T2826552

UNIVERSITÀ DEGLI STUDI DI GENOVA
FACOLTÀ DI INGEGNERIA
Corso di Laurea Specialistica in Ingegneria Elettronica
TESI DI LAUREA
________
Analog-to-Digital Converters for 100 Gbit/sec Optical
Transmission: Modelling and Evaluation of Photonic
Transport System Performances
Relatore: Chiar.mo Prof. Ing. Daniele Caviglia
Correlatore: Ing. Gianmarco Bruno
Candidata: Veronica Sant
22 marzo 2013
Anno Accademico 2011 - 2012

Abstract
The development of optical communications in recent decades has made possible the
huge growth of wired communications, leading to new widespread services like the
internet. All the services which rely on wired communications are in expansion, and the
bandwidth demand is always increasing.
The aim of this thesis is to study 100 Gb/s optical coherent transmission systems and
ADC performances. The thesis can be divided in four parts that deal with foundamentals of
physical layer issues of optical transport networks, techniques for coherent signal
generation and detection and introduction to optical network design concepts and standards
with experimental activity with high-speed optical transmission equipment.
This thesis confirms that 100 Gb/s systems will become feasible in the future using
DSP and coherent detection, that are the basis of higher-speed optical systems
development.
II
Università degli Studi di Genova
Dipartimento di Ingegneria navale, elettrica, elettronica e delle telecomunicazioni

Alla Commissione di Laurea e di Diploma
Alla Commissione Tirocini e Tesi
Sottopongo la tesi redatta dalla studentessa Veronica Sant dal titolo "Convertitori
Analogico/Digitali per Trasmissione Ottica a 100 Gbit/sec: Modelling e Valutazione delle
Performance in un Sistema di Trasporto Fotonico".
Ho esaminato, nella forma e nel contenuto, la versione finale di questo elaborato
scritto, e propongo che la tesi sia valutata positivamente assegnando i corrispondenti
crediti formativi.
Il Relatore Accademico
Prof. Daniele Caviglia
III

Acknowledgements
There are so many people I would like to thank. Since I think it is impossible to
thank them all, I apologies with all of those that are not mentioned.
First of all, my acknowledgment to my family that supported me during University
years: thank you very much.
Another special thank you goes to my supervisor Daniele Caviglia for proposing me
this great opportunity that was really interesting and formative; thank also for your kind
help before, during and after my thesis experience.
I would like to thank my industrial supervisor Gianmarco Bruno for guiding and
helping me every time I was stuck with my work. I will always be indebted and it was a
pleasure working with you.
After that, my special thanks to my boyfriend Enzo for all the support and the
moments spent together.
IV

List of acronyms
ADC Analog-to-Digital Converter
ASPL Average Shortest Path Length
BER Bit Error Rate
CD Chromatic Dispersion
CMOS Complementary Metal-Oxide Semiconductor
DC Direct Current
DCF Dispersion Compensating Fiber
DCM Dispersion Compensation Module
DeMUX Demultiplexer
DML Directly Modulated Lasers
DP Dual Polarization
DQPSK Differential Quadrature Phase Shift Keying
DSL Digital Subscriber Line
DSP Digital Signal Processing
EAM Electro-Absorption Modulator
EDFA Erbium Doped Fiber Amplifier
FBG Fiber Bragg Gratings
FEC Forward error correction
V

List of acronyms
FF Feedforward
FFT Fast Fourier Transform
FIR Finite Impulse Response
FWM Four-Wave-Mixing
GVD Group-Velocity Dispersion
IFFT Inverse Fast Fourier Transform
IM/DD Intensity Modulation Direct Detection
LHC Left-Hand Circular
LLR Log-Likelihood Ratio
LO Local Oscillator
MEMS Micro-Electro-Mechanical System
MIMO Multiple-Input Multiple-Output
MMSE Minimum Mean-Square-Error
MZM Mach-Zehnder Modulator
NLPN Nonlinear Phase Noise
NLSE Nonlinear Schrödinger Equation
OFDM Orthogonal Frequency-Division Multiplexing
OOK On-Off Keying
ORN Optically-Routed Network
OSNR Optical Signal-to-Noise Ratio
OXC Optical Cross-Connect
PAPR Peak to Average Power Ratio
PBS Polarization Beam Splitter
PM Polarization Multiplexing
PMD Polarization-Mode Dispersion
PolMux Polarization Multiplexing
PXC Photonic Cross-Connect
QAM Quadrature-Amplitude Modulation
QPSK Quadrature Phase Shift Keying
RF Radio Frequency
VI

