Optical Fiber Technology

Transcription

1 Optical Fiber Technology 17 (2011) Contents lists available at ScienceDirect Optical Fiber Technology nvited Papers Coherent DWDM technology for high speed optical communications Ross Saunders Opnext Subsytems nc., 151 Albright Way, Los Gatos, CA 95032, USA article info abstract Article history: Available online 7 September 2011 Keywords: DWDM Coherent Optical DSP PSK AM The introduction of coherent digital optical transmission enables a new generation of high speed optical data transport and fiber impairment mitigation. An initial implementation of 40 Gb/s coherent systems using Dual Polarization uadrature Phase Shift Keying (DP-PSK) is already being installed in carrier networks. New systems running at 100 Gb/s DP-PSK data rate are in development and early technology lab and field trial phase. Significant investment in the 100 Gb/s ecosystem (optical components, ASCs, transponders and systems) bodes well for commercial application in 2012 and beyond. Following in the footsteps of other telecommunications fields such as wireless and DSL, we can expect coherent optical transmission to evolve from PSK to higher order modulations schemes such as Mary PSK and/or AM. This will be an interesting area of research in coming years and poses significant challenges in terms of electro-optic, DSP, /DAC design and fiber nonlinearity mitigation to reach practical implementation ready for real network deployments. Ó 2011 Published by Elsevier nc. 1. ntroduction To keep pace with the rapidly growing volumes of data network traffic driven by the growth of the internet, service providers are always looking to increase the fiber capacity and wavelength spectral efficiency in their networks [1]. Typical Dense Wavelength Division Multiplexing (DWDM) networks of today employ a 50 GHz channel spacing, as per the international standard [2]. At 10 Gb/s data rate spectral efficiency was not a major concern and simple On Off Keying (OOK) modulation format was adequate for operation on the 50 GHz DWDM grid. At 40 Gb/s, the spectral width of the signal is 4x larger for OOK, yielding a signal spectral width that iss too wide to fit through 50 GHz channel spacing optical filters without inducing excessive penalties. So at 40 Gb/s data rate system and transponder developers investigated alternate modulations schemes to enable 40 Gb/s propagation over the same 50 GHz DWDM grid, such as Phase Shaped Binary Transmission, PSBT [1], Differential Phase Shift Keying (DPSK) [3] and DP-PSK [4]. PSBT and DPSK offered increased spectral efficiency over OOK, whilst still coding 1 bit per symbol. DP-PSK, on the other hand, codes 4 bits per symbol (in-phase and quadrature phase components of each polarization tributary). Coding more bits/symbol, enabled by the advent of digital coherent transmission [5], reduces the spectral width of the signal (to 1st order proportional to the baud rate). n fact, DP-PSK is so spectrally efficient that it can propagate a higher data rate of 127 Gb/s through many cascaded 50 GHz optical filters, such as Reconfigurable Optical Add/Drop Multiplexers (ROADMs) [6]. Fax: address: [email protected] This higher 127 Gb/s data rate not only allows payload transport of 100GE traffic [7], but also OTU4 link management overhead [8] and 20% overhead, Soft Decision Forward Error Correction (SD-FEC) [9 11] for high performance applications. Therefore, 100 Gb/s transmission using DP-PSK offers the promise of a good modulation format fit for DWDM networks operating on a 50 GHz grid [12]. This was observed several years ago and was the reason why this format was adopted by the Optical nternetworking Forum (OF) as a recommended modulation format for 100 Gb/s line systems [13]. This industry forum has helped to focus investment and multi-source agreements at the optical component and module level to help foster an ecosystem that should accelerate network adoption of 100G DP-PSK transmission. Looking to the future, as the internet growth continues with expanding services such as High Definition (HD) video, mobile broadband and telecommuting, the question is how will optical transmission technology keep pace? Learning from other telecommunications fields such as wireless, satellite, radio and Digital Subscriber Line (DSL) broadband access, we can say that all these mediums utilize coherent transmission and all increase transmission rates and spectral efficiency by coding more bits per symbol. For optical fiber technology development we should surely follow the lead from these other telecommunications industries but we have some fundamental and unique challenges that makes our life difficult. Challenges such as: (i) operation at the bleeding edge highest electronics speed of >100 Gb/s for the key technologies such as /DAC/DSP/FEC/RF electronics/electro-optics; (ii) optical signalto-noise ratio (OSNR) requirements become tough as Shannon s Limit dictates that as we increase spectral efficiency via higher-order modulation we need more OSNR and (iii) fiber nonlinearity poses a major obstacle as high density signal constellations such /$ - see front matter Ó 2011 Published by Elsevier nc. doi: /j.yofte

