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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9742–9754
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Inserting a cyclic prefix using arrayed-waveguide grating routers in all-optical OFDM transmitters

Arthur James Lowery  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 9742-9754 (2012)
http://dx.doi.org/10.1364/OE.20.009742


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Abstract

Arrayed-Waveguide Grating Routers (AWGR) can be used as multiplexers and demultiplexers in optical OFDM systems, as they provide both the serial-to-parallel converter and the optical Fourier transform in one component. This paper shows how the design of the AWGR at the transmitter can be modified to insert a cyclic prefix or postfix (CP). We use simulations of a 4-subcarrier system to compare systems without the CP, with a guard-interval, and with a CP. We show that the CP greatly improves the orthogonality of the subcarriers and resilience to timing errors. Furthermore, the CP allows for uncompensated fiber dispersion, especially if the relative timing of the subcarriers upon transmission is adjusted.

© 2012 OSA

1. Introduction

Implementing Fourier transforms using optical circuits [1

1. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987). [CrossRef] [PubMed]

] has recently become extremely topical [2

2. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010). [CrossRef] [PubMed]

], because optical orthogonal frequency division-multiplexed (O-OFDM) communications systems [3

3. A. Sano, E. Yoshida, H. Masuda, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30 × 100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in European Conference on Optical Communication (Berlin, Germany, 2007), Postdeadline paper 1.7.

,4

4. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–588 (2006). [CrossRef]

] require Fourier transforms at their receivers, and sometimes at their transmitters. O-OFDM itself is of interest, as it offers high spectral efficiencies, because the spectra of individual subcarriers are allowed to overlap, as they can be demultiplexed without interference using the Fourier transform. Many optical circuits have been proposed to implement the Fourier transform on serial optical waveforms, including ‘unwrapped’ fast Fourier transforms (FT) formed with couplers, phase-shifters and delays [2

2. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010). [CrossRef] [PubMed]

] and, more recently, modified designs of Arrayed-Waveguide Grating Routers (AWGRs) [5

5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

8

8. Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express 19(5), 4501–4512 (2011). [CrossRef] [PubMed]

]. All designs share a common purpose of outputting a phase-weighed sum of a time-series of input samples for each demultiplexed channel, and this can be achieved by many equivalent optical circuits.

Cyclic Pre- or Post-fixes (CP) can also be added to ‘all-optical’ implementations of O- OFDM, though early designs used guard-interval-less optical OFDM [3

3. A. Sano, E. Yoshida, H. Masuda, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30 × 100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in European Conference on Optical Communication (Berlin, Germany, 2007), Postdeadline paper 1.7.

]. In addition to accommodating some dispersion in the link, a CP makes the system more tolerant to the practical limitations of real components in the system, such as electronic timing errors. At the receiver, optical implementations of FTs only produce a valid output during a fraction of an OFDM symbol, usually the duration of the symbol, Tsymb, divided by the number of the OFDM subcarriers. This means a fast sampler (optical or electronic) is required after the FT [10

10. K. Lee, C. T. D. Thai, and J.-K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16(6), 4023–4028 (2008). [CrossRef] [PubMed]

], with a similar performance to that of a sampler used in a time-division multiplexed system. Adding a CP increases the width of the valid region by the duration of the CP, TCP. A downside of a CP is that it reduces the data throughput of the system, as each subcarrier’s baud rate is reduced to1/(Tsymb+TCP).

Although an optical circuit with a response at least approximating a FT is required at the receiver, to give close to zero inter-subcarrier interference, all-optical OFDM systems do not necessarily require an FT at the transmitter. Instead, the data modulators each modulate a separate optical wavelength, before all of the modulators’ outputs are combined using an optical coupler, as shown in Scheme 1 of Fig. 1 in Reference 6

6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

. A caveat is that the data streams should be synchronized so that the subcarriers of a given OFDM symbol all arrive in unison at the receiver. The optical wavelengths can come from separate lasers [11

11. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express 17(24), 21350–21361 (2009). [CrossRef] [PubMed]

], although they are commonly obtained by demultiplexing an optical comb source (such as a mode-locked laser fiber) using narrow filters [12

12. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011). [CrossRef]

]. Because the comb lines are themselves narrow, the exact shape of the optical filter is unimportant, as is its phase response.

