Abstract
With the increase in demand to Backbone networks, one became fundamental the application of new telecommunication technologies for efficient use of devices and optical links, such as xPSK modulations with dual polarization, dispersion compensating fibers, coherent detection and digital processing signals. Thus, network planning using analytical models have been proposed in the last years for this purpose. In this paper we propose the use of numerical simulations in wavelengthdivision multiplexing networks planning via a novel iterative method with highperformance processing, which does an analysis of the quality of transmission in transparent networks.
Optical fiber networks; Coherent communications; Crosslayer design
I. introduction
Optical networks can fall into four broad categories: access, metropolitan, datacenter and backbone. Access networks are the interface with the enduser, mainly, they are based on tree topologies using time, frequency and wavelength multiplexing technologies. Metropolitan networks aggregate access data in multiring topologies. Wavelength Division Multiplexing (WDM) with Intensity Modulation/ Direct Detection (IM/DD) is the current technology to interconnect the nodes in optical networks.
A typical datacenter contains thousands of servers arranged into one or more clusters [^{1}1 C. Lam, H. Liu, B. Koley, X. Zhao, V. Kamalov, and V. Gill, “Fiber optic communication technologies: What’s needed for datacenter network operations?” IEEE Communications Magazine, vol. 48, no. 7, pp. 32–39, Jul. 2010.]. Clusters are further networked through layers of cluster aggregation switches, which are then connected to datacenter routers. The datacenter routers connect to the rest of the network through Internet points of presence (POPs), where traffic flows from datacenter networks to end users and vice versa. Long haul WDM systems provide the connectivity between datacenters and population centers in different metro areas. Metro WDM transport links are used to interconnect datacenters and POPs located within the same metro area.
The Backbone or longhaul networks, which are the main focus of this paper, cover a wide geographical area with fiber spans ranging from hundred to thousands of kilometers. In backbone networks fiber resources are scarce, expensive and time consuming to acquire and build. Most of the existing networks are based on Optical Transport Network (OTN) technology [^{2}2 ITUT, “Recommendation G.709/Y.1331 (02/2012). Interfaces for the optical transport network,” Feb. 2012.], [^{3}3 ITUT, “Recommendation G.872 (2001). Architecture of optical transport networks,” 2012.] with a wide range of line rates. Recently International Telecommunication Union (ITU) made an update on ITUT Rec. G.709 to add 100 Gb/s transport capability.
To maximize the utilization of the optical fibers, such networks need to provide high spectral efficiency and, at the same time, minimize the number of regenerators since they cause a significant increase in Capital Expenditure (CapEx) and Operational Expenditure (OpEx). Coherent optical systems [^{4}4 E. Ip and J. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” IEEE Journal of Lightwave Technology, Journal, vol. 28, no. 4, pp. 502–519, Feb. 2010.] with electronic digital signal processing techniques make use of joint phase, amplitude, and polarization encoding to achieve high spectral efficiency. Phase modulation also results in larger Amplified Spontaneous Emission (ASE) noise tolerance and longer unregenerated reach. Stateoftheart commercial coherent receivers use polarizationdivision multiplexed quaternary phase shift keying (PDMQPSK) modulation. Such systems can achieve 100 Gb/s transmission on 50 GHz ITU channel grid. Other benefits of coherent receivers include high tolerance to Polarization Mode Dispersion (PMD) and Chromatic Dispersion (CD) since practically all the PMD and CD effects can be corrected with linear digital electronic filters at the expense of energy consumption [^{5}5 B. Pillai, B. Sedighi, K. Guan, N. Anthapadmanabhan, W. Shieh, K. Hinton, and R. Tucker, “Endtoend energy modeling and analysis of longhaul coherent transmission systems,” IEEE Journal of Lightwave Technology, Journal, vol. 32, no. 18, pp. 3093–3111, September 2014.]. The spectral efficiency of coherent PDMQPSK modulation is 4 bits/symbol. Higher spectral efficiency requires more complex modulation schemes and higher Optical Signal to Noise Ratio (OSNR).
In alloptical networks the signals undergo changes due to the accumulation of the physicallayer impairments, which generates a degradation of the quality of transmission (QoT), hence an ”link by link” analysis must be performed to take account wavelengths have arrived degraded at a particular Reconfigurable Optical Add/Drop Multiplexers (ROADM) node [^{6}6 B. J. SoléPareta, S. Subramanianm, D. Careglio, and S. Spadaro, “CrossLayer Approaches for Planning and Operating Optical ImpairmentAware Optical Networks,” Proceedings of the IEEE, vol. 100, no. 5, p. 12, 2012.]. For this type of network analysis we propose an approach based on iterations. However, for this type of simulation to be feasible, the use of high performance computing platforms such as the Graphics Processing Unit (GPUs) is essential due to the high computational cost required.
Optical reach is the distance an optical signal can travel before the signal quality degrades to a level that necessitates regeneration. Many factors affect the optical reach; for example, the type of amplification, the launched power of the signal, and the modulation format of the signal. Compared to the 500 km optical reach of traditional systems, the optical reach of longhaul systems currently being deployed is on the order of 2000 to 4000 km.