2 446 R. Saunders / Optical Fiber Technology 17 (2011) as M-ary uadrature Amplitude Modulation are very sensitive to phase errors due to nonlinear phase noise and Cross Phase Modulation (XPM). Although these challenges appear daunting and formidable it would be unwise to bet against theses problems being solved by human engineering ingenuity given time and money, as history has proven. This will be an extremely fertile area of optical communication research over the next decade and beyond Gb/s DP-PSK implementation 2.1. Technology The basic functional block diagrams for an optical coherent detection modulation scheme, with control of the amplitude of both in-phase, and quadrature phase,, components of the modulated signal is shown in Fig. 1. Note that although the data throughput is 100 Gb/s, extra overhead bytes are required for 64B/66B Ethernet PCS encoding, OTU4 framing overhead, training sequence and FEC, which in combination adds 28% to the line rate. This modulation format codes 4 bits per symbol (for the n-phase, and uadrature-phase, components of the each polarization multiplexed tributary), yielding a symbol rate of 32 Gbaud. The transmit side consists of nested Mach Zehnder Modulators (MZM) structures. The coherent receiver requires mixing the received signal light with a tunable laser local oscillator. Polarization Beam Splitters (PBS) and optical phase hybrids are included in the receive structure to provide polarization and phase diversity. A key advantage is that the Carrier Phase Estimator (CPE), polarization and & demultiplexing is all achieved in the electronic domain using very fast Analog-to-Digital Converter () and Digital Signal Processing (DSP). This alleviates the traditional problem with optical coherent technology in that a highly stable optical Phase Locked Loop (PLL) is not required in this design. The critical enabling technology in this design is the digital coherent receiver, as shown in Fig. 2. The distorted signal coming from the four balanced photodiodes is first quantized using quad 6 bit s. The adaptive equalizer in the DSP then provides the equalization of CD, PMD, ROADM filtering distortion and unwanted S21 transfer function imperfections in the Tx/Rx electro-optic drive chains. Another critical enabling technology is next-generation soft decision FEC, enabling up to 3 db higher coding gain than current state-of-the-art FEC. A FEC algorithm called Low Density Parity Check (LDPC) is used, with increased overhead [9] and uses soft decision decoding of the input. This is in contrast to all optical transport systems today which use hard decision decoding. As the digital coherent receiver already generates a quantized version of the analog signal, this quantized signal can then be passed to a soft decision FEC decoder. Fig. 3 shows the LDPC FEC coding gain as a function of soft decision bit resolution and overhead rate for an idealized case with no implementation penalty. FEC design optimization is a tradeoff between decoder complexity/chip size vs performance in selection of bit resolution and electro-optic bandwidth/roadm tolerance vs performance in selection of the overhead rate. Another important property of any metro, regional or long haul technology is the capability to express through multiple cascaded optical 50 GHz channel spacing ROADMs, without incurring a large penalty. DP-PSK offers excellent tolerance to narrowband optical filtering due to the low baud rate, which reduces the spectral width of the signal, and the adaptive equalizer in the Rx, which cleans-up filtering distortion. Results comparing DP-PSK with alternative 100G modulation formats are shown in Fig. 4. As can be seen, DP-PSK modulation format shows excellent tolerance to extremely narrowband optical filtering. Depending on the ROADM bandwidth and profile, 100G DP-PSK is capable of expressing through up to 10 cascaded ROADMs at 50 GHz channel spacing [6]. For 100G deployments to be cost-effective in Long Haul DWDM networks, it is critical that the optical reach is sufficiently large that the requirement for OEO regenerators is limited, ideally non-existent. The optical reach is maximized using two critical technologies: (i) coherent detection (buys 2.5 db) and (ii) LDPC soft decision FEC (buys up to 3 db). Optical reach up to 2000 km with EDFA only, 5000 km with EDFA + Raman and 7000 km for submarine links is possible using 100G DP-PSK technology, with deployable margin. The propagation performance depends on fiber type and whether in-line DCMs are deployed or not. Nonlinearity is mitigated by not deploying in-line DCMs and performing all CD compensation within the Opnext 100G module. Fig. 5 shows propagation results over different fiber types, with and without in-line DCMs. Note that the optimum fiber type is SMF-28 fiber without in-line dispersion compensation. This is also the lowest cost fiber plant for the carrier Photonic and electronic integration A 100 Gb/s DP-PSK offers the ultimate in optical performance and meets all the key marketing requirements dictated by large Tx Block Diagram 4x32Gb/s [32Gbaud] inputs TE MZ π/2 CW laser PBS MZ MZ π/2 out TM MZ Rx Block Diagram in Local Oscillator 90 hybrid (phase/polarization diversity) /DSP 4x32Gb/s [32Gbaud] outputs Fig. 1. A 128 Gb/s DP-PSK Tx/Rx implementation.

