Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

(1)

Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

Campus Monterrey

School of Engineering and Sciences

Nonlinear equalizer for Coherent OFDM Optical Systems

A dissertation presented by

Jos´e Antonio Torres Zugaide

Submitted to the

School of Engineering and Sciences

in partial fulfillment of the requirements for the degree of Doctor of Philosophy

in

Information and Communication Technologies Major in Optical Communications

Monterrey, Nuevo Le´on, June 15^th, 2020

(2)

Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

Campus Monterrey

School of Engineering and Sciences

The committee members, hereby, certify that have read the dissertation presented by Jos´e An- tonio Torres Zugaide and that it is fully adequate in scope and quality as a partial requirement for the degree of Doctor of Science in Information and Communication Technologies, with major in Optical Communications.

Dr. Gerardo Antonio Castañón Avila Tecnológico de Monterrey School of Engineering and Sciences Principal Advisor

Dr. Gabriel Campuzano Trevi˜no Tecnol´ogico de Monterrey School of Engineering and Sciences Committee Member

Dr. Cesar Vargas Rosales Tecnol´ogico de Monterrey School of Engineering and Sciences Committee Member

Dr. Alejandro Arag´on Zavala Tecnol´ogico de Monterrey School of Engineering and Sciences Committee Member

Dr. Joaqu´ın Beas Bujanos Qualcomm Technologies Incorporated Committee Member

Dr. Rubén Morales Menéndez, Dean of Graduate Studies School of Engineering and Sciences Monterrey, Nuevo León, June 15^th, 2020

i

(3)

Declaration of Authorship

I, Jos´e Antonio Torres Zugaide, declare that this thesis titled, ”Nonlinear equalizer for Coher- ent OFDM Optical Systems” and the work presented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for a research degree at this University.

• Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.

• Where I have consulted the published work of others, this is always clearly attributed.

• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this dissertation is entirely my own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Jos´e Antonio Torres Zugaide Monterrey, Nuevo Le´on, June 15^th, 2020

ii

(4)

Dedication

I dedicate this dissertation to my father Jos´e Santos† who inspired and motivated to initiate this journey, my mother Palmira who encouraged me to pursue my dreams and finish my dissertation, my sisters Andrea and Rosa, and brother Jos´e Luis for all your unconditional confidence, support, patience, and encouragement.

iii

(5)

Acknowledgements

I would like to express my sincere gratitude to my advisor Dr. Gerardo Antonio Casta˜n´on for the continuous support of my PhD study research.

Besides my advisor, I would like to thank Dr. Ivan Aldaya for his patience and immense knowledge who help me in the research.

My sincere thanks also goes to Dr. Joaquin Beas and Dr. Gabriel Campuzano for the time they gave me, their talks, and guidance.

Thanks to my friends Zorel, Azucena, Susy and Humberto for the sleepiness nights and all the fun we had during the last four years.

I would like to thank my family: my mother Palmira, my sister Andrea and Rosa, my brother Jos´e Luis for all your support.

Finally, Jos´e Torres-Zugaide acknowledges support from CONACyT for a PhD grand and Tecnol´ogico de Monterrey support on tuition.

iv

(6)

Nonlinear equalizer for Coherent OFDM Optical Systems by

Jos´e Antonio Torres Zugaide Abstract

Given the exponential increase of data rates demand in the recent years, optical communications offers an attractive solution due to several advantages when compared with wireless communications, some of them are unlimited bandwidth and low losses for long distances communications, due to those advantages optical networks have become a natural choice for supporting ever-increasing broadband services for future high-speed networks like 5G and 6G networks.

This document consists of six chapters covering various topics related to optical communication networks including characteristics, challenges, and novel algorithms permitting to improve the optical network performance.

As a start, an introduction for a general perspective of the dissertation is presented in chapter I and the definition of different concepts of optical networks are presented in Chap- ter II, in this chapter the concept of passive optical network (PON), Orthogonal frequency multiplexing (OFDM) and other concepts that are important to understand are described.

In Chapter III, the concept of elastic optical network is defined and the problem of routing and spectrum allocation (RSA) in elastic optical networks is defined, in this chapter an exhaustive review of the state of the art to solve the RSA problem is presented with a summary of key parameters that need to be taken into account for optical networks under different topology.

An innovative method to mitigate the optical nonlinearities of long haul coherent optical networks is presented in Chapter IV. The presented method is an improvement in the state of the art, the method uses the Hammerstein model to describe mathematically the optical fiber link and by using an equalizer inspired by the inverse Hammerstein model it is possible to improve the optical reach distance in long haul coherent OFDM access networks.

An invention to monitor the optical communications links and detect failures is presented in chapter V, the subject of the presented invention is an improvement of optical amplifiers used in the radio over glass systems (RoG) systems and it is applied to CATV networks.

Finally, chapter VI presents general conclusions and future work.

v

(7)

List of Figures

2.1 A block diagram of an OFDM transmitter. . . 4

2.2 Cyclic prefix description. . . 4

2.3 Architectures of time division multiplexed PON where OLP = Optical line transmitter, ONU = Optical network unit, ODN = optical distribution network. 5 2.4 Architectures of time division multiplexed PON where OLP = Optical line transmitter, ONU = Optical network unit, ODN = optical distribution network. 6 2.5 Coherent optical system block diagram. . . 9

3.1 Comparison of WDM and EON spectrum signals. . . 12

3.2 Example of EON with four nodes [48] . . . 13

3.3 Spectrum assignment in EON [48] . . . 15

3.4 Optical grooming in an elastic optical network. . . 18

3.5 Multi-core fibers and core switching. . . 20

4.1 Inverse Hammerstein-based nonlinear equalizer (IH-NLE) . . . 29

4.2 Block diagram for the optimization of the proposed NLE. . . 30

4.3 Comparison of the computational complexity between DBP-NLE and the proposed IH-NLE in terms of the number of FLOPs to 32 subcarriers and different values of Ko. . . 31

4.4 (a) Scheme of long reach PON system, (b) Architecture of the OLT, where: DAC=digital to analog converter, CP= cyclic prefix, STP= serial to parallel. (c) Architecture of the ONU, where: ADC = analog to digital converter, DDC = digital to digital converter. . . 32

4.5 OFDM signals at 10 Gbps with 9 dBm LOP after 130 km of total link distance for different values of Ko in frequency domain. . . 32

4.6 Optimum φ1 and φ2 for different link lengths and overall average launched optical power (LOP): (a)-(d) Magnitude of φ₁and φ₂as a function of the LOP for 10 Gbps. (e)-(h) Magnitude of φ1 and φ2 as a function of the LOP for 40 Gbps. . . 33

4.7 System performance for 10 Gbps with L₁ = 120 km and L₂ = 20 km considering different Ko values. (a) BER curves and (b) Constellations at optimum LOP. . . 34