In this paper we present a multilayer network planning tool called Optical Network Design and Analysis (ONDA). ONDA is a collection of softwares modules that can combine physical topology design, optimized optical equipment placement, routing wavelength assignment, and physical layer simulation including IM/DD, coherent transmission and Optical Orthogonal Frequency Division Multiplexing (OOFDM) transmission systems. This tool can be used to design access, metropolitan, datacenter and backbone networks but this paper is focused only in backbone networks with coherent transmission.
The remaining of the article is organized as follows. In Section II, we will give a highlevel view of the strategies we have adopted for the problem of the backbone network planning. Section III presents details of the coherent transmission system we have used in our simulations. The planning tool is presented in Section IV. All the validation process and an example of network planning are presented in Section V. Finally, we draw our conclusions in Section VI.
II. NETWORK PLANNING STRATEGY
In this paper we consider the network design problem for todays realistic backbone networks. We assume that at least the physical topology and a set of traffic demands are provided. The size, i.e. the number of nodes of most of known networks range from ten to one hundred nodes [^{7}7 M. Cousineau, P. Perron, C. G., M. Paiva, and M. Segatto, “RWA problem with geodesics in realistic OTN topologies,” Optical Switching and Networking, vol. 15, no. 0, pp. 18–28, 2015.].
Optical backbone networks typically operate in the Cband portion of the spectrum with fixed grid by ITU standard ITU G.694 [^{8}8 ITUT, “Recommendation G.694.1 (02/2012). Spectral Grids for WDM Applications: DWDM Frequency Grid,” 2012.]. Each network node can be equipped with ROADMs to route wavelength connections optically, a set of transponders with bit rates ranging from 10 Gb/s to 100 Gb/s [^{9}9 E. Lach and W. Idler, “Modulation formats for 100G and beyond,” Optical Fiber Technology, vol. 17, no. 5, pp. 377–386, Oct. 2011.]. Spectral efficiency is achieved with optical coherent technology for line rates higher than 40 Gb/s. Optical Amplifiers (AO) and Dispersion Compensation Modules (DCM) can be used in each node or at intermediate nodes where there is no traffic exchange.
Planning a network is often a multi objective task with conflicting restrictions. Our primary goal is to minimize CapEx and maximize the network throughput while minimizing the overall network energy consumption. To produce such optimal networks it is necessary to deploy computationally complex algorithms that require a huge amount of time for the design of realistic networks. A planning tool for optical network must perform at least the following tasks [^{10}10 J. M. Simmons, “Network design in realistic ”AllOptical” backbone networks,” IEEE Communications Magazine, vol. 44, no. 11, pp. 88–94, November 2006.]:
Compute Physical Layer Impairments
The signal’s QoT is degraded by physical impairments, such as Attenuation, ASE noise, CD or Group Velocity Dispersion (GVD) [^{11}11 G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. Academic Press, 2007.], PMD [^{12}12 D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the ManakovPMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” IEEE Journalof Lightwave Technology, vol. 15, no. 9, pp. 1735–1746, 1997.], Polarization Dependent Loss (PDL) [^{13}13 D. Wang and C. Menyuk, “Calculation of penalties due to polarization effects in a longhaul WDM system using a stokes parameter model,” IEEE Journal of Lightwave Technology, vol. 19, no. 4, pp. 487–494, Apr. 2001.], Self Phase Modulation (SPM), Crossphase Modulation (XPM), Four Wave Mixing (FWM) and Crosspolarization Modulation (XPolM) [^{14}14 M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMDinduced system impairments,” IEEE Journal of Lightwave Technology, no. 11, pp. 4127–4137.]–15 Y.H. Wang and I. Lyubomirsky, “Impact of DPQPSK pulse shape in nonlinear 100 G transmission,” IEEE Journal of Lightwave Technology, Journal, vol. 28, no. 18, pp. 2750–2756, 2010.[^{16}16 A. Bononi and P. Serena, “Which is the dominant nonlinearity in longhaul PDMQPSK coherent transmissions?” in 36th ECOC, no. 0, 2010, pp. 19–21. [Online]. Available: http://ieeexplore.ieee.org/xpls/absall.jsp?arnumber=5621217.
http://ieeexplore.ieee.org/xpls/absall.j...
]. For systems based on IM/DD technology it is possible to compute the QoT using analytical and semianalytical models [^{17}17 F. O. Lima, “Strategies for optical transport network planning,” PhD, Federal University of Espírito Santo, 2015, in portuguese.], [^{18}18 S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Computer Networks, vol. 53, no. 7, pp. 926–944, 2009.]. For coherent systems it is necessary to solve a modified version of the nonlinear Schrödinger equation to incorporate the polarization effects to obtain a more precise value for the QoT [^{19}19 O. Sinkin, R. Holzlöhner, J. Zweck, and C. Menyuk, “Optimization of the splitstep Fourier method in modeling opticalfiber communications systems,” Journal of Lightwave Technology, vol. 21, no. 1, p. 61, 2003. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?id=71748.
http://www.opticsinfobase.org/abstract.c...
]. Unfortunately this set of equations can not be solved analytically.
Compute routes with or without protection
Each traffic demand between a pair of nodes has to be mapped into a set of ligthpaths. If the demand is smaller or equal to the transponder capacity, only one ligthpath will be used. The planning tool is responsible for finding the routes for all demands taking into account the protection required by the user. Many different algorithms can be used to find the shortest path, the kshortest path or the shortest cycle. A study dedicated to these algorithms is found in the book [^{20}20 R. Bhandari, Survivable Networks: Algorithms for Diverse Routing, ser. The Springer International Series in Engineering and Computer Science. Springer, 1999. [Online]. Available: https://books.google.com.br/books?id=SIkfR0lAN1wC.