Lee, Thai and Rhee [10

10. K. Lee, C. T. D. Thai, and J.-K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16(6), 4023–4028 (2008). [CrossRef] [PubMed]

], Huang et al. [13

13. Y.-K. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-polarization 2×2 IFFT/FFT optical signal processing for 100-Gb/s QPSK-PDM all-optical OFDM,” in Conference on Optical Fiber Communication, OFC (Optical Society of America, San Diego, CA, 2009), paper OTuM4.

], and Wang et al. [8

8. Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express 19(5), 4501–4512 (2011). [CrossRef] [PubMed]

], have studied systems using an inverse FT at the transmitter, following the modulators (Scheme 2 in Fig. 1 of Reference 6

6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

). Recently, Lowery and Du [6

6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

] have shown that this arrangement is beneficial as lower-bandwidth modulators can be used, because the modulators are fed with optical pulses, so that they only have to have the correct phase state during a small fraction of the OFDM symbol. Another benefit of feeding the modulators with pulses is that phase modulators can be substituted for complex optical modulators in the case of 4-QAM (QPSK) [13

13. Y.-K. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-polarization 2×2 IFFT/FFT optical signal processing for 100-Gb/s QPSK-PDM all-optical OFDM,” in Conference on Optical Fiber Communication, OFC (Optical Society of America, San Diego, CA, 2009), paper OTuM4.

]. This is because, for a phase modulator illuminated with a CW source, the 3π/2 transition path – around ¾ of a circle in the complex plane – would cause a substantial frequency shift or chirp, so a complex optical modulator is conventionally used to make this transition cross the origin to remove the chirped portion of the signal. On the other hand, the illumination of a phase modulator with pulses forces the transitions to cross the origin.

An open question is how a cyclic pre- or post-fix can be added to an optical transmitter’s FT in the case where the FT is after the modulators. In this paper, we show that the problem is more complex than extending the data’s bit period by TCP, as would work for transmitters where the modulators follow the optical filter. This paper shows how an AWGR can be modified to insert a CP. We use simulations to show that a CP is advantageous for all-optical networks as it increases the dispersion tolerance and decreases the sensitivity to the exact sampling point.

2. AWGR with cyclic prefix

2.1 Initial design

Figure 2
Fig. 2 All-optical OFDM transmitter using a source of short pulses to sample the state of the modulators. The top is a possible implementation using planar waveguides in an AWGR-like structure. The bottom is the equivalent signal-processing representation, which is used to model the practical implementation.
shows a possible layout of an integrated-optic circuit designed to perform an optical inverse Fourier transform on modulated inputs, followed by a parallel-to-serial conversion to produce one OFDM symbol per input pulse. Also shown is the equivalent signal-flow diagram, which can be used to describe the digital implementation of this function. From left to right, the first slab coupler simply divides an input pulse to feed four parallel data modulators. The modulators are driven so that the data arrives at the input to the second slab coupler in synchronism, and may modulate the phase and/or amplitude of a given input pulse. The outputs of the modulator are effectively the Fourier coefficients of the OFDM waveform. The second slab coupler performs an inverse Fourier transform by forming a weighted sum of its inputs (m = 0, 1, 2, 3) for each of its outputs (n = 0, 1, 2, 3), the weights being phase shifts dependent on m and n [6

6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

]. The wanted outputs appear simultaneously (that is, in parallel) at the right-hand side of the second slab coupler, so need parallel to serial conversion. This is accomplished by applying a different delay to each output, then summing the delayed outputs with a third slab coupler. The delays are imposed by the array of grating waveguides. Note that the first and third slab couplers are simply a 1:N splitter and a N:1 couplers, so they could be implemented with different technologies. The second slab coupler is an N:N coupler with specific phase shifts, and is usually designed using Rowland circle methods to obtain the desired phase shift values [5

5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

].