4.8 System performance for 40 Gbps with L₁ = 100 km and L₂ = 20 km considering different Ko values. (a) BER curves and (b) Constellations at optimum LOP. . . 34

vi

(8)

4.9 Resume of the LOP with minimum BER of LE and NLE for different values of Ko (a) 10 Gbps and (b) 40 Gbps and comparison of link range of LE and

NLE for different values of Ko(c) 10 Gbps and (d) 40 Gbps. . . 35

5.1 Active Ethernet – POINT TO POINT (P2P)[94].. . . 38

5.2 Diagram for single transmitter on RFoG scheme . . . 39

5.3 Basic EDFA configuration. . . 39

5.4 Description of the system with fault detection, NI: Network interface, SMF: single mode fiber, ONU: optical network unit. . . 41

5.5 Simplest way to generate intensity-modulated optical signal. . . 41

5.6 Main circuits for CATV analog optical transmitter with low frequency tone added. . . 42

5.7 General block diagram for EDFA system used in mayor CATV nodes. . . 42

5.8 Description of EDFA modification with the proposed new elements to estimate the condition of the fiber. . . 43

5.9 Remote PHY technology. . . 44

5.10 Remote transmitter with failure detection method technology. . . 44

5.11 Analog Transmitter with failure detection improvement. . . 45

5.12 Experiment setup. . . 45

5.13 Measured BsOP as function of the link distance. . . 46

5.14 Scenario to verify a fault detection. . . 46

5.15 Experiment of a fault for a link of 17.5 km and fault located a 5 km. . . 47

6.1 Qualitative comparison of the developed (1) chip-based self-CO-OFDM system with (2) SBS processed on a fiber, and (3) a state-of-the-art carrier- suppressed CO-OFDM. Image taken from [36]. . . 49

vii

(9)

List of Tables

3.1 Key performance metrics and key characteristics to solve RSA problem . . . 16 3.2 Summary of main algorithms to solve RSA in EON with static traffic: (a)

Heuristics and (b) Meta-heuristics . . . 22 3.3 Dynamic RSA algorithms In EON . . . 23

viii

(10)

Chapter 1 Introduction

The concept of elastic bandwidth allocation in optical networks has been recently proposed in place of the traditional ITU-T fixed frequency grid. The scheme of Elastic Optical Net- works (EON) increases spectral efficiency by assigning variable spectral resources to satisfy bandwidth demands. Thus, the problem of Routing and Wavelength Assignment (RWA) in fixed optical networks has to be reformulated into the problem of Routing and Spectrum Al- location (RSA) in EON. The RSA problem combines both the routing decision for all the node pairs traffic demands and the sub-carrier allocation to satisfy the corresponding request transmission. In chapter 3 is presented a comprehensive survey of algorithms and optimization models that were proposed to solve the problem of RSA, in order to identify the main research opportunities areas there were highlighted the principal figures of merit to be considered to minimize the utilized spectrum, energy consumption, spectrum fragmentation, and blocking probability.

Considering the high-speed demand driven by bandwidth-consuming applications, such as video streaming and cloud computing, is exceeding available network capacity and operators are forced to implement innovative technologies to increase the throughput offered to the end-user. In particular, passive optical networks (PONs) with a full-duplex capacity of 10 Gbps over a 40-km span are expected to be developed shortly. However, the range of such systems is severely penalized due to fiber and splitter losses. In order to increase the transmission distance of PONs, coherent optical (CO) communications have regained attention. Orthog- onal frequency division multiplexing (OFDM) has been proposed as modulation format due to its robustness to chromatic dispersion, its high spectral efficiency, and its flexibility. The high peak-to-average ratio of OFDM signals makes them, however, very vulnerable to fiber nonlinear distortion. In chapter 4 is proposed a novel low-complexity equalizer based on the inverse Hammerstein model to partially compensate nonlinear distortion in CO-OFDM PON.

Numerical simulations using the split-step Fourier transform method reveal a potential link increase of 20 and 5 km for bitrates of 10 and 40 Gbps, respectively, when compared with linear equalization.

Finally, because of the explosive demand for broadband applications (video-streaming, cloud applications, internet of things, etc. [27]), cable networks operators are forced to increase their transmission bit-rates offered for end-users; one of the solutions that meet those user requirements is Radio Frequency over Glass (RFoG) which the coax portion of the hybrid fiber coax (HFC) network is replaced by a single-fiber passive optical network (PON)

1

(13)

CHAPTER 1. INTRODUCTION 2

[94]. RFoG allows network operators to continue to leverage traditions HFC equipment with the new FTTH deployments. By using a RFoG scheme, extensive deployments are expected in the near future, due to that, it is important to implement network solutions to detect network failures instantly. In chapter 5 describes a low-cost method that takes advantage of high optical power used in optical amplifiers or high-power transmitters in distributed access architecture (DAA) to estimate the distance of the optical link where failure occurs. This method monitors the Backscattering Optical Power (BsOP) and performs digital processing to estimate the parameters that describe the optical link. The implantation of the proposed scheme in the physical layer will allow network operators to be more resilient and perform preventive actions to mitigate attenuation’s in the optical link or recover the functionality of the networks in case of failure rapidly by fixing the fault in less time.

(14)

Chapter 2 General Background and Basic concepts

2.1 Orthogonal Frequency Division Multiplexing

Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation format and the prevalent technology deployed in wireless communications because it provides robustness against frequency selective fading and narrowband interference, and is efficient mit- igating the multi-path delay spread [41]. OFDM divides the available spectrum into many carriers, each one being modulated by low rate data streams which are utilized in parallel transmission.

2.1.1 OFDM transmitter

The OFDM modulated signal can be represented by

S_n(t) =

N −1

X

k=0

S_n,ke^{j2π∆f t}, 0 ≤ t ≤ T_s (2.1)

where {Sn,k}^{N −1}_k=0 are the complex symbols to be transmitted at the nth OFDM block, T_s, ∆f, and N are the symbol duration, the sub-channel space, and the number of sub- channels of OFDM signals, respectively. The sampled version of the base-band OFDM signal s (t) of Eq.2.1can be represented as

s_n

mT_s

N

=

N −1

X

k=0

S_n,ke^j2π^N ^mk (2.2)

as it is observed, Eq. 2.2 is the representation of the inverse discrete Fourier transform (IDFT) of the transmitted symbols {S_n,k}^{N −1}_k=0 and can be efficiently calculated at the receiver side by the fast Fourier transform (FFT). Using this basic principle, the block diagram of the OFDM modulator is described in Fig. 2.1, where the steps that are necessary to obtain the OFDM signal are described.

3

(15)

CHAPTER 2. GENERAL BACKGROUND AND BASIC CONCEPTS 4

Figure 2.1: A block diagram of an OFDM transmitter.