https://books.google.com.br/books?id=SIk...
].
Allocate ROADM and Regenerator
Given the physical topology, the planning tool has to find the minimum combination of ROADMs and regenerators since they are the most expensive items of the network. The ROADM degree is basically defined by the node physical degree [^{17}17 F. O. Lima, “Strategies for optical transport network planning,” PhD, Federal University of Espírito Santo, 2015, in portuguese.]. Each ROADM placed increases the number of optical amplifiers used in the network and compromises the optical reach of each ligthpath. Usually, the regenerators are placed in the same site of the ROADM [^{10}10 J. M. Simmons, “Network design in realistic ”AllOptical” backbone networks,” IEEE Communications Magazine, vol. 44, no. 11, pp. 88–94, November 2006.].
Allocate Optical Amplifier
The amplifier placement is a very important step in any planning tool. Four parameters must be taken into account: Gain, gain tilt (or ripple), saturation power, and the amplifier Noise Figure (NF). Gain and NF have a direct impact on the optical reach, since they are related to the received power and OSNR.
Assign Wavelengths
A key parameter is the maximum number of wavelengths per fiber. It is possible to compute a lower bound for the number of wavelengths of a given physical topology [^{7}7 M. Cousineau, P. Perron, C. G., M. Paiva, and M. Segatto, “RWA problem with geodesics in realistic OTN topologies,” Optical Switching and Networking, vol. 15, no. 0, pp. 18–28, 2015.]. The planning tool can use a variety of algorithms to find the best combination of wavelengths inside the ITU grid [^{21}21 H. Zang, J. P. Jue, and B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelengthrouted optical wdm networks,” Optical Networks Magazine, vol. 1, no. 1, pp. 47–60, 2000.]. A survey of the physical layer impairments aware routing and wavelength assignment algorithms in optical networks was presented in [^{18}18 S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Computer Networks, vol. 53, no. 7, pp. 926–944, 2009.].
III. COHERENT SYSTEMS
In a typical coherentlydetected PDMQPSK system, the data traffic is mapped into I and Q signals, inphase and quadrature, respectively in two orthogonal states of polarization. At the transmitter side, a Mach Zehnder Modulator (MZM) is used to modulate the optical field. The propagation link is, in general, composed of, singlemode fibers and optical amplifiers with or without dispersion management [^{22}22 I. Kaminow, T. Li, and A. Willner, Optical Fiber Telecommunications Volume VIB: Systems and Networks, ser. Optics and Photonics. Burlington, MA: Elsevier Science, 2013.]. At the receiver, a laser is used as the local oscillator for coherent detection and two hybrid 90 degree interferometer enable the detection of the complete electric field of the input optical signal. After the signals are obtained by the detector, they are converted to digital format by the A/D converter. Then, the Digital Signal Processing module (DSP) performs a series of operations to recover the transmitted data [^{9}9 E. Lach and W. Idler, “Modulation formats for 100G and beyond,” Optical Fiber Technology, vol. 17, no. 5, pp. 377–386, Oct. 2011.].
At the receiver, a DSP module performs chromatic dispersion compensation using Finite Impulse Response (FIR) filters [^{23}23 G. Li, “Recent advances in coherent optical communication,” Advances in Optics and Photonics, vol. 1, no. 2, p. 279, Feb. 2009.]. The signal is sampled every T_{adc} seconds and recovered with tap weights h_{cd}[k] given by [^{24}24 S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 16, no. 5, pp. 1164–1179, Sep. 2010.]
where is an upper bound and
where β_{2} is the GVD and L_{total} the total propagation distance. For example, for a 1000 km Standard Singlemode Fiber (SSMF) with D = 16 ps/(km.nm) operating at a rate of 28 Gbaud, a FIR filter of 401 taps is required to compensate the accumulated dispersion in the link [^{22}22 I. Kaminow, T. Li, and A. Willner, Optical Fiber Telecommunications Volume VIB: Systems and Networks, ser. Optics and Photonics. Burlington, MA: Elsevier Science, 2013.].
Because PMD is a stochastic impairment, it is necessary a dynamic channel equalization. Such compensation can be achieved by using FIR filters through the Continuous Modulus Algorithm (CMA) [^{25}25 D. Godard, “Selfrecovering equalization and carrier tracking in twodimensional data communication systems,” IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867–1875, 1980.], which is a blind algorithm. These filters are organized in a Butterfly structure, and are constantly updated to follow the disturbances of the channel. They can be modeled in the Jones matrix of the transmission line. Then, the equalizer task is to estimate the inverse Jones matrix, in order to reverse the signal degradation caused by the impairments along the transmission. A modified version of CMA was used in this study to avoid the singularity problem [^{26}26 L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization demultiplexing in optical coherent receivers,” Optical Fiber Communication Conference and National Fiber Optic Engineers Conference, no. 2, p. OMT2, 2009.].