3 R. Saunders / Optical Fiber Technology 17 (2011) Adaptive Algorithm Error signal + TE nput distorted data TE TM TM Σ Decision Circuit Recovered output data A>D converters Adaptive Equalizer (n tap Digital FR filter) Fig. 2. Digital coherent receiver. NECG (db) soft decision 3 to 4dB gain hard decision % 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% FEC Overhead Current gen EFEC Fig. 3. LDPC soft decision FEC performance. 6 bits 4 bits 3 bits 2 bits 1 bit (db) LEAF (no DCM) SMF-28 (no DCM) LEAF (with DCM) SMF-28 (with DCM) Launch Power (dbm) Fig. 5. A 128 Gb/s DP-PSK propagation over a 1520 km link. Min w/ margin LDPC FEC cliff photonics transmit side, a single optical assembly contains the nested MZMs, PBS and splitters, as per OF implementation agreements [14]. On the photonics receive side, a single optical assembly houses the PBS, phase hybrids, balanced photodetectors and Trans-mpedance Amplifiers (TAs). This integration is shown in Figs. 6a and b. This high level of integration greatly eases the manufacturability of the module Dynamic optical networking Fig. 4. A 128 Gb/s DP-PSK optical filtering tolerance. carriers. The challenge is that this is a much more complex modulation scheme than previous generations of optical transport equipment. Both the electronic and photonic complexity has been increased substantially. This creates a design challenge in terms of cost, manufacturability, reliability and footprint. The industry approach to tackling this significant challenge has been to develop components with a high level of electronic and photonic integration. On the electronic side, SiGe MUX and CMOS modem chips with large gate count and integrated system functionality. On the Looking to the future it can be envisaged that future optical networks will utilize some level of all-optical switching to facilitate fast restoration and protection of optical circuits. One limitation of early 40 Gb/s systems is that Chromatic Dispersion (CD) tuning can take a relatively long time, on the order of seconds or even minutes. This is true for both direct detection systems that typically use a thermally tuned optical tunable dispersion compensator and for 1st generation coherent systems where the CD equalizer hunts for the optimum CD value of the link. By designing coherent transmission systems with in-built training sequences, it is possible for the CD equalizer to know virtually instantaneously the optimum tap weight coefficients in the equalizer to compensate for an unknown link CD, without requiring this hunting algorithm. This enables very fast (ms) timeframe CD acquisition and equalization. The Jones matrix equalizer inside the MODEM can also rapidly adapt to the optimum State of Polarization (SOP) and DGD compensation of the link. This rapid

4 448 R. Saunders / Optical Fiber Technology 17 (2011) MUX RZ PULSE CARVER (OPTONAL) PSK MODULATOR Drive = 2Vπ BW > ⅛ R SGNAL PBS 90 deg Hybrid Mixer X X X X PS PBC SGNAL DSP LASER ~ CLOCK MUX PSK MODULATOR LOCAL OSCLLATOR PS 90 deg Hybrid Mixer Y Y Y Y Fig. 6. A 128 Gb/s DP-PSK photonic and electronic integration. (a) Transmit. (b) Receive. MODEM equalization of CD and PMD enables fast optical path restoration/protection, a key requirement for dynamic optical networking architectures of the future. Another advantage of coherent transmission is that the MODEM itself provides real-time link parameter performance monitoring. This allows in-skin monitoring of CD, PMD, SOP and SNR for link troubleshooting and link quality metrics (e.g. could be used for pre-emptive switching criteria) without the use of intrusive external test equipment. As next-generation DWDM line systems often advocate colorless, directionless ROADMs to allow versatile optical wavelength routing, another advantage of coherent is that a colorless receiver can be used, such as optical splitters. The correct DWDM wavelength is then selected by tuning the laser Local Oscillator (LO) in the receive transponder. This eliminates the use of colored DWDM demultiplexers (fixed single wavelength per fiber output) and allows more flexible dynamic optical networking architectures. 