2.1.2 Ciclic Prefix

In order to mitigate the inter block interference (IBI) that is caused by delay spread and the inter carrier and inter-carrier interference (ICI) introduced by transmission channel distortion, a cyclic prefix (CP) is inserted, this guard interval is critical for OFDM signals, as it is observed in Fig. 2.2 the CP is usually inserted between adjacent OFDM blocks, without the CP, the length of the OFDM symbol is T s, as it was mentioned Eq.2.1. With the CP, the transmitted signal is extended to T = T_g+ T_sand can be expressed as

˜ sn

mT_s

N

=

N −1

X

k=0

Sn,ke^j2πmk^N , −Tg ≤ t ≤ Ts (2.3)

Figure 2.2: Cyclic prefix description.

2.2 Passive Optical Networks (PONs)

Passive optical networks (PONs) have the advantages of almost unlimited bandwidth, low cost, flexibility, and scalability. Given those advantages PONs are the natural option to be considered the best solution to support the increasing demands in broadband services for access networks and the primary option to support future high speed networks like 5G [64].

For PON, the two basic schemes where more complex systems are derived are time-division multiplexing (TDM)-PON and wavelength division multiplexing PON (WDM-PON) [142].

The general description for both schemes is in the following subsections.

(16)

2.2.1 Time Division Multiplexed Passive Optical Networks (TDM-PON)

TDM-PON were developed for fiber to the home (FTTH) in the late 1980s [103] and from that time virtually all commercially deployed PONs have been of the TDM-PON variety, those networks are highly cost-effective and have easily met capacity demands. The general architecture of TDM-PONs system is shown in Fig.2.3.The system consist in broadcasting all the signal upstream from the optical line transmitter to the optical network units (ONUs) in specific time slots. Those time slots are controlled by the OLT. In the optical distribution network (ODN) a splitter is used to share the signal to all ONUs. The upstream transmission of TDM-PON is in burst mode, which means every burst is generated by a different optical network unit (ONU) so that each burst experiences a different optical path and contains a different degree of chromatic dispersion (CD) or nonlinearity.

Figure 2.3: Architectures of time division multiplexed PON where OLP = Optical line transmitter, ONU = Optical network unit, ODN = optical distribution network.

2.2.2 Wavelength Division Multiplexed PON (WDM-PON)

In order to increase the transmission capacity of TDM-PON, the WDM-PON architecture provides a solution by adding multiple wavelengths (λ₁,λ₂,..,λ_n), this scheme was proposed for future PONs and most of the research of future networks is focus on this technology [31]. As it is described in Fig. 2.4 for the distributing network, the splitter is replaced by demultiplexer (arrayed waveguide grating), which demultiplex the optical signals according to wavelength and send them to the corresponding ONU in downstream transmission.

The optical transceiver of the OLT section in a WDM-PON system has different wavelength channels to receive and transmit optical signals separately. In this system, the ONU section communicates with the OLT using different wavelengths in upstream transmission.

(17)

Figure 2.4: Architectures of time division multiplexed PON where OLP = Optical line transmitter, ONU = Optical network unit, ODN = optical distribution network.

2.3 Optical Channel Impairments

In order to understand the advantage of the different optical architectures, it is important to assimilate first the different optical fiber impairments that could be excited by using those schemes since increasing the speeds and optical powers of signals in optical fiber will increase fiber nonlinear effects, below it is a summary of the main induced distortions that affect optical WDM communication networks.

2.3.1 Chromatic Dispersion

One of the main studied and well know critical phenomena of the optical fiber systems is the Chromatic dispersion (CD). The CD parameter D is expressed in units of ps/(km-nm) and is caused by a variation of the group velocity v_g in fiber as a function of optical frequency as it is described below

D (λ) = ∂

∂λ

1 v_g

, (2.4)

D (λ) = −2πc

λ² β2, (2.5)

where c is the speed of light in a vacuum, λ is the wavelength, and β2 is know as the group velocity dispersion (GVD) [3]. For chromatic dispersion of standard SMF-28 fiber at 1550 nm the CD parameter is approximately 17 ps/(km-nm) and exhibit zero CD at 1300 nm wavelength region. When an intensity-modulated transmitter with high laser chirp (change in optical frequency vs. modulation) is exposed to dispersive media, the incidental frequency modulation is converted to intensity modulation, which mixes with the original intensity modulation and leads to the generation of intermodulation distortion with 2nd order distortion being the most harmful. The impact of dispersion is greatly reduced if the transmitter has a very low chirp. Additionally, the effects can be removed through the use of electronic delay

(18)

circuit compensation or dispersion compensating fiber (DCF) with equivalent and opposite dispersion characteristics [68].

2.3.2 Four Wave Mixing

Four-wave mixing (FWM) is a 3rd order non-linearity, comparable to the Composite triple beat distortion (CTB) inter-modulation effect exhibited in electrical systems, due to the power sensitive refractive index of optical fiber. If three optical fields with carrier frequencies ω1, ω2

and ω₃ co-propagate inside the fiber simultaneously, the third order nonlinear susceptibility generates a four field whose frequency ω4is relatively to other frequencies by a relation ω4 = ω₁ ± ω₂ ± ω₃ which in turn generates crosstalk at those channels [3]. Four-wave mixing is most troublesome in systems that launch at high powers and utilize a large number of densely packed wavelengths in low dispersion environments.

2.3.3 Stimulated Brillouin Scattering

Stimulated Brillouin Scattering (SBS) is a nonlinear interaction between laser light and the molecular structure of the fiber which generates acoustic waves causing a variation in the index of refraction corresponding to the intensity of the wave. This causes partial scattering of the light in the backward direction from the resultant index diffraction gratings [3]. This can produce an avalanche effect if the intensity of the light is high enough, resulting in high attenuation and induced noise in the forward direction. This acts as a limiting factor as to how much power can be launched into fiber for single wavelength transport.

The frequency of the reflected beam is slightly lower than that of the incident beam;

the frequency difference v_B corresponds to the frequency of emitted phonons. This so-called Brillouin frequency shift is set by a phase-matching requirement. For pure backward Brillouin scattering, the Brillouin shift can be calculated as it is described in Eq. 2.6

v_B = 2¯nv_A

λp , (2.6)

where ˜n is the refractive index,v_a the acoustic velocity, and λ_p the vacuum wavelength [3]. Since the bandwidth in which this scattering process can take place is very narrow, the threshold power needed to initiate this effect can be raised significantly by widening the optical linewidth of the source. This can be accomplished through various methods of dithering the laser, either directly or indirectly, causing a spread in the optical spectrum beyond that of the Brillouin bandwidth (tens of MHz depending on the fiber characteristics). Since this linewidth spread can result in performance degradation when operating in the highly dispersive 1550 nm region of standard fiber, most externally modulated transmitters use some method of phase modulation using single or multiple high frequency tones to effectively breakup the optical signal into a number of separate carriers, each at a reduced level from the original spectra in which case the highest of these individual modes sets the SBS threshold.