The waveguide in green is an additional waveguide designed to create a second copy of the n = 0 output of the second slab coupler, then delay it, so that it becomes the last sample of the waveform. In this way, it forms a cyclic postfix. Unfortunately, splitting the power of the n = 0 output means that the first sample of the OFDM waveform is halved in power, and the CP is also halved in power. This could be compensated for by redesigning the tapered regions of the waveguides to double the power at the n = 0 output. A second problem is that the CP requires the longest delay, so the arrayed waveguide has to take a serpentine path, which may increase its losses. That said, this design is conceptually very close to the digital signal processing approach, shown as a signal flow diagram below the slab waveguides; of course, reusing values in digital signal processing does not reduce their magnitude, but it does in optical signal processing.

2.2 Simplified design

Figure 3
Fig. 3 Simplified design for the system in Fig. 2. Here the periodic nature of the field at the right-side of the second slab coupler is used to obtain a convenient signal for the additional waveguide (green) that implements the CP.
shows a more elegant implementation of the transmitter with CP. The design is identical to Fig. 2, up to the output of the second slab coupler. An additional output (n = 4) has been added to the second slab coupler, and this passes through the longest waveguide before reaching the third slab coupler. In this way, it forms a cyclic postfix, so that every input pulse forms five output pulses of the transmitter: four for the OFDM symbol and one for the postfix.

This design avoids splitting the power of the n = 0 power and the associated problems of balancing the powers. This is because the n = 4 output can be designed to give identical phase shifts to the n = 0 output, if differences that are multiples of 2π are ignored. Thus, if the input waveguides of the second slab coupler are designed with appropriate tapers, so that they illuminate all outputs near-uniformly, the magnitude of the postfix should match the magnitude of all samples of the OFDM symbols, as is required. Alternatively, it may be possible to use attenuating regions in the waveguides and slabs to balance the powers. The positioning of the longest waveguide is also more convenient, as it follows a monotonic progression in waveguide lengths. Note that this is not simply an AWGR design with five arrayed waveguides, because the additional waveguide is placed strategically at the output of the second slab coupler, beyond the position that most AWGR designs would use.

3. System design process

The design process of the AWGR is closely linked to the system design. For example, the following process would give the major functional requirements for the AWGR, before the AWGR itself is designed:

  • Decide on a subcarrier spacing, ΔfSC. This is limited by the bandwidth of the optical modulators; obviously more low-bandwidth modulators could be traded against fewer higher-bandwidth modulators. Recent work has shown that the optimum spacing in terms of fiber nonlinearity is dependent on the total transmission distance and in the order of a few GHz [14

    14. L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express 19(9), 8079–8084 (2011). [CrossRef] [PubMed]

    ].
  • The duration of the OFDM symbol, TOFDM, without a CP is simply the inverse of the subcarrier spacing, that is
    TOFDM=1/ΔfSC.
    (1)
  • Decide on the number of data-carrying subcarriers, NSC. This depends on the data rate, R, to be carried by a wavelength channel (a group of subcarriers managed as one wavelength), the modulation format used for each subcarrier and whether polarization-multiplexing should be used. For example, for systems without a CP using m-QAM and a single polarization, the payload data rate will be
    R=NSCΔfSClog2(m).
    (2)

    Additional subcarriers will be required if a cyclic prefix is used, as the data rate per subcarrier will be reduced.

  • Decide on the number of nulled subcarriers, Nnull, around the data-carrying subcarriers. These can be used as frequency guard-bands around a wavelength channel. The guard-bands carry the tails of the subcarrier’s sinc spectra, and so are necessary for the subcarriers to remain orthogonal. Typically, two nulled subcarriers either side of the data-carrying subcarriers would be sufficient; that is, Nnull = 4.
  • At this stage, the number of points in the Fourier transform, NFT, can be calculated. Unlike designs based on trees of optical couplers [1

    1. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987). [CrossRef] [PubMed]

    ,2

    2. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010). [CrossRef] [PubMed]

    ] this does not need to be a power of two.
    NFT=NSC+Nnull.
    (3)
  • The total spectral bandwidth of the wavelength channel, Δfλ, can be estimated from
    Δfλ=(NSC+Nnull)ΔfSC.
    (4)

    The spectral efficiency of a multi-wavelength system will depend on whether the wavelengths are combined to overlap (which is possible with OFDM), or a frequency guard-band is used between the wavelength channels. A guard-band makes conventional wavelength management, such as add-drop multiplexing, easier, but reduces the spectral efficiency by a factor of NSC/(NSC+Nnull).

