14)

Since the transfer function of the fiber has a constant magnitude over the entire signal band, it can be neglected in the following comparisons, since it has the same effect on the received signal power in both cases. Then the received electrical signal is the product of the virtual carrier and the data signal:
r1(t)=(AcwamCejωBt)(Acwamx+(t))=(Acwam)2CejωBtx+(t).
(15)

Now consider a transmitter which adds the carrier through a waveguide parallel to a single MZM. In this case, the data signal y(t) is a DSB signal and let E[y2(t)] = E[x2(t)]. In order to make a fair comparison with the virtual carrier transmitter, the MZM should be driven with a signal of the same power in both cases. Since no virtual carrier is present here, the MZM should be driven with 2y(t). For simplicity, we consider an optical filter which generates an ideal SSB output:
F(ω)={1ifω>00otherwise
(16)
Thus, the DSB signal y(t) is converted to the SSB signal y+(t).

As before, the amplitude of the field from the CW source is Acw. It is split into two paths, one which passes through an MZM and the other unmodulated. It can be easily shown that the receiver’s signal is largest when the split is equal in both paths. Thus, the output of the unmodulated waveguide is Acw/2 (we can neglect the phase without changing the results) and the output of the modulated and filtered branch is (1/2)Acwamy+(t). The resulting signal at the transmitter output is
e2(t)=Acw2+12Acwamy+(t).
(17)
The received electrical signal is product of the carrier and the data signal:
r2(t)=24Acw2amy+(t).
(18)

8. Acknowledgments

The authors would like to acknowledge the financial support of Finisar Corporation. The authors also thank Prof. Olav Solgaard of Stanford University for helpful discussions.

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J. Campello, “Practical bit loading for DMT,” in “Proc. Global Telecommun. Conf. (GLOBECOM ’99),” (Vancouver, Canada, 1999), pp. 801–805.

23.

S. Lee, F. Breyer, S. Randel, M. Schuster, J. Zeng, F. Huijskens, H. van den Boom, A. Koonen, and N. Hanik, “24-Gb/s transmission over 730 m of multimode fiber by direct modulation of an 850-nm VCSEL using discrete multi-tone modulation,” “OFC/NFOEC,” (2007), p. PDP6.

24.

D. J. F. Barros and J. M. Kahn, “Comparison of orthogonal frequency-division multiplexing and on-off keying in amplified direct-detection single-mode fiber systems,” J. Lightw. Technol. 28, 1811–1820 (2010). [CrossRef]

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E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express 19, 4280–4293 (2011). [CrossRef] [PubMed]

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation
(060.4510) Fiber optics and optical communications : Optical communications

ToC Category:
Optical Communications

History
Original Manuscript: December 27, 2013
Revised Manuscript: February 28, 2014
Manuscript Accepted: March 1, 2014
Published: March 18, 2014

Citation
William A. Ling and Ilya Lyubomirsky, "Electronic dispersion compensation in a 50 Gb/s optically unamplified direct-detection receiver enabled by vestigial-sideband orthogonal frequency division multiplexing," Opt. Express 22, 6984-6995 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6984


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