Taking advantage of the mitigation techniques described above and with other more significant effects highly contingent on wavelength parameters, SBS would not be a major factor in determining optimal multi-wavelength schemes.

(19)

2.3.4 Stimulated Raman Crosstalk

Stimulated Raman Scattering (SRS) is a nonlinear parametric interaction between laser photons and the molecular structure of the fiber which causes partial inelastic scattering of the light signal due to excitation. The scattered light is shifted downward in frequency (upward in wavelength), corresponding to the molecular vibration frequency, which results in energy transfer between the original wavelength and the generated scattered wavelengths. If additional wavelengths are within the range of the newly generated scattered photons, crosstalk will occur. The triangular shape of the Raman gain (excitation) profile peaks at a wavelength spacing of approx. 100 nm so while the magnitude of the Raman coefficient is much smaller than that of the Brillouin coefficient, it’s bandwidth of influence is much wider. Since the ITU grid DWDM wavelengths are usually spaced 100 or 200 GHz apart (approximately 0.8 and 1.6 nm respectively at 1550 nm), it’s a major source of crosstalk in a multiwavelength system.

The threshold power Pth is defined an the incident power at which half of the pump power is transferred to the stokes field at the output end of the fiber length L. It is estimated from [101]

P_th ≈ 16A_{ef f}

g_RL_{ef f} (2.7)

were g_Ris the peak value of the Raman gain, L_{ef f} is the effective interaction length and A_{ef f} is the optical fiber effective core area.

2.3.5 Self-Phase Modulation

When the light interacts with the matter a phenomena a nonlinear phase modulation is self- induced called self-phase modulation (SFM) witch is produced when the pulse light travels in a medium and the light pulse will induce a varying refractive index of the medium due to the optical Kerr effect [3]. This variation in refractive index will produce a phase shift in the pulse as it is described in Eq. 2.8 and as result the frequency spectrum of the light pulse is changed.

φ_{N L} = γP_inL_{ef f} (2.8)

where γ = 2π/ (A_{ef f}λ) is the nonlinear Kerr parameter and L_{ef f} is the effective interaction length.

2.3.6 Crossphase Modulation

Cross-Phase modulation crosstalk is due to the non-linear index of refraction of fiber. The modulation power from one channel causes a small change in the index of refraction which results in a phase modulation of each channel traveling through the fiber. Chromatic dispersion due to the fiber then converts the phase modulation into an amplitude modulation.

Cross-phase modulation tends to increase as the spacing between wavelengths decreases and the distance traveled increases. The phase shift for the jthchannel becomes [3]

(20)

φ^j_{N L} = γL_{ef f} P_j + 2X

m6=j

P_m

!

(2.9) where the sum extends over the number of channels, γ is the nonlinear Kerr parameter and Lef f is the effective interaction length.

2.4 Optical Coherent System

Coherent optical transmission is a technique that uses modulation of the amplitude and phase of the light, as well as transmission across two polarization’s, it allow us to increase the transported information through a fiber optic cable. Fig.2.5describes the main elements that integrates a coherent optical communication system with single polarization.

Figure 2.5: Coherent optical system block diagram.

Using coherent communications bring some advantages over legacy intensity modulated direct detection systems, some of them are described below:

– Better sensitivity, as it is observed in Fig.2.5the receiver include a local oscillator and by increasing the power of the LO laser in coherent optical receivers, receiver sensitivity approaches the shot noise limit [60].

– Signal Processing, considering the multiple optical signal degradation due to the linear an nonlinearities of the optical fiber, using coherent system, when the signal is received the linear and nonlinearities could be equalized and by digital processing [133].

– Multi Level Modulation, as it is observed in Fig.2.5, the coherent system uses external modulation performed by Mach-Zehnder modulator, it allows to use multi level modulation and improving the transmission bitrate.

– Better Selectivity of Channel, for coherent system, the transmitted signal should have the same central wavelength than the receiver local oscillator, due to that, for a WDM system, it is possible to tune the desired central wavelength that allow us to change the optical channel at the receiver side without the need of optical filters [131].

(21)

2.5 Conclusion

In this chapter, there was introduced the main concepts of optical networks that serve as a preamble and introduction of the following chapters.

(22)

Chapter 3 Routing and Spectrum Allocation in E.O.N.

3.1 Introduction

Optical Transport Network (OTN) are constantly being expanded and improved to meet the exponential traffic growth, principally associated with multimedia transmission services such as video streaming, cloud computing, VoIP, etc [105,21]. Whereupon, it is expected that the transmission capacity of OTN will increase at the growth rate of about 1.4 to 1.5 times a year [71].

The current Wavelength Division Multiplexing (WDM) systems follow the traditional 50 GHz International Telecommunication Union (ITU) recommendations, that divides the C-band (1530-1565 nm) into fixed 50GHz or 100GHz spectrum slots [43]. Although current WDM architectures offer advantages of reconfigurable wavelength switching, nowadays WDM systems with up to 40 Gb/s to 400 Gb/s capacity per channel have been deployed in backbone networks [132], and recent investigations in optical communication systems show that by the introduction of advanced modulation formats and digital communications techniques it is also possible to route optical transparent networks, and it is possible to achieve transmissions capacities of up to 400 Gb/s to 1T b/s per channel [49, 108], nevertheless, the fixed grid does not support bit rates of 400 Gb/s and 1 Tb/s at standard modulation formats, as they overlap with at least one 50 GHz grid boundary [33]. In addition to this, if sufficiently broad spectrum is available, high data rate signals become increasingly difficult to transmit over long distances at high spectral efficiency, then WDM systems leads to low optical spectrum utilization.

Given the mentioned disadvantages of WDM systems, it is important to develop new schemes which would allow us to make an efficient use of optical communication networks.

Approaches such as optical packet switching (OPS) and optical burst switching (OBS) have been proposed in the literature [137], nevertheless, these approaches can be viewed as long- term solutions since their enabling technologies are not yet mature [17].

In 2009 a novel spectrum efficient and scalable OTN architecture was proposed called spectrum sliced elastic optical path network (SLICE) [49, 47, 48]. This technology ensures high spectrum efficiency and scalability for future OTN using flexible rate optical transceivers based on Optical Orthogonal Frequency Division Multiplexing (O-OFDM) and Bandwidth

11

(23)

CHAPTER 3. ROUTING AND SPECTRUM ALLOCATION IN E.O.N. 12

AmplitudeAmplitude

Frequency

Frequency O-OFDM Network

WDM Network

Saved Spectrum

50 GHz 50 GHz

Figure 3.1: Comparison of WDM and EON spectrum signals.