List of acronyms
ROADM Reconfigurable Optical Add-Drop Multiplexer
RHC Right-Hand Circular
Rx Receiver
RWA Routing and Wavelength Assignment
SMF Single Mode Fiber
SNR Signal-to-Noise Ratio
SPM Self-Phase Modulation
Tx Transmitter
WDM Wavelength Division Multiplexing
WSS Wavelength Selective Switches
WXC Wavelength Cross Connect
XPM Cross-Phase Modulation
VII

Introduction
Thesis project was performed in Research Group in Ericsson Telecommunications
S.p.A. of Genoa under the supervisor of Gianmarco Bruno.
Ericsson
The leader in the development and deployment of telecommunications systems
around the world, Ericsson is continuing research into innovative solutions for mobile
networks and core networks and keeps these networks running at optimal efficiency with
its operations support systems.
In Italy Ericsson is the main provider of mobile and fixed telecommunications
operators and its best products are Opto Supply, master factory and delivery center for
optical systems worldwide.
In Genoa there is one of the Ericsson research unity where activities provide the
development of next generation optical transport networks, focusing on optical integration
technology solutions and backhauling networks. The objectives of this centre of excellence
are to develop new system concept and advanced systems prototypes, test new
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Dipartimento di Ingegneria Biofisica ed Elettronica