The carrier phase estimation (Viberti and Viberti (V&V) [^{27}27 A. Viterbi, “Nonlinear estimation of pskmodulated carrier phase with application to burst digital transmission,” IEEE Transactions on Information Theory, vol. IT29, no. 4, 1983.]), which is the last compensation module used in our simulations, is used to retrieve and subsequently remove the remaining phase mismatch, φ, between the local oscillator and the signal [^{23}23 G. Li, “Recent advances in coherent optical communication,” Advances in Optics and Photonics, vol. 1, no. 2, p. 279, Feb. 2009.]. The estimation of the inconsistency is made in the central sample only, using the following algorithm: first, the mth power of the complex symbol is considered for the purpose of removing any encoded information in the signal phase (m being the amount of phase modulation levels, 4 in the QPSK case). Second, an average window of N_{w} + 1 elements is calculated by summing the result over the N_{w} /2 previous symbols and the N_{w} /2 subsequent symbols. Then, the argument is taken, since we are interested only in phase. Finally, the resulting phase is divided by m to correct the initial lift for mth power. For the range of π to π , we have [^{24}24 S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 16, no. 5, pp. 1164–1179, Sep. 2010.]:
At the end of this process, an unwrapping function is used to allow large timevarying excursions of the signal phase, as for instance when a carrier frequency detuning with respect to the local oscillator is present.
IV. THE PLANNING TOOL
As stated in Section I we have developed a multilayer network planning tool called Optical Network Design and Analysis (ONDA). ONDA is a collection of software modules that can combine physical topology design, optimized optical equipment placement, routing, wavelength assignment, and physical layer simulation, including IM/DD, coherent transmission and OOFDM transmission systems.
The main module of the software package ONDA is called Keplan (Kernel for Planning) [^{17}17 F. O. Lima, “Strategies for optical transport network planning,” PhD, Federal University of Espírito Santo, 2015, in portuguese.]. As shown in Figure 1, it is divided in two main parts: Frontend and Kernel. The Frontend is responsible for the pre and posprocessing. The input parameters are i) the physical topology of the network including traffic exchange nodes, amplification and/or regeneration sites, fiber cables, and their characteristics; ii) the traffic matrix demands, which include a variety of traffic, such as 1GbE, 10GbE, STM16 to STM256 and OTU1 to OTU4 [^{3}3 ITUT, “Recommendation G.872 (2001). Architecture of optical transport networks,” 2012.], iii) an equipment portfolio with all kinds of transponders, optical amplifiers, DCMs, and ROADMs available; iv) a set of impairments for the network planning, and v) the design goals.
An eXtensible Markup Language (XML) parser is used to exchange data between Kernel and Frontend. Figure 2 shows the Kernel in details. It starts the planning process by identifying network nodes to be configured as ROADM, taking into account the required demands and the physical topology connections. After that, the phase of link feasibility optimally places optical amplifiers and DCMs, minimizing the costs with equipments and ensuring the signal power levels. Lastly, the routing is solved with the required protection and a simplified solution for wavelength allocation is provided, thus completing a solution to the Routing and Wavelength Assignment (RWA) problem. In the routing, either the shortest path or the minimum disjoint cycle is used. The network optimization in carried out using the generalized version of Suurballe [^{28}28 J. W. Suurballe and R. E. Tarjan, “A quick method for finding shortest pairs of disjoint paths,” Networks, vol. 14, no. 2, pp. 325–336, 1984.], providing the minimal length cycle, with the minimum of sharing nodes for the minimum of sharing links possible. The practical feasibility and the location of the regenerators are checked in this module, taking into consideration the physical impairments, the numerical and the analytical models.
Finally, a numerical analysis is performed on the planned routes to verify the QoT of the WDM channels, considering the linear and nonlinear impairments. This analysis is done link by link, assuming that the network is opaque (nrun == 1), i.e., all optical channels begin and end on the same link. The data from this first stage are stored for use in other runs, when the network is considered transparent (nrun > 1), i.e., a link can receive optical channels coming from other links of the network.
Algorithm 1 describes the proposed approach in this paper to the planned ligthpaths analysis. First, the numerical simulator takes as input the general parameters (line 1.1), such as: (i) path of the XML file generated by the Keplan, (ii) number of symbols, points per symbol and modulation format, (iii) the OSNR level, (iv) the symbol rate (v) the characteristics of transmission and reception lasers, (vi) the characteristics of the coherent detector and (vii) the parameters of the DSP modules.
Using the XML file generated by the Keplan module (line 1.2), the simulator captures information concerning the spacing, ITU channels, network nodes and their functions, fiber segments and their parameters, amplifiers, links, ligthpaths, optical channels associated with each ligthpath, interfaces of each node, ROADMs, and DCMs. With these data, the generation of a matrix of lambdas versus links (line 1.3) is mounted to store the information concerning optical network ligthpaths.
After reading the input arguments, the simulator starts the scanning of the links (line 1.5), from first to last in the sequence identified in the XML file received. This scan will be performed #RUNS
times (line 1.4), considering that in the first run the network is opaque. The #RUNS  1 remaining runs already consider the channels bypass via ROADMs nodes of the network (line 1.10), which are the transparent runs. An ideal amount of runs is equal to the number of links pertaining to the longest ligthpath of the network.
For each link, one can verify the fiber segments which compose it and what the channels generated from the first node to the last node of this link are (lines 1.61.8). Then, PDMQPSK signals are built for each channel (in case the first run and/or this channel starts in this link), or it is checked whether the channel has been stored from a previous iteration (lines 1.91.15) for the transparent runs.