Variable Wavelength Cross-connects (BV-WXCs). O-OFDM is a multi-carrier transmission technology that transmits a high speed data stream by splitting it into multiple parallel low speed data channels or slots (e.g., 6.25 GHz or 12.5 GHz) [44], optical connections can be allocated into a variable number of these slots and thus can provide fine granularity capacity to connections by the elastic allocation of sub-carriers according to the service demands [138]

as shown in fig. 3.1.

The scheme of Elastic OFDM-based Optical Networks (EON) increases spectral efficiency by assigning variable spectral resources to satisfy the spectrum demands [56]. Thus, EON have, in principle, several advantages over conventional rigid optical networks: They offers a new mechanism for fractional bandwidth connectivity service using sub-wavelength accommodation; enable the creation of a super-wavelength optical path contiguously combined in the optical domain, thus ensuring high utilization of spectral resources; enables spectrally efficient direct accommodation of mixed data bit rates in the optical domain because of the flexible assignment of spectrum [98]. However, the concept of EON poses new challenges at the networking level, since the architecture allows elastic bandwidth variation of an optical path, the problem of Routing and Wavelength Assignment (RWA) in fixed optical networks has to be reformulated to the problem of Routing and Spectrum Allocation (RSA) in EON.

Therefore, a new network controls and management schemes have to be explored [18].

Anther concept similar to EON is the Flexi-grid Optical Networks (FON), until boot concepts have similar principles the main difference is that FON means that the grid spacing can be flexible, i.e. not limited to 50GHz, but despite this, guard band is necessary between each channel to avoid any interference or cross talk [90].

The RWA problem is NP-complete, correspondingly, the optimization version of the RSA problem which jointly optimizes the RSA is NP-hard [123]. Given the difficulty of the problem, most of the solutions found in the literature use heuristics algorithms and compare

(24)

Client node

BV Transponder

BV-WXC

Fiber

Figure 3.2: Example of EON with four nodes [48]

the results with the Integer Linear Programing (ILP) method. Moreover, as SLICE scheme involve the adoption of new different technologies with different new advantages, the solution of the problem of RSA has been handled using different points of view highlighting some particular characteristic that this new technology offers such as: energy consumption [91], spectrum efficient [55, 45], span restoration [124], spectrum fragmentation [83], spectral de-fragmentation [97], level modulation [44], optical grooming [139, 138], re-generator placement [51], etc. Due to those aspects, to achieve the required intelligence for efficiently managing such networks it is necessary the introduction of an optical control plane for pro- viding intelligent mechanisms to dynamically provision switched connections with quality of service (QoS) [13,69,15].

In this chapter we present a comprehensive classification of the main heuristics applied to the RSA problem, highlighting the main research opportunity areas. The remainder of the document is organized as follows: Section3.2describes in a general way the main elements of an EON; Section3.3presents a description of the principal characteristics of the EON that must be taken into account to solve the RSA problem; sections3.4 and3.5present the most common heuristic found in the literature to solve the static and dynamic problems, respectively; section3.6describes the research opportunities related to the problem of RSA in EON.

Finally, section3.7summarizes and provides a thorough overview of the work.

3.2 Elastic Optical Network Technologies

The concept of EON is integrated by the following key enabling technologies: Bandwidth Variable Transponders (BV-T) at the network edge, BV-WXCs in the network core, and the O-OFDM as a highly spectrally efficient bandwidth variable modulation format. Thus, as is presented in the example of figure3.2, the BV-T generates an optical signal using O-OFDM that uses just enough spectral resources to transmit the bitrate demanded by the users. At the same time, every WXC on the route of the optical path, allocates a cross-connection with the corresponding spectrum-bandwidth to create an appropriate sized end-to-end optical path, the BV-WXC is integrated by a block of variable bandwidth wavelength selective switches (WSS) that enables wavelength demultiplexing/multiplexing and optical switching functions using integrated spatial optics [23].

(25)

3.2.1 Bandwidth variable transponders

The BV-T is a key element of an EON due to the capacity to change the traffic rate (increasing or decreasing the number of subcarriers), and the ability to change the modulation level according to the channel condition, transmission impairments and bit rate request, all this managed by a control plane [104].

The BV-T is composed of a set of devices with multi-wavelength source (mode lock laser or multiple wavelength sources) of n equally-spaced contiguous sub-carriers according to the required spectrum needs [80]. In a photonic integrated circuits (PIC) each sub-carrier is modulated. An switching matrix enables to insert/drop traffic through to the proper PIC to modulate a subcarrier. The matrix enables each tributary traffic to be selected, groomed and associated with any of the optical connections or light-path. After the PICs, sub-carriers enter in a sliceable aggregator (SA), based on splitters or WSSs. Through proper control settings, the SA can aggregate all the sub-carriers (generated by a single sliceable transponder) toward a single output port, or alternatively, direct each sub-carrier toward different output ports [5].

Software-defined BV-T allow reconfiguring the transmission scheme with a suitable selection of these flexible parameters, for an optimal resource usage in a EON.

3.2.2 Bandwidth variable wavelength cross-connector

The BV-OXC enables to upgrade the optical capacity in agreement with the actual trend of traffic growth, due to the possibility to add, drop and selectively switch high-speed channels, this operations are commanded by the control plane to ensure the required network flexibility [5].

In principle, every add/drop port pair has the flexibility to:

i) Use any wavelength, it means that any wavelength can be added/dropped at any port (colorless); ii) Connect to any direction or degree, it means that any channel added on a port can be directed to any outbound nodal degree, and vice versa (directionless); iii) Utilize any wavelength channel independent of all other channels in use (contentionless) [58].

Such capabilities enable network operators to quickly and flexibly respond to network changes, such as establishing new light-paths or releasing existing light-paths.

3.2.3 OFDM and Elastic Optical Networks

The introduction of Optical Orthogonal Frequency Division Multiplexing (O-OFDM) format brings unique benefits in terms of high spectral efficiency due to the partially overlapping subcarriers, adaptive data rate modification, and the elasticity obtained by changing the number of subcarriers which increases the overall spectral efficiency of the network when compared to the conventional ITU WDM network [48].

The principle of OFDM is to transmit the data through a large number of multiple orthogonal subcarriers, from the signal synthesis perspective, the O-OFDM signal could be generated from two different schemes [95]: i) Electronically the subcarriers are generated in digital domain domain using IFFT (Inverse Fast Fourier Transform). The O-OFDM transmitter is composed of a radio frequency (RF) OFDM transmitter and a RF-to-optical up-converter, while the receiver is composed of an optical-to-RF down-converter, and a RF OFDM receiver

(26)

Frecuency slot example f=193.1Thz

1 2 3 4 5 6 . . . . . . -6 -5 -4 -3 -2 -1

H H H H

H

L L L L L

Assigned slot spectrum range

Figure 3.3: Spectrum assignment in EON [48]

[100]; ii) Optically the signal is generated modulating the individual optical subcarriers and subsequently combining them with an optical coupler. The optical frequency tuning and spectral bandwidth adjustment of the O-OFDM signal are achieved by changing the carrier laser optical frequency, and adjusting the number of subcarriers, respectively [66].