Introduction
technologies, sperimentaly demonstrate the feasibility of studied solutions also with
collaborations of University of Genoa.
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Sintesi in italiano
Convertitori Analogico/Digitali per Trasmissione Ottica a
100 Gbit/sec: Modelling e Valutazione delle Performance
di un Sistema di Trasporto Fotonico
Obiettivo della tesi
Lo sviluppo delle comunicazioni ottiche negli ultimi decenni ha reso possibile
l'enorme crescita delle comunicazioni cablate, permettendo la diffusione capillare di
servizi, come, ad esempio, Internet. Tutti i servizi correlati, ovvero quelli che si basano su
comunicazioni via cavo, sono in espansione, e la domanda di larghezza di banda è sempre
in aumento. Questo fatto rappresenta uno degli aspetti più critici dal punto di vista
tecnologico, in quanto, se da un lato c'è la volontà dei grandi fornitori di servizi telefonici
di sfruttare la tecnologia disponibile, dall'altro troviamo gli sforzi del mondo scientifico per
rendere realizzabili le nuove soluzioni per l'adeguamento alla richiesta di capacità
superiori.
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Sintesi in italiano
Una risposta a questo problema viene dalle fibre ottiche che sono già utilizzate per la
maggior parte del traffico voce e dati in tutto il mondo. Il trend delle attività di ricerca in
campo ottico si rivolge alle tecniche di rilevamento coerente, le quali, seppur richiedendo
un'architettura più complessa del ricevitore, ne consentono una sensibilità maggiore e
l'impiego di formati di modulazione spettralmente più efficienti. Altro ampio campo di
ricerca riguarda lo studio di tecniche efficaci per la compensazione totalmente elettronica
degli impairments lineari e non lineari del segnale ricevuto.
Lo scopo della tesi è quello di studiare i sistemi ottici di trasmissione coerente a 100
Gb/s e valutarne le prestazioni. La tesi è organizzata come segue:
• Analisi delle possibili architetture per la realizzazione di trasmettitori e ricevitori
ottici con una particolare attenzione ai formati di modulazione applicati in
combinazione con il rilevamento coerente e l'equalizzazione elettronica delle
distorsioni del segnale per aumentare l'efficienza spettrale e di ridurre complessità
del sistema di trasmissione a lungo raggio;
• Studio dei fondamentali problemi a livello di trasporto ottico e di rete;
• Introduzione ai concetti di progettazione di reti ottiche con attività sperimentali di
simulazione di generazione e trasmissione di segnali ottici con
VPItransmissionMaker e l'analisi degli algoritmi proprietari Ericsson per la
rilevazione dei segnali implementati in Matlab.
Introduzione
Il sistema preso in analisi (Fig. 2.1) consiste in un set di laser con lunghezze d'onda
differenti per generare i segnali ottici. Ogni segnale è modulato da un modulatore esterno
(Mach-Zehnder). Il principale formato di modulazione utilizzato è il quadrature phase shift
keying (QPSK) con multiplazione di polarizzazione (PolMux) e rivelazione coerente.
Dopo il multiplexer un amplificatore ottico (EDFA) viene inserito per aumentare la
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Sintesi in italiano
potenza del segnale. Lungo la linea di trasmissione, il segnale viene amplificato
periodicamente (circa ogni 80-100 km).
In ricezione, le diverse lunghezze d'onda devono essere demultiplate mediante filtri
ottici passa banda. Il rilevamento coerente dei segnali necessita, inoltre, di un laser
aggiuntivo per generare un segnale all'uscita di un oscillatore locale. Questo segnale viene
mixato con il segnale in ingresso al ricevitore coerente utilizzando un cosiddetto ibrido a
90°. Dopo la conversione digitale eseguita da un ADC, il segnale viene sottoposto ad
equalizzazione, (per compensare le distorsioni lungo la linea di trasmissione) attraverso un
DSP.
Architettura dettagliata per trasmettitori e ricevitori ottici
Un trasmettitore POLMUX-QPSK è costituito da due modulatori DQPSK e da un
PBS per multiplare le due polarizzazioni ortogonali. Tipicamente il modulatore DQPSK è
realizzato con un laser, il cui segnale prodotto viene diviso, per permettere a ciascuno dei
due modulatori MZM di imprimervi una modulazione in fase, e sottoposto all'azione di un
combiner per ottenere un unico segnale in uscita.
L'impiego di entrambe le polarizzazioni del segnale e il formato di modulazione
prescelto (2 bit per simbolo) permettono una trasmissione a un bit-rate alto (112 Gb/s) ma
con un symbol-rate relativamente basso (28 Gbaud), tale da migliorare la tolleranza
rispetto alle distorsioni lineari e non lineari lungo la linea.
A differenza del trasmettitore appena descritto, un trasmettitore 16-QAM necessita di
un modulatore in ampiezza e uno in fase, in relazione allo specifico formato di
modulazione considerato: 16-QAM offre di fatto un'efficienza spettrale due volte superiore
rispetto a QPSK e riduce ulteriormente il symbol-rate richiesto per ottenere l'equivalente
bit-rate, sebbene a scapito di un maggiore OSNR richiesto, e peggiori prestazioni in
termini di sensibilità alle distorsioni lineare e non lineare.
Il ricevitore digitale coerente non solo compensa i disturbi deterministici del canale,
(CD e PMD), ma consente anche il monitoraggio completo delle prestazioni ottiche e di
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Sintesi in italiano
misurare la qualità del segnale. Il segnale in ingresso al ricevitore viene diviso in due
polarizzazioni ortogonali arbitrarie, le quali sono mixate con l'uscita del LO, rivelate da
fotodiodi e convertite nel dominio digitale dal ADC, il quale quantizza l'ampiezza dei
campioni del segnale ottenuto. La risoluzione degli ADC, attualmente richiesta per non
avere distorsioni dovute dal processo di quantizzazione, è di 5-6 bit.
Il processing digitale del segnale ottico sta emergendo come soluzione pratica per le
comunicazioni ottiche a lungo raggio da alcuni anni. I DSP sono usati sia per la
compensazione degli impairments trasmissivi che per il demultiplexing di polarizzazione e
una delle sfide principali è quella di perfezionarne gli algoritmi per consentire
un'elaborazione dei dati in tempo reale ad alta velocità. La prima fase di un ricevitore
digitale coerente è la conversione optoelettronica della doppia polarizzazione che recupera
il segnale modulato in banda base: le uscite analogiche di questa fase sono passate
attraverso filtri anti-aliasing e quindi campionate. Le