  • Decide on the duration of the CP, TCP. This depends on several factors as the CP fulfills several purposes. The CP should be at least the fiber’s differential delay across all data-carrying subcarriers (including their tails), so is governed by the link length, fiber type, and use of dispersion-compensating modules. A reasonable estimate for a link with an uncompensated dispersion of DL (s/m) operating at a wavelength λ, would be
    TCP=DL.(λ2.Δfλc).
    (5)

    The CP’s duration could also be increased to lengthen the duration of the valid sampling window at the receiver, to allow for slow sampling gates and for polarization-mode dispersion.

  • The duration of the CP is constrained to be an integer multiple, NCP, of the differential delay between the AWGR’s arrayed waveguides, ΔTwg. The differential delay between the arrayed waveguides is
    ΔTwg=TOFDMNSC+Nnull.
    (6)

    In transmitters using an optical comb source rather than a pulse source, the duration of the CP is not constrained to be an integer multiple of ΔTwg.

  • After adding a CP of duration NCP. ΔTwg, the duration of the OFDM symbol increases to
    TOFDM+CP=TOFDM(NCP+NSC+NnullNSC+Nnull)
    (7)

  • The pulse repetition frequency, PRF, of the optical source feeding the modulators (which is equal to the data rate of the modulator drives), is simply
    PRF=1/(TCP+TOFDM).
    (8)

    In contrast, the repetition rate in designs that use the MLL as a spectral comb source that is demultiplexed to feed the modulators is not affected by the CP, and is simply equal to the subcarrier spacing.

At this stage, there is enough information to calculate the key parameters the AWGR itself.

  • Without a CP, the number of arrayed waveguides is simply NFT.
  • The differential delay between the waveguides is equal to ΔTwg.
  • The slab region of the AWGR has to be designed so optical paths across the input slab, from inputs to the arrayed waveguides, have the appropriate phase delays to implement the Fourier transform and the cyclic prefix [5

    5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

    ].
  • The addition of the CP simply requires NCP additional arrayed waveguides, either longer (postfix), or shorter (prefix) than the waveguides in a design without a CP. The differential delays between these new waveguides are identical to the differential delays between the non-CP waveguides.

The full design of the AWGR, to mask level, would require simulations using planar waveguide simulators. The AWGR design for an FFT requires that the losses from any input to any output are substantially uniform [5

5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

]. This could be achieved by designing the waveguide tapers to produce a substantially uniform illumination of the waveguides at the opposite side of the second slab coupler, though this would increase the loss of the system, due to power spilling beyond the output waveguides.

4. System simulations

4.1 System without CP

An OFDM system carrying four data-carrying subcarriers (NSC = 4) was simulated using VPItransmissionMaker v8.6, to assess the effectiveness of adding the cyclic prefix optically. Considering the simulations without a CP, the subcarriers are spaced at ΔfSC = 10 GHz, giving an OFDM symbol duration of 100 ps. 4-QAM (QPSK) was modulated onto each subcarrier, giving a data capacity of 80 Gbit/s per polarization, though only a single polarization was simulated. To allow for spectral guard bands, the AWGR was designed with 8 guides, to give a free-spectral range of 80 GHz, so Nnull = 4 and NFFT = 8. The differential delay between the adjacent arrayed waveguides is (100/8) ps = 12.5 ps. The sample rate of the simulation was set to be 3.125 ps, giving a simulation bandwidth of 320 GHz.