Single optical fields are generated for each PDMQPSK electrical signal (lines 1.16) and the signal is propagated in the fiber segments of the link (line 1.18). For each arrival node, the node type is checked: Amplifier, DCM (line 1.19), or ROADM (line 1.24). If the node is a ROADM, the reception of each channel is performed (line 1.24).
For each lambda, the source and the target are checked (line 1.27). If a channel is not intended for a given network node, the data is stored for later retrieval (line 1.32). Otherwise, the channel is coherently detected and goes through the DSP module, getting the lowest QFactor value at the end [^{29}29 F. Zhang, Y. Luo, Y. Wang, and L. Li, “Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems,” IEEE Photonics Technology Letters, vol. 23, no. 18, pp. 1343–1345, 2011.], considering the components of polarization, phase, and quadrature (lines 1.28 to 1.30). These QFactor values are assigned to the link in which the lambda ends. All the simulation results are written to log files.
V. Results
We start our analysys with the validation of the physical layer simulator using as a reference the experiments performed by Mussolin et al. in [^{30}30 M. Mussolin, M. Forzati, J. Martensson, A. Carena, and G. Bosco, “DSPbased compensation of nonlinear impairments in 100 Gb/s polmuxQPSK,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on. IEEE, 2010, pp. 1–4.]. It consists of an 100 Gb/s PDMQPSK coherent optical transmission system with 16 WDM channels and 50 GHz spacing as shown in Figure 3.
100 Gb/s PDMQPSK coherent optical transmission system with 16 WDM channels and 50 GHz spacing used for validation purposes.
The transmitter consists of two IQ MZMs driven by a PseudoRandom Bit Sequence (PRBS) De Bruijn grade 15, with 32bit delay between I (inphase) and Q (quadrature) and of 915 bits between the polarizations. The transmission link consists of a loop of 63.6 km of SSMF and Erbium Doped Fiber Amplifiers (EDFA). The fibers were modeled with the Coupled Nonlinear Schrödinger Equations (CNLSE), whose solution was obtained with the Splitstep Fourier Algorithm (SSFA) with adaptive step size [^{19}19 O. Sinkin, R. Holzlöhner, J. Zweck, and C. Menyuk, “Optimization of the splitstep Fourier method in modeling opticalfiber communications systems,” Journal of Lightwave Technology, vol. 21, no. 1, p. 61, 2003. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?id=71748.
http://www.opticsinfobase.org/abstract.c...
], [^{31}31 P. Serena. Optilux: Matlab/octave toolbox to simulate optical communication systems. [Online]. Available: www.optilux.sourceforge.net.
www.optilux.sourceforge.net...
]. The fiber dispersion at the central wavelength was 16.3 ps/(nm.km).
In our simulations we have used a receiver with 2 Hybrid 90 degrees interferometers perfectly and balanced photodetectors, where the optical noise was added to the received signals for OSNR levels of 15 dB and 20 dB. The data sampling is performed at a rate of 2 samples per symbol. The DSP performs the chromatic dispersion and PMD compensations with standard linear equalization.
The simulations have been performed using a total of 16 loops representing 1017.6 km of fiber without optical dispersion compensation. Figure 4 shows the received signal for the central wavelength following respectively the A/D conversion, chromatic dispersion compensation, polarization demultiplexing of the components via CMA, and finally, the phase estimation algorithm via V&V.
Received signal for the central wavelength after 1017.6 km of fiber without optical dispersion compensation.
In order to validade our physical layer simulator we have performed Bit Error Rate (BER) measurements considering the central wavelength and the input optical power ranging from 1.2 dBm to 1.6 dBm. Figure 5 shows the comparison between the results of our simulations and the experimental results reported in [^{30}30 M. Mussolin, M. Forzati, J. Martensson, A. Carena, and G. Bosco, “DSPbased compensation of nonlinear impairments in 100 Gb/s polmuxQPSK,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on. IEEE, 2010, pp. 1–4.].
Comparison between the experimental results presented in [30] and the physical layer simulator developed in this paper.
After the validation process of the physycal layer simulator with one link, we have started the validation process for the Keplan using a threenodes network with distances between each pair of nodes of 80 km, 120 km, and 150 km as illustrated in Fig. 6. The input file contains a description of the physical topology including 3 midspan sites for optical amplifier and DCM placement, optical fiber characteristics, the equipment portifolio and traffic demands. In this case, we have considered only OTU4 demands between each pair of nodes and full network protection.
Network with 3 ROADM nodes (1 to 3). Links of the 80150 km. Dashed lines representing the bidirectional optical lightpaths.
As expected for this case, the Keplan has returned 12 lightpaths and three wavelengths as shown in Table I. Three optical amplifiers and three DCM have been allocated at the mid span sites. The amplifier gain for each amplifier correspond to the overall span losses including the ROADMs. We have tested two wavelength assingment algorithms, Firstfit and Random with all wavelengths in the Cband. The results for the Qfactor are presented in columns 4 and 5 respectively. A route is feasible only if its BER ≦ 3.8 10^{3} before Forward Error Correction (FEC) [^{9}9 E. Lach and W. Idler, “Modulation formats for 100G and beyond,” Optical Fiber Technology, vol. 17, no. 5, pp. 377–386, Oct. 2011.], [^{32}32 M. Nölle, J. Fischer, L. Molle, C. SchmidtLanghorst, D. Peckham, and C. Schubert, “Comparison of 8 x 112 Gb/s PSQPSK and PDMQPSK signals over transoceanic distances,” Optics Express, vol. 19, no. 24, Nov. 2011.]–33 K. Balemarthy, “LongHaul Optical Fiber Networks: 100 Gbps and Beyond,” International Conference on Fiber Optics and Photonics, pp. 13–15, 2012.[^{34}34 G. Tzimpragos, C. Kachris, I. Djordjevic, M. Cvijetic, D. Soudris, and I. Tomkos, “A Survey on FEC Codes for 100G and Beyond Optical Networks,” IEEE Communications Surveys & Tutorials, 2014.]. It corresponds to a QFactor ≧2.67 dB. For Firstfit 4 lightpaths are not feasible while for Random only two lightpaths are not allowed. The arrows in the last column indicate an increase (↑) or a decrease (↓) in the Qfactor for the Random algorithm when compared to Firstfit.