3. Mary AM for Beyond 100Gb/s 3.1. ntroduction A high data rate can be achieved by coding multiple bits/symbol and using coherent detection and Mary uadrature Amplitude Modulation (M-AM) modulation format. Present day optical transport speeds are limited by electronics speed, whereas this technique allows data rates many multiples higher than the electronics speed. Although the use of AM is well known in other industries, such as satellite and wireless communications, it has not been implemented to date for optical transmission. A novel advantage of using M-AM in DSP is that by enabling programmable modulation (e.g. from PSK to 256-AM) the bit rate transmitted can be traded for optical reach. This technique will maximize the data rate for any given link length and distortion properties of the channel. This capability is analogous to rate adaptive DSL modems that maximize the data rate over local copper Tx Block Diagram n-phase NRZ data Baud rate, b n π MZ π/2 DSP/DAC CW laser out uad-phase NRZ data Baud rate, b n MZ π One polarization tributary shown for simplicity Rx Block Diagram N.B. Needs polarization diversity or tracking for in and LO mixing in Local Oscillator 90 hybrid (phase diversity) /DSP Fig. 7. M-AM Tx/Rx implementation.

5 R. Saunders / Optical Fiber Technology 17 (2011) connections from local office to customer premise, using a training sequence at installation. The increased data throughput without any significant increase in the number of active electro-optic components should yield a reduction in field failure rate and improved reliability vs today s optical transponder technology Mary AM mplementation The transmit/receive block diagrams are shown in Fig. 7. This shows the basic functional block diagrams for an optical coherent detection modulation scheme, with control of the amplitude of both in-phase, and quadrature phase,, components of the modulated signal. n this case, the nominal baud rate, b n, is constant, but the baud rate could also be rate adaptive to offer more continuous rate adaption, rather than the discrete steps from moving between M-AM symbol spaces. Note that 2 polarizations can be utilized (only 1 shown in Fig 7) to double the traffic carrying capacity, using a polarization beam combiner and separate quadrature modulators for each orthogonal polarization state. The Rx consists of a synchronous coherent detection scheme. The method shown in Fig. 7 uses a free-running optical Local Oscillator (LO) and feed forward carrier recovery, polarization demultiplexing, CD/PMD compensation using analogue to digital conversion followed by an adaptive digital Finite mpulse Response (FR) filter. As an example, the baud rate could be set to 25Gbaud (the design could also support variable baud rate to maximize capacity for a given optical channel filter) and both polarizations modulated. To maximize reach, the transponder could be configured to transmit DP-BPSK, as shown in Fig. 8. This would give the maximum OSNR sensitivity and maximum launch power possible, therefore maximizing the distance that can be transmitted between signal 3R regeneration points in the network. The capacity in this example would be 50 Gb/s (1 bits/s/hz). f the specific channel has excess performance margin, the transponder could reconfigure to PM-PSK as shown in Fig 8(b). Note that in this case the OSNR sensitivity is the same ( and component noise is independent) but that the launch power would be slightly lower than DP-PSK as it is more sensitive to nonlinear phase noise (90 between symbol states for PSK, whereas 180 for PSK). This doubles the capacity to 100 Gb/s. n a similar fashion, if the channel has still more margin (i.e. typically if it operates over a shorter reach) the transponder can re-configure as DP-8AM (Fig. 8c), DP-16AM (Fig. 8d), DP-32AM (Fig. 8e), DP-64AM (Fig. 8f), DP-128AM (Fig. 8g) and DP-256AM (Fig. 8h). As can be seen from the constellation diagrams in Fig. 8, each time the M-AM bits/symbol rate is incremented, the channel carrying capacity increases, at the expense of an increase in the required OSNR. This is all done in DSP/software. The OSNR increase is due to the reduction in the minimum Euclidean distance from symbol to symbol. For denser M-AM constellations, more SNR is required per symbol for a given BER. This is shown in Fig. 9. An analytic estimation of required OSNR sensitivity (assumes ideal implementation) for different M-AM bit rates in shown in Fig. 10. Fig. 8. Different M-ary AM constellations, required DAC/ bit resolutions.