The optical spectrum is discretized in the frequency domain as shown figure3.3and the smallest unit of a spectrum is referred to as a wavelength slot. Thus, the allocated optical spectrum to serve an optical path is defined in terms of the number of consecutive wavelength slots. Between two adjacent optical paths there are two guard bands denoted by L and H, so that the BV-OXC is able to add or drop any of the paths [114,18]. It is important to mention that the amount of spectrum saving in EON depends significantly on network topology, network size, traffic pattern, physical parameters of node and link, and so on. It also depends on the efficiency of the RSA algorithm.

3.3 Key performance metrics and key characteristics of EON to solve the RSA problem

The RSA problem contains both the routing decision for all the node-pairs with non-zero traffic demands, and the sub-carrier allocation to satisfy the corresponding traffic demands, the algorithms have to consider the spectrum continuity (the spectrum frequency remain the same from source to destination) and sub-carrier continuity constraints while assigning a spectrum path to any incoming connection [123]. Moreover, to provide certain QoS, additional to spectrum minimization, others key performance metrics such as the energy consumption and blocking probability need to be considered. On the other hand, as SLICE scheme in- volves the adoption of different new technologies it is important to consider additional key characteristicsinherent of this technology to manage the problem in a efficient way, table3.1 summarizes the principal key performance metrics and the key characteristics found in the literature related to the solution of the RSA problem.

3.3.1 Key performance metrics

In addition to the global spectrum minimization, it is important to measure the following key performance metricsto notice the network performance and provide fast acting mechanisms to deal with different network requirements.

(27)

Table 3.1: Key performance metrics and key characteristics to solve RSA problem

Key performance metrics

Performance metric Ref. Description Year Topology

Energy Consumption

[65] Energy efficiency in FWDM Networks 2011 Any [91] Power consumption of network components 2011 Any [67] Energy efficiency in OTN 2012 Any [115] Energy efficiency analysis OFDM vs WDM 2012 Any [78] Realistic Design for planning OTN 2012 Any [127] Energy-Efficient Survivable Grooming 2017 Any [61] Energy Efficiency in Space Division Multiplexing EONs 2020 Any

Spectrum fragmentation

[86] Defragmentation of FWDM 2011 Any

[106] Make-before-break rerouting 2011 Any [92] Measuring fragmentation using Markov chain 2012 Any [16] Dynamic routing and spectrum (re)allocation 2012 Any [97]Spectral De-fragmentation using auxiliary graph 2013 Any [63]An algorithm based on spectrum-aware is put forward 2016 Any [89]Path-based fragmentation metric 2019 Any

Links Balanced Load

[54] Routing, Mod. level and Spectrum Assignment 2011 Any [121] Routing and spectrum allocation 2011 Any [122] Routing, Mod. Level, and Spectrum Allocation 2012 Any [62] Energy efficient grooming and hybrid crosstalk solution 2020 Any

Key characteristics

Key characteristic Ref. Description Year Topology

Modulation level

[44] Distance-Adaptive Spectrum Resource Allocation 2011 Ring [54] Off-line algorithms for RMLSA 2011 Any [106] Dynamic routing and frequency slot assignment 2011 Any

[40,117] Novel RMLSA algorithms 2012 Any

[14] Control plane using K-shortest paths 2012 Any

[93] Metro Ring Networks 2013 Ring

[143] Nonlinear Impairment-Aware 2015 Any [22] Routing of traffic through multiple hops in virtual topology 2017 Any [135] Resource Allocation in Space-Division Multiplexed EON 2018 Any [72] Crosstalk-Aware Resource Allocation in EON 2020 Any

Optical grooming

[139,140] Bandwidth-variable optical cross-connectors 2012 Any [93] Modulation Level, Optical Metro Ring Networks 2013 Ring [77] Grooming in Optical Metro Ring Networks 2013 Ring [141] Sliceable Bandwidth-Variable Transponder-Enabled EON 2015 Any [30] Dynamic Multipath-Routing in EON 2015 Any [127] Energy-Efficient Survivable Grooming 2017 Any

Multicast traffic

[87] Multicast traffic grooming in FWDM Networks 2012 Any [119] Analysis of Multicast Traffic 2012 Any [39] Resource allocation for all-optical multicasting 2013 Any [12] RSA in EON With Shared Protection 2016 Any [73] Resource allocation for multicasting in EON 2017 Any

(28)

• Energy consumption: It is expected that the transmission capacity of OTN will increase at the growth rate of to about 1.4 to 1.5 times a year, this expansion is a steady growth in the overall energy consumption of the network. Because of this, the energy efficiency issue gains more attention as a design factor for the planning and operation of telecommunication networks [71, 61]. With the introduction of the EON concept important energy savings are obtained when comparing performance with that of conventional fixed grid WDM networks [115, 70]. In general, as shown in Ec. 3.1, the total network power consumption (En) is calculated as the sum of the power consumption of router ports (Er), transponders (Et) and optical amplifiers (Ea) [91]. Then, for the RSA problem in addition to minimize the spectrum, it is important to minimize the power consumption.

E_n = E_r+ E_t+ E_a (3.1)

• Spectral fragmentation: The RSA problem could be handled in two different ways:

i) The first one considers static traffic (planning problem), it is assumed that all the light-path traffic demands are given a priori, and the main objective of the assignment is to minimize the required spectrum resources; ii) The second approach considers time varying traffic (dynamic RSA problem), the frequent set-up and tear down of connections can lead to significant fragmentation of spectral resources and several small spectrum slots in between connections remain unused.

Fragmentation becomes a problem, especially when the incoming connection requests have larger bandwidth than the available contiguous spectrum slots. Given this issues, spectral fragmentation in EON decreases the spectral efficiency and increases the blocking probability. One way to reduce the spectral fragmentation is to reconfigure existing connections with the goal of consolidating the spectrum and to improve the spectrum utilization [86,106]. The problem is that, rerouting usually causes service disruptions that should be avoided or minimized since reallocations are not admissible for certain classes of services. Then, in a dynamic scenario it is important to quantify the fragmentation in elastic optical networks and calculate the blocking probability [92].

• Light paths congestion: Most of the proposed algorithms assigns the light paths in function of pre-calculated shortest paths distances (the number of hops), but the efficiency of this methodology is highly dependent of the network topology, as a result, some links are overloaded and consequently the global number of frequency slots in the frequency spectrum is incremented. Due to this aspect, to assign the light paths (in addition to the distance) it is important to consider the concept of balancing the load potentially minimize the maximum number of sub-carriers on a fiber. With this metric, the light paths are selected in terms of the congestion or a collision metric [54,121,122].