We also have analysed a 7nodes mesh network considering realistic distances for an OTN as illustrated in Fig. 7. For this mesh network the distance between node range from 50 km to 655.60 km. Our goal is to compare the number of feasible routes considering opaque and transparent simulations. The demand matrix contain 21 bidirectional demands of OTU4 channels, standard singlemode fibers for all spans, dispersion compensator modules and EDFAs and optical coherent transponder modules.
Keplan has returned all optical lightpaths, a cromatic number of 82 and lightpaths ranging from 1 to 5 hops. The most occupied link has 14 wavelengths while the least occupied has only 5. We have used Firstfit to assign the wavelengths since it represents the worse case scenario. All wavelengths are in the Cband.
For the physical layer simulations we have used 2^{16} symbols, 64 points per symbol, symbol rate used is 28 Gbaud/s with NRZ sinc pulses, samplingrate = 56 GSample/symbol and ENOB = 12 bits. The CMA convergence parameter used was 10^{3} with the number of taps optimized for each link of the network.
Table II describes the link number for all network nodes. Tables III and IV show color diagrams representing the results of the opaque and transparent simulations respectively. For the transparent simulation we have considered #RUNS = 5. The feasibilty analyses was based on the QFactor = 2.67dB. In both tables n_{λ} and L represent the number of the wavelengths and the link number, respectively. Each colored rectangle represents: blue: start node, gray: bypass node, green: end node with a feasible lightpath, and red: end node with a nonfeasible lightpath. Most of the lightpaths in the opaque and transparent simulations are feasible but for example n_{λ} = 4 wich starts at link number 5, goes through link number 8 and ends at link 10 is approved in the opaque run, but it is disapproved in the transparent run. For the opaque run we have had 22 failed channels witch represents around 27%. This number is doubled after the transparent run.
In the ”red” category, results apparently most obvious are those in which the channel is approved in the opaque run, but it is reproved in the transparent run (e.g.: lambda, 6, 12, etc), because they go through by ROADMs nodes interacting with other copropagating channels on different wavelength grids. However, we can emphasize some interesting cases in the reported results. First, in the opaque run, we had two links of 50 km (links 10 and 13) with 2 out of 14 channels disapproved. Considering the nonlinear length L_{nl} for a multichannel system, given by [^{23}23 G. Li, “Recent advances in coherent optical communication,” Advances in Optics and Photonics, vol. 1, no. 2, p. 279, Feb. 2009.]
where P_{T} =Σ_{m} E_{m}^{2} is the total launched power, γ is the nonlinearity coefficient, and C is the amount of copropagating channels; we have for these links P_{T} = 14mW, C = 14 and γ≅ 1.3(W.km)^{1}, then L_{nl} ≅ 28km < 50km. This means that these lambdas were penalized by nonlinear effects, i.e, the XPM and XPolM influenced the QoT of some channels.
We have another ”intriguing” case when some lambdas are disapproved in the opaque run, but they are approved in transparent run. This is overtly due to the fact the copropagating channels can be influenced by different lambdas along their lightpaths through interaction between linear and nonlinear effects, similar to the soliton system. What we can note here is an adjustment or accommodation of the channel when they are going through the links (e.g.: links 10 and 26).
VI. CONCLUSIONS
Optical networks using ROADM and tunable lasers are on track to evolve to alloptical mesh networks in the near future. Transparent networks allow the data to be kept in the optical domain and, thus, causing considerable reduction in project costs. However, physical impairments degrade the signal along the transmission when the signal is transmitted through one or more links, therefore limiting the system reach. Thus, special techniques such as coherent detection and digital signal processing have to be used to retrieve the optical channels degraded during its propagation, such as in 100 Gb/s systems.
The physical layer impairments is the main focus of the Optical Network Design and Analysis (ONDA) suite. Therefore, an iterative approach from an opaque initial run was proposed in this paper as a solution to the design of practical networks. We validated the tool for one link through an 100 Gb/s PDMQPSK coherent optical transmission system with 16 WDM channels and 1017.6 km of fiber without optical dispersion compensation. Then, a threenode network planning was performed to study the behavior of lightpaths with a few changes in the coloring step.
Finally, some preliminary results were obtained through a semirealistic sevennodes network to allow the verification of the requirement of a linkbylink analysis, with accumulation of distortions, for the design of transparent networks. Despite the need for substantial use of computing power in numerical simulations using intensive parallel computing in GPUs, the approach was effective and identified a possibility of alloptical networks analysis with higher accuracy in measuring the ITU channels QoT.
REFERENCES