The pulsed laser was simulated as a 3.25-ps pulse at a 10 GHz repetition rate. These pulses are modulated by complex optical modulators fed with QPSK data. The outputs of the modulators feed a model of the transmitter AWG, which is a network of splitters, delay lines, phase shifters and star-couplers designed to implement the signal-processing representation of the transmitter circuit of Fig. 3. The output of the transmitter is bandlimited with an optical filter to 80-GHz bandwidth, within the free-spectral range of the AWGR. This represents the wavelength multiplexers at the transmitter and receiver. The output of the filter is passed to a linear model of a dispersive standard single-mode optical fiber (D = 16 ps/nm/km), whose length can be parametrically swept. The output of the fiber is amplified and passed to a model of the receiver Fourier transform circuit (including the serial to parallel converter) [5

5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

]. The outputs of this circuit are passed to coherent receivers with a 25-GHz electrical bandwidth and then sampled using an electrical sampler, then equalized by training the system with known data, to form a constellation diagram. The main performance parameter was the quality, Q, of the electrical signals after the coherent receiver [15

15. A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25(1), 131–138 (2007). [CrossRef]

].

4.2 System with CP

This is similar to the system without a CP except that two extra arrayed waveguides are added to the transmitter AWGR. These have delays of 100 ps and 112.5 ps, relative to the first guide, so extend the length of the OFDM with CP symbol to 125 ps. The outputs of these guides receive the same phase shifts as the first and second guides (with delays of 0 ps and 12.5 ps) as they traverse the phase shift network. The pulse repetition frequency of the laser also has to be reduced to 8 GHz, to accommodate the extended symbol length. Furthermore, the extended symbol length means that the phases of the local oscillators at the receiver advance from symbol to symbol, so the equalizers need to add a phase shift of npπ/2 per symbol, where n = −1,0,1,2 is the receiver index and p is a integer up-counter incremented every OFDM symbol. The receiver’s AWGR is identical to the system without the CP.

4.3 System with guard interval (GI)

The system with a CP can also be operated as a system without a CP, but with a (time-domain) guard interval (GI) between the symbols. In wireless OFDM, the term guard interval is used to convey an interval where no power is transmitted: this definition is used herein. A system with a GI uses the same the design parameters as for an AWGR with a CP, but the additional waveguides for the CP are deleted from in the mask layout. In the simulation, this simply means blocking the additional waveguides in the model, while keeping the lowered repetition rate at the source, and the evolving phase at the equalizer.

5. Simulation results

5.1 System with zero dispersion, no CP nor a GI

5.2 System with zero dispersion, with GI

5.3 System with zero dispersion, with CP

Figure 6
Fig. 6 Spectrum (a), eye diagrams for Channel 1 (b) and Channel 2 (c), Q vs. sample point (d) and constellation at the optimum sample point (e) for a system with a cyclic postfix. The eye diagrams are the width of an OFDM symbol plus the cyclic postfix (125 ps).
plots the spectrum, eye diagrams, and the Q versus sample point, for a noiseless back-to-back system with no dispersion, but with a cyclic postfix added after each OFDM symbol. Because the postfix is coherent with the signal within the OFDM symbol, there is some interference, causing nulls and peaks in the spectrum. The eye diagrams have very flat upper and lower rails. These flat rails are a result of choosing the optical bandwidth to be 80 GHz; increasing the bandwidth makes the rails have deterministic ripples, as each Channel becomes carried by several interfering subcarriers spaced at the free-spectral range of the AWGR, so the sampling point becomes critical. Compared with Fig. 4 and Fig. 5, the Q versus sample point has a broadened peak, meaning timing is much less critical, which is expected from the flatness of the eyes. The high value of Q indicates the channels are nearly orthogonal. Thus, adding a CP is far preferable to adding a guard interval, and offers the same spectral efficiency as with a guard interval.