6 450 R. Saunders / Optical Fiber Technology 17 (2011) Fig. 9. M-AM symbol error rate probability. Fig. 10. M-AM bit rate vs OSNR sensitivity tradeoff. n addition to the challenging OSNR levels required for M-AM optical transmission, M-AM is more sensitive to nonlinear phase noise and distortion, so fiber nonlinearity provides a major obstacle to transmission distance. This is an active area for further study. Reducing nonlinearity by using more distributed optical amplification, such as Raman amplification or more frequent Erbium Doped Fiber Amplifiers (EDFAs) will help to reduce peak power and hence nonlinear distortion. The key optical component to help reduce the nonlinearity is indeed the optical fiber itself. New optical fibers with reduced attenuation, reduced nonlinear coefficient n2 and higher effective core area would all help to reduce nonlinearity and enable higher optical launch powers and hence increased reach. Such Super Large Effective Area (SLA) fibers already utilized in submarine network deployments are already a good step in the right direction [14,15] Advanced coding techniques The two front battle between diminishing OSNR sensitivity and increasing tolerance to nonlinear distortion for higher order modulation schemes has some other weapons at its disposal. nevitably these techniques come at the expense of increased implementation complexity so they are bounded by what is practical to fit into MOD- EM ASCs and thermal management limitations. CMOS migration to lower geometries such as 28 nm will help open-up the possibilities here, both in terms of transistor speed and gate count density. Some potential areas of future study: 1. Soft Decision Forward Error Correction (SD-FEC). Need further study here to improve net coding gain and reduce implementation penalty through more efficient algorithms, more decoder iterations/bit resolution, code puncturing, etc.

7 R. Saunders / Optical Fiber Technology 17 (2011) Trellis/Block Coded Modulation (TCM/BCM). With coded modulation additional coded bits can be used to provide redundancy rather than send extra symbols (e.g. mapping raw 16-AM into Trellis-coded 32-AM, 1 extra bit coding redundancy). This effectively expands the signal constellation and increases the minimum Euclidean distance between adjacent symbols, relaxing the OSNR sensitivity requirements [16]. 3. Optimized constellation geometry. Rectangular AM constellations as shown in Fig. 8 are not the most efficient but are easier to realize. A more optimized M-AM constellation, such as circular, increases the minimum Euclidean distance and OSNR sensitivity. n addition, nonlinear phase noise is intensity dependent and should be considered in the constellation design. This optimization of the M-AM constellation will come at the expense of added complexity, likely higher DAC resolution and RF drive chain linearity/s-parameter performance. 4. Optimized symbol mapping. The M-AM symbol mapping should be carefully designed and optimized holistically combined with the SD-FEC and TCM/BCM code designs. Symbol mapping diversity minimizes bit errors and optimum combinations of M-AM symbol mapping with SD-FEC/TCM design should be sought. 5. Nonlinear compensation/mitigation. Coherent MODEMs can be designed with some level of nonlinear compensation using techniques such as digital backpropagation [17]. n addition the carrier phase estimation filter shape and bandwidth profile can be optimized to mitigate against effects such as XPM, possibly in a dynamic or programmable manner. These techniques should allow increased optical launch power and hence higher received OSNR but once again at the expense of increased electronic DSP complexity. 6. Use of multiple carrier Orthogonal Frequency Division Multiplexing (OFDM). t has been claimed that the use of OFDM can reduce nonlinearity vs single carrier transmission, at least in certain applications such as highly periodic dispersion managed systems [18]. This needs further study to weigh-up the pros and cons. Whether single carrier or multiple carriers are used in coherent systems, if spectral efficiency is to increase then higher-order modulation such as M-AM is needed in either case. 4. Conclusions The advent of coherent DWDM technology is enabling 100GE optical transport over backbone optical networks with link engineering rules similar to 10 Gb/s OOK channels. This enables a 10 scaling of network/fiber capacity and is possible without any change in DWDM channel spacing or DWDM