^{1}C. Lam, H. Liu, B. Koley, X. Zhao, V. Kamalov, and V. Gill, “Fiber optic communication technologies: What’s needed for datacenter network operations?” IEEE Communications Magazine, vol. 48, no. 7, pp. 32–39, Jul. 2010.

^{2}ITUT, “Recommendation G.709/Y.1331 (02/2012). Interfaces for the optical transport network,” Feb. 2012.

^{3}ITUT, “Recommendation G.872 (2001). Architecture of optical transport networks,” 2012.

^{4}E. Ip and J. Kahn, “Fiber impairment compensation using coherent detection and digital signal processing,” IEEE Journal of Lightwave Technology, Journal, vol. 28, no. 4, pp. 502–519, Feb. 2010.

^{5}B. Pillai, B. Sedighi, K. Guan, N. Anthapadmanabhan, W. Shieh, K. Hinton, and R. Tucker, “Endtoend energy modeling and analysis of longhaul coherent transmission systems,” IEEE Journal of Lightwave Technology, Journal, vol. 32, no. 18, pp. 3093–3111, September 2014.

^{6}B. J. SoléPareta, S. Subramanianm, D. Careglio, and S. Spadaro, “CrossLayer Approaches for Planning and Operating Optical ImpairmentAware Optical Networks,” Proceedings of the IEEE, vol. 100, no. 5, p. 12, 2012.

^{7}M. Cousineau, P. Perron, C. G., M. Paiva, and M. Segatto, “RWA problem with geodesics in realistic OTN topologies,” Optical Switching and Networking, vol. 15, no. 0, pp. 18–28, 2015.

^{8}ITUT, “Recommendation G.694.1 (02/2012). Spectral Grids for WDM Applications: DWDM Frequency Grid,” 2012.

^{9}E. Lach and W. Idler, “Modulation formats for 100G and beyond,” Optical Fiber Technology, vol. 17, no. 5, pp. 377–386, Oct. 2011.

^{10}J. M. Simmons, “Network design in realistic ”AllOptical” backbone networks,” IEEE Communications Magazine, vol. 44, no. 11, pp. 88–94, November 2006.

^{11}G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. Academic Press, 2007.

^{12}D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the ManakovPMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” IEEE Journalof Lightwave Technology, vol. 15, no. 9, pp. 1735–1746, 1997.

^{13}D. Wang and C. Menyuk, “Calculation of penalties due to polarization effects in a longhaul WDM system using a stokes parameter model,” IEEE Journal of Lightwave Technology, vol. 19, no. 4, pp. 487–494, Apr. 2001.