5.4 Effect of fiber dispersion

5.5 Dispersion precompensation by retiming the data modulators

One interesting observation while performing the simulations in Section 5.4 was that the optimum sample time for each subcarrier is different. This is because each subcarrier receives a different group delay from the fiber, so does not arrive synchronized with the other channels at the receiver. This de-synchronisation also causes the ‘OFDM condition’ [9

9. A. J. Lowery and L. B. Du, “Optical orthogonal frequency division multiplexing for long-haul communications: A review of the first five years,” Opt. Fiber Technol. 17, 421–438 (2011). [CrossRef]

] to be broken if the differential delay exceeds the duration of the CP. Figure 8
Fig. 8 Eye diagram for the system with CP and 15-km of uncompensated dispersion.
shows an eye for a system with 15-km of uncompensated dispersion, which is beyond what the CP can accommodate; the randomness of the paths (compared with Fig. 5) indicates that there is significant inter-symbol interference between the OFDM symbols.

A possible solution to the desynchronization is to delay the transmission of higher-frequency channels at the transmitter relative to the frequency channels [16

16. A. J. Lowery, “Reducing cyclic prefix overhead in optical OFDM systems,” in 35th European Conference on Optical Communication Proceedings (IEEE VDE Verlag, GMBH, 2009), paper 1.3.4.

]. The fiber will delay the lower-frequency channels so that all channels arrive in synchronism at the receiver. By sweeping the precompensation delay for a 10-km link, we found that the Q over the four subcarriers could be improved by 1 dB, from 18.4 dB to 19.5 dB. The optimum precompensation was to advance the transmission of the subcarriers (1, 2, 3, 4) by (9.375, 3.125, −3.125, −9.375) ps, respectively. The main effect was to increase the performance of the outer subcarriers (1, 4) by 3 dB, so they no longer limited the overall Q. For a 20-km link, the optimum timing advances were double those for 10-km, and the improvement in the worst subcarrier of each set was 0.7 dB. Thus, precompensation only gives a small improvement, probably because each subcarrier has wide spectral tails which suffer from large group delays.

6. Conclusions

This paper has demonstrated that a CP can be easily added to an all-optical OFDM transmitter based on an AWGR placed after the modulators, by adding one or more extra waveguides from the output of the slab coupler. Importantly, these waveguides need to be placed so they receive identical signals (apart from a phase shift which is a multiple of 2π) to the shortest waveguides. In this way, the layout of the transmitter’s AWGR is much simplified. If a variable-duration CP is required, or a guard-interval is preferred, one or more of these waveguides could be switched out of the optical circuit, for example, using variable attenuators.

Interestingly, the pulse source also has to be modified so that the pulse repetition rate is lower than the frequency spacing of the subcarriers. This is in contrast with systems using separate CW sources for the subcarriers, where the pulse repetition rate equals the subcarrier spacing, even when a CP is added. Although a variable-length CP is more easily added to systems using CW sources, by lowering the data rate driving the modulators, these systems require higher-electrical-bandwidth modulators to maintain signal orthogonality [6

6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

].

This paper has defined a design process for the system and transmitter and receiver AWGRs, then use simulations to verify that the CP has a beneficial effect on the performance of a dispersion-limited system, far exceeding the performance improvement when a simple (signal power free) guard interval is added between the OFDM symbols. This paper also shows that precompensation can be applied to the transmitters, by delaying the relative transmission times of the subcarriers, to provide some mitigation of the effect of dispersion.

Acknowledgments

I should like to thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMakerWDM V8.5. This work is supported under the Australian Research Council’s Discovery funding scheme (DP1096782).

References and links

1.

M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987). [CrossRef] [PubMed]

2.

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010). [CrossRef] [PubMed]

3.

A. Sano, E. Yoshida, H. Masuda, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30 × 100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in European Conference on Optical Communication (Berlin, Germany, 2007), Postdeadline paper 1.7.

4.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–588 (2006). [CrossRef]

5.

A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express 18(13), 14129–14143 (2010). [CrossRef] [PubMed]

6.

A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express 19(17), 15696–15704 (2011). [CrossRef] [PubMed]

7.

K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Integrated-optic OFDM demultiplexer using slab star coupler-based optical DFT circuit,” in European Conference on Optical Communications (Torino, 2010), Postdeadline paper 1–4.

8.

Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express 19(5), 4501–4512 (2011). [CrossRef] [PubMed]

9.

A. J. Lowery and L. B. Du, “Optical orthogonal frequency division multiplexing for long-haul communications: A review of the first five years,” Opt. Fiber Technol. 17, 421–438 (2011). [CrossRef]

10.