common equipment design. The formation of a 100G DWDM ecosystem in the OF in the infancy of this technology has helped focus R&D capital investment and should act as a catalyst driving early technology adoption by system vendors and service providers. Standardization by the EEE on 100GE and TU on OTU4 encapsulation has also been critical in laying the foundation for this technology. Moreover, the collaboration between EEE and TU on 100GE encapsulation into OTU4 frame format and commonality in such things as the electrical interface PMD has really helped to focus engineers and minimize time wasted reinventing the wheel. The stage is now set for service providers to start certification testing and initial field applications of 100 Gb/s DWDM wavelengths. As always for new technology introduction there will be a period of frantic bug-fixing, ASC re-spins and hardware design fixes as system vendors and service providers run thorough verification lab testing and robustness is built into 100G transponder designs. First office field rollouts are expected in 2012 timeframe and as volume begins to ramp optical vendors will already be working on cost-reduced, footprintreduced, performance enhanced next-gen 100G solutions to meet the very high volumes expected in 2013/14 as volumes ramp [19]. Migrating to data rates beyond 100 Gb/s faces some real challenges in terms of OSNR sensitivity and nonlinearity. Perhaps we will just utilize more wavelengths and fibers without increasing spectral efficiency but that method will also run into scaling issues as fibers run-out and managing too many DWDM overbuilds becomes unwieldy for carriers. Coherent transmission certainly opens-up the capability of moving to higher-order modulation formats and increased spectral efficiency but to meet the optical reach requirements we may need a fundamental improvement in optical fiber and/or optical amplification technology. This will be a fertile area of optical research in coming years as engineers tackle how to scale optical transport data-carrying capability whilst staying within the fundamental constraints of Shannon s Limit [20]. References [1] M. Birk et al., Field trial of a 40 Gbit/s PSBT channel upgrade to an installed 1700 km 10 Gbit/s system, in: Proc. OFC 2005, Paper OTuH3, Los Angeles, CA. [2] TU-T Rec. G.694.1, Spectral Grids for WDM Applications: DWDM Frequency Grid, 06/2002. [3] A.H. Gnauck et al., EEE Photon. Technol. Lett. 15 (3) (2003). [4] C. Laperle et al., Wavelength Division Multiplexing (WDM) and Polarization Mode Dispersion (PMD) Performance of a Coherent 40 Gbit/s Dual Polarization uadrature Phase Shift Keying (DP-PSK) Transceiver, Paper PDP16, NFOEC [5] M. Taylor, Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments, EEE Photon. Technol. Lett. 16 (2) (2004) [6] B. Zhang et al., Penalty Free Transmission of 127 Gb/s Coherent PM-PSK over 1500 km of NDSF with 10 Cascaded 50 GHz ROADMs, Paper NTuC5, NFOEC/ OFC [7] EEE P802.3ba, 40 Gb/s and 100 Gb/s Ethernet Task Force. < [8] TU-T Rec. G.709, nterfaces for the Optical Transport Network, Edition 3.0, 12/ [9]. Djordjevic et al., Generalized low-density parity-check codes for optical communication systems, J. Lightw. Technol. 23 (5) (2005) [10] M. Scholten et al., Enhanced FEC for 40G/100G, ECOC 2009, Workshop Presentation WS1-06. [11] F. Chang, K. Onohara, T. Mizuochi, Forward error correction for 100G transport networks, EEE Commun. Mag. 48 (3) (2010) S48 S55. [12] M. Birk et al., Field trial of a real-time, single wavelength, coherent 100 Gbit/s PM-PSK channel upgrade of an installed 1800 km link, in: Proc. OFC/NFOEC, 2010, Paper PDPD1. [13] OF, 100G Ultra Long Haul DWDM Framework Document. < [14] Vascade Optical Fiber Data Sheet, Corning nc. < opticalfiber/pb7098_05-01.pdf>. [15] UltraWave Ocean Fibers, OFS Fitel nc. < UWOceanFiber-fiber-115.pdf>. [16] D. Lin, D.J. Costello, Error Control Coding: Fundamentals and Applications, second ed., SBN: , [17] E. p, J.M. Kahn, Compensation of dispersion and nonlinear impairments using digital backpropagation, J. Lightw. Technol. 26 (20) (2008) [18] L. Du, A. Lowery, Fiber Nonlinearity Compensation for CO-OFDM Systems with Periodic Dispersion Maps, Paper OTu01, OFC/NFOEC [19] D. nnis et al., OVUM Market Research: The 40G and 100G Optical Modules, Components, C, Actives and Passives Forecast: Revenues, Unit Volumes, and ASPs, November 29, [20] C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (July, October) (1948) , < njas/doc/shannon1948.pdf>.