3.3.2 Key characteristics

It is important to take in consideration the following concepts to efficiently solve the RSA problem, the adaptive modulation level is an inherent characteristic of EON, in another hand, optical grooming and multi-cast traffic are characteristics that depend of the traffic pattern request.

(29)

BV-OXC BV-OXC

1 2 3 4 5 6 7

G G

1 2 3 4

G G

5 6 7

G G

Node A

Link A-B

Link B-C

Link B-D Node B

Node D Node C

Figure 3.4: Optical grooming in an elastic optical network.

• Adaptive modulation level: In 2010 the concept of spectrally efficient optical networking with distance adaptive spectral allocation by adjusting the number of modulation levels was introduced [44] and it was proposed to change the modulation format with respect to the current Signal to Noise Ratio (SNR). Hence, for every 3 dB gain in SNR, an additional bit can be added per symbol [9]. The increase of the modulation level reduces the symbol rate while maintaining a fixed bit rate and the minimum necessary spectral resource is adaptively allocated according to the end-to-end physical condition of an optical path. Modulation format and optical filter width are used as parameters to determine the necessary spectral resources to be allocated for an optical path, transmission reaches of 4000, 2000, 1000, 500, 250 and 125 km have been assumed for BPSK, QPSK, 8QAM, 16QAM, 32QAM and 64QAM, respectively [10].

• Optical grooming: The concept of optical grooming was originally introduced for WDM rings, where multiple low-rate connections are groomed onto a high-rate wavelength channel [34]. In EON the concept of optical grooming aggregates and distributes traffic directly at the optical level, and as such, eliminates Optical-Electrical-Optical (OEO) conversions at intermediate nodes, by separately switching different O-OFDM subcarriers originating from the same bandwidth-variable transponder [140, 140]. Using super channels, the guard band between signals transmitted by two different transceivers in adjacent spectrum slices is not needed as long as the whole signal is transmitted and received by the same source/destination nodes.

As shown in Fig. 3.4, when a sub-wavelength optical path needs to be separated from the optical tunnel at an intermediate node, the original optical tunnel is split into multiple optical tunnels. Because non guard band is required, significant transmitter and spectrum savings can be achieved by the optical grooming versus the non-grooming scenario. Finally, it is important to remark that most of the work found in the literature that solve the RSA problem do not consider optical grooming.

• Multicast traffic: The multicast concept has been widely used for WDM networks [24, 50] and is used to support point to multipoint applications, such as, video conferencing,

(30)

digital audio, IP television, distributed simulations, etc. Moreover, it is expected that multicast will play a prominent role on the Internet in the coming years, then, it is important to develop efficient multicast RSA algorithms for EON in order to achieve high spectrum utilization. A request with multicast traffic consists of several connection level links from one node to multiple nodes called multicast tree, and to minimize the maximum number of frequency slots of spectrum it is important to calculate the shortest path tree or the minimal spanning tree to assign a light-path connection, because of this, the problem complexity of RSA in EON is increased [39].

3.3.3 Additional technological improvements for future consideration

The following concepts involve the introduction of additional technologies to the scheme of EON and most of them are under development. Thus, there are a few work-related to those concepts, nevertheless, it is important to have them in mind because those are key tools that improve the spectrum efficiency and, in a general way, give a better method to obtain the solution of the RSA problem.

• Re-generator placement: In a large-scale network, the assumption that each pair of nodes is connected with a direct light-path may not be realistic, as the optical signal of a light-path cannot be transmitted for an unlimited distance (i.e., limited optical reach) before signal regeneration is required [51,46,110].

• Spectrum converters: Are employed to realize the spectrum de-fragmentation and enable on-demand light-path provisioning in flexible bandwidth networks [125]. How- ever, spectrum conversion devices are expensive and introduce some delay in the demands (due to the conversion) that may not be admissible for certain classes of services [84].

• Light-path fragmentation: In a dynamic scenario, if a traffic demand cannot be served because the number of slots requested exceeds the size of any available spectral gap in the candidate paths between the source and destination nodes, it may still be possible to accommodate it by splitting the demand into multiple independent lower data-rate signals, and allocating them into multiple non adjacent spectral gaps, assuming that enough spectral resources exist in any of those candidate paths [83,76].

• Multi-core fibers: In the case of single-core EON, multiple data cannot be transmitted to the next node simultaneously if partial spectra are overlapped. On the other hand, in the case of the multi-core fiber (MCF) in EON, as shown in Fig. 3.5, multiple signals are transmitted in parallel by distributing the data into multiple cores at a time, in space division multiplexing (SDM) over MCF the cores can be switched freely on different links during routing of the network traffic [74]. Therefore, the spectrum continuity constraints of the RSA problem are mitigated when compared to those of a single-core network [32,128].

(31)

Figure 3.5: Multi-core fibers and core switching.

3.4 RSA in EON with Static Traffic: The Planning Problem

In the planning problem it is assumed that a traffic matrix with the requested transmission rates of all connections is provided and the main objective is to serve all the connections while minimizing the utilized spectrum (it is assumed that the network has sufficient capacity to serve all demands), with constraints of the spectrum contiguity and assuming that non spectrum overlapping is allowed between these connections [18].

3.4.1 Formulation of the RSA planning problem

The RSA planning problem can be formally stated as follows, Given:

• An EON represented by a graph G (V, E), being V the set of optical nodes and E the set of fiber links connecting two nodes in V with distance d_sd of each unidirectional link sd ∈ E.

• An ordered set S of frequency slots in each link in E; S = {s₁, s₂, ..., s_n}. A guard band B is required between two spectrum contiguous allocations.

• A demand set D, where each demand is represented by the tuple (s_d, t_d, b_d) where s_d and t_d are the source and the destination nodes respectively, and b_d is the requested bandwidth.

Find: The route over all (s, d) nodes in the EON and the spectrum assignment of every transported demand.

Objective: Minimize the used spectrum (in terms of the maximum number of subcarriers allocated on any fiber).

The ILP of RSA formulation cannot be solved in practical time, therefore, most of the authors present a decomposition method that breaks the ILP formulation into two sub- problems: a demand routing sub-problem and a spectrum allocation sub-problem. Since both sub-problems are solved sequentially, global optimality cannot be guaranteed. Therefore, most of the authors propose heuristics and meta-heuristics where the former are dependent of the RSA problem and the latter are referred to algorithms applied to a diversity of optimization problems. To measure the algorithm efficiency, authors compare them in terms of key performance metrics (e.g. spectrum usage [18], energy efficiency [65, 20, 91]) and the computational time. One of the pioneers in [44], solves the problem using an heuristic based

(32)

in fixed-alternate routing algorithm and a first fit frequency assignment, where fixed routes for each source-destination pairs are pre-calculated based on a depth first search algorithm where routes are selected from the list sequentially and then the lowest available contiguous slots are selected. Until this solution gives a good performance in terms of computational time, the results of spectral efficiency would be improved.