^{14}M. Karlsson and H. Sunnerud, “Effects of nonlinearities on PMDinduced system impairments,” IEEE Journal of Lightwave Technology, no. 11, pp. 4127–4137.

^{15}Y.H. Wang and I. Lyubomirsky, “Impact of DPQPSK pulse shape in nonlinear 100 G transmission,” IEEE Journal of Lightwave Technology, Journal, vol. 28, no. 18, pp. 2750–2756, 2010.

^{16}A. Bononi and P. Serena, “Which is the dominant nonlinearity in longhaul PDMQPSK coherent transmissions?” in 36th ECOC, no. 0, 2010, pp. 19–21. [Online]. Available: http://ieeexplore.ieee.org/xpls/absall.jsp?arnumber=5621217
» http://ieeexplore.ieee.org/xpls/absall.jsp?arnumber=5621217 
^{17}F. O. Lima, “Strategies for optical transport network planning,” PhD, Federal University of Espírito Santo, 2015, in portuguese.

^{18}S. Azodolmolky, M. Klinkowski, E. Marin, D. Careglio, J. Pareta, and I. Tomkos, “A survey on physical layer impairments aware routing and wavelength assignment algorithms in optical networks,” Computer Networks, vol. 53, no. 7, pp. 926–944, 2009.

^{19}O. Sinkin, R. Holzlöhner, J. Zweck, and C. Menyuk, “Optimization of the splitstep Fourier method in modeling opticalfiber communications systems,” Journal of Lightwave Technology, vol. 21, no. 1, p. 61, 2003. [Online]. Available: http://www.opticsinfobase.org/abstract.cfm?id=71748
» http://www.opticsinfobase.org/abstract.cfm?id=71748 
^{20}R. Bhandari, Survivable Networks: Algorithms for Diverse Routing, ser. The Springer International Series in Engineering and Computer Science. Springer, 1999. [Online]. Available: https://books.google.com.br/books?id=SIkfR0lAN1wC
» https://books.google.com.br/books?id=SIkfR0lAN1wC 
^{21}H. Zang, J. P. Jue, and B. Mukherjee, “A review of routing and wavelength assignment approaches for wavelengthrouted optical wdm networks,” Optical Networks Magazine, vol. 1, no. 1, pp. 47–60, 2000.

^{22}I. Kaminow, T. Li, and A. Willner, Optical Fiber Telecommunications Volume VIB: Systems and Networks, ser. Optics and Photonics. Burlington, MA: Elsevier Science, 2013.

^{23}G. Li, “Recent advances in coherent optical communication,” Advances in Optics and Photonics, vol. 1, no. 2, p. 279, Feb. 2009.

^{24}S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 16, no. 5, pp. 1164–1179, Sep. 2010.

^{25}D. Godard, “Selfrecovering equalization and carrier tracking in twodimensional data communication systems,” IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867–1875, 1980.

^{26}L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization demultiplexing in optical coherent receivers,” Optical Fiber Communication Conference and National Fiber Optic Engineers Conference, no. 2, p. OMT2, 2009.

^{27}A. Viterbi, “Nonlinear estimation of pskmodulated carrier phase with application to burst digital transmission,” IEEE Transactions on Information Theory, vol. IT29, no. 4, 1983.

^{28}J. W. Suurballe and R. E. Tarjan, “A quick method for finding shortest pairs of disjoint paths,” Networks, vol. 14, no. 2, pp. 325–336, 1984.

^{29}F. Zhang, Y. Luo, Y. Wang, and L. Li, “Experimental comparison of different BER estimation methods for coherent optical QPSK transmission systems,” IEEE Photonics Technology Letters, vol. 23, no. 18, pp. 1343–1345, 2011.

^{30}M. Mussolin, M. Forzati, J. Martensson, A. Carena, and G. Bosco, “DSPbased compensation of nonlinear impairments in 100 Gb/s polmuxQPSK,” in Transparent Optical Networks (ICTON), 2010 12th International Conference on. IEEE, 2010, pp. 1–4.

^{31}P. Serena. Optilux: Matlab/octave toolbox to simulate optical communication systems. [Online]. Available: www.optilux.sourceforge.net.
» www.optilux.sourceforge.net 
^{32}M. Nölle, J. Fischer, L. Molle, C. SchmidtLanghorst, D. Peckham, and C. Schubert, “Comparison of 8 x 112 Gb/s PSQPSK and PDMQPSK signals over transoceanic distances,” Optics Express, vol. 19, no. 24, Nov. 2011.

^{33}K. Balemarthy, “LongHaul Optical Fiber Networks: 100 Gbps and Beyond,” International Conference on Fiber Optics and Photonics, pp. 13–15, 2012.

^{34}G. Tzimpragos, C. Kachris, I. Djordjevic, M. Cvijetic, D. Soudris, and I. Tomkos, “A Survey on FEC Codes for 100G and Beyond Optical Networks,” IEEE Communications Surveys & Tutorials, 2014.
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Mar 2016