K. Lee, C. T. D. Thai, and J.-K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16(6), 4023–4028 (2008). [CrossRef] [PubMed]

11.

S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express 17(24), 21350–21361 (2009). [CrossRef] [PubMed]

12.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011). [CrossRef]

13.

Y.-K. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-polarization 2×2 IFFT/FFT optical signal processing for 100-Gb/s QPSK-PDM all-optical OFDM,” in Conference on Optical Fiber Communication, OFC (Optical Society of America, San Diego, CA, 2009), paper OTuM4.

14.

L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express 19(9), 8079–8084 (2011). [CrossRef] [PubMed]

15.

A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25(1), 131–138 (2007). [CrossRef]

16.

A. J. Lowery, “Reducing cyclic prefix overhead in optical OFDM systems,” in 35th European Conference on Optical Communication Proceedings (IEEE VDE Verlag, GMBH, 2009), paper 1.3.4.

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4080) Fiber optics and optical communications : Modulation
(060.4230) Fiber optics and optical communications : Multiplexing
(080.1238) Geometric optics : Array waveguide devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 21, 2012
Revised Manuscript: April 3, 2012
Manuscript Accepted: April 3, 2012
Published: April 13, 2012

Citation
Arthur James Lowery, "Inserting a cyclic prefix using arrayed-waveguide grating routers in all-optical OFDM transmitters," Opt. Express 20, 9742-9754 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9742


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References

  1. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett.12(1), 63–65 (1987). [CrossRef] [PubMed]
  2. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express18(9), 9324–9340 (2010). [CrossRef] [PubMed]
  3. A. Sano, E. Yoshida, H. Masuda, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30 × 100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in European Conference on Optical Communication (Berlin, Germany, 2007), Postdeadline paper 1.7.
  4. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–588 (2006). [CrossRef]
  5. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers,” Opt. Express18(13), 14129–14143 (2010). [CrossRef] [PubMed]
  6. A. J. Lowery and L. Du, “All-optical OFDM transmitter design using AWGRs and low-bandwidth modulators,” Opt. Express19(17), 15696–15704 (2011). [CrossRef] [PubMed]
  7. K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Integrated-optic OFDM demultiplexer using slab star coupler-based optical DFT circuit,” in European Conference on Optical Communications (Torino, 2010), Postdeadline paper 1–4.
  8. Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express19(5), 4501–4512 (2011). [CrossRef] [PubMed]
  9. A. J. Lowery and L. B. Du, “Optical orthogonal frequency division multiplexing for long-haul communications: A review of the first five years,” Opt. Fiber Technol.17, 421–438 (2011). [CrossRef]
  10. K. Lee, C. T. D. Thai, and J.-K. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express16(6), 4023–4028 (2008). [CrossRef] [PubMed]
  11. S. Chandrasekhar and X. Liu, “Experimental investigation on the performance of closely spaced multi-carrier PDM-QPSK with digital coherent detection,” Opt. Express17(24), 21350–21361 (2009). [CrossRef] [PubMed]
  12. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics5(6), 364–371 (2011). [CrossRef]
  13. Y.-K. Huang, D. Qian, R. E. Saperstein, P. N. Ji, N. Cvijetic, L. Xu, and T. Wang, “Dual-polarization 2×2 IFFT/FFT optical signal processing for 100-Gb/s QPSK-PDM all-optical OFDM,” in Conference on Optical Fiber Communication, OFC (Optical Society of America, San Diego, CA, 2009), paper OTuM4.
  14. L. B. Du and A. J. Lowery, “Optimizing the subcarrier granularity of coherent optical communications systems,” Opt. Express19(9), 8079–8084 (2011). [CrossRef] [PubMed]
  15. A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol.25(1), 131–138 (2007). [CrossRef]
  16. A. J. Lowery, “Reducing cyclic prefix overhead in optical OFDM systems,” in 35th European Conference on Optical Communication Proceedings (IEEE VDE Verlag, GMBH, 2009), paper 1.3.4.

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