Heuristics

Given the complexity of the RSA problem in EON [54] some authors usually take advantage of some particularities of EON to solve the RSA problem and based on these particularities they propose greedy solutions. The issue with these solutions is that they usually get trapped in a local optimum, in table 3.2.a the main proposed heuristics to solve the RSA planning problem in EON are shown.

In general, to solve the RSA planning problem, the first step is to choose a criteria to determine the order of the serving request. As shown in table 3.2.a, most of the authors agree on selecting most sub-carriers first (MSF) or most request demand first (MRDF) -when considering multi level modulation transmissions-, or to combine this rule with other criteria like paths distance or the load link in order to minimize the used spectrum. The second step is to choose the light path, which is the main difference between the main proposed heuristics, as we can see, in addition to spectrum saving this step give us an option to minimize other key features (e.g. energy or spectrum fragmentation). Finally the serving requests are sequentially served following the chosen criteria.

In [54] an heuristic called Adaptive Frequency Assignment - Division and Collision Avoidance (AFA-DCA) is proposed. In this heuristic the shortest paths are selected in terms of their congestion. Similar concepts were applied in [122,121], although this heuristic achieves efficient spectrum utilization, its main disadvantage is the required computational time.

Meta-Heuristics

Meta-heuristics are general algorithms applied to different optimization problems. For the RSA problem in EON table 3.2.b shows a summary of the main meta-heuristics algorithms, there are two main approaches to apply meta-heuristics to the RSA problem, the first one is to use evolutionary algorithms that use the heuristics described in table3.2.a to generate the sample space, then the meta-heuristic minimizes the key performance metric. In this approach the main disadvantage is the high computational time because the meta-heuristics requires to give a solution for each sample in the sample space [20,39,40].

The second approach is to find efficient serving requests and evaluation criteria rules, this rules commonly given as functions could be obtained using meta-heuristics [130] (training stage).

Finally, most of the solutions use relaxed assumptions and complement the problem using greedy based algorithms, then, it is clear that in order to find better results it is important to find better decision rules based in the topology and traffic patterns.

(33)

Table 3.2: Summary of main algorithms to solve RSA in EON with static traffic: (a) Heuristics and (b) Meta-heuristics

(a) Heuristics

Heuristic Evaluation criteria for route assignation Year

Most subcarriers first (MSF)

Longest path first (LPF)[20] Lowest starting spectrum 2011

Routing modulation level spectrum assignment [65] Minimum energy considering k-paths and

multilevel modulation 2011

Routing modulation level spectrum assignment [91]

1) Minimum energy considering if fail, 2) Backup paths if fail,

3) Sulti-hop of paths of k-paths

2011

Shortest path with maximum spectrum reuse [121,122] Shortest path 2011

Balanced load spectrum allocation [121,122] Shortest path considering the load of a fiber 2011 Adaptive frequency assignment - collision avoidance [53] Shortest path considering a collision metric 2011 Greedy, Shortest path routing , wavelength assignment,

and SA algorithm [88]

Breadth-first search algorithm, Minimum Available

wavelength slots beginning with k-shortest paths 2012 Auxiliary Graph for Waveband Paths Heuristic

and First Fit Spectrum Largest Waveband Heuristic [111] Lowest starting spectrum 2011

Least spectrum grooming (LSG) [140] Shortest path 2012

Group integer linear programming [143] Shortest path 2015

RSA in Elastic Optical Networks With Shared Protection [12] Distance-constrained minimum-cost anycast path 2016 Strictly Xt-Aware RMCSA with Hybrid Protection scheme [72] Modulation level for the primary and backup path 2020

(b) Meta-Heuristics

Meta-Heuristic Description Year

Simulated annealing [20] Ordering the Demands and Simulated Annealing 2011

Genetic algorithm [39] Adaptive genetic algorithm for EON planing

with static multi-cast traffic 2013

Genetic algorithm [40] Genetic algorithm based on distance-adaptation 2013

Particle swarm optimization [130] The coefficients are determined by a global optimizer,

called Particle Swarm Optimizer (PSO) 2013

PRVONE [102] optical path ranking system to provide scalable embeddings 2019

Colony optimization and genetic algorithm [26] Minimize the fragmentation of the entire network 2019 Hybrid meta-heuristic approach for RSA in EON[102] Enhanced SFLA based spectrum fragmentation 2020

3.5 RSA in EON with Dynamic Traffic: On-line Problem

The main difference between the static and dynamic problem is the serving request, in the static case the first step is to sort the serving request in appropriate way, in the dynamic case the requests arrive randomly and the challenge is to select the best route (commonly given in a set of pre-calculated paths), after that, assign the spectrum based on the spectrum availability in order to minimize a given performance metric. Since the bandwidth requests are not known in advance, fragmentation of the optical spectral resources is one of the most important and

Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

School of Engineering and Sciences

Nonlinear equalizer for Coherent OFDM Optical Systems

Jos´e Antonio Torres Zugaide

Instituto Tecnol´ogico y de Estudios Superiores de Monterrey

Declaration of Authorship

Dedication

Acknowledgements

Nonlinear equalizer for Coherent OFDM Optical Systems by

Jos´e Antonio Torres Zugaide Abstract

List of Figures

List of Tables

Contents

Chapter 1 Introduction

Chapter 2

General Background and Basic concepts

2.1 Orthogonal Frequency Division Multiplexing

2.1.1 OFDM transmitter

2.1.2 Ciclic Prefix

2.2 Passive Optical Networks (PONs)

2.2.1 Time Division Multiplexed Passive Optical Networks (TDM-PON)

2.2.2 Wavelength Division Multiplexed PON (WDM-PON)

2.3 Optical Channel Impairments

2.3.1 Chromatic Dispersion

2.3.2 Four Wave Mixing

2.3.3 Stimulated Brillouin Scattering

2.3.4 Stimulated Raman Crosstalk

2.3.5 Self-Phase Modulation

2.3.6 Crossphase Modulation

2.4 Optical Coherent System

2.5 Conclusion

Chapter 3

Routing and Spectrum Allocation in E.O.N.

3.1 Introduction

3.2 Elastic Optical Network Technologies

3.2.1 Bandwidth variable transponders

3.2.2 Bandwidth variable wavelength cross-connector

3.2.3 OFDM and Elastic Optical Networks

3.3 Key performance metrics and key characteristics of EON to solve the RSA problem

3.3.1 Key performance metrics

3.3.2 Key characteristics

3.3.3 Additional technological improvements for future consideration

3.4 RSA in EON with Static Traffic: The Planning Problem

3.4.1 Formulation of the RSA planning problem

3.5 RSA in EON with Dynamic Traffic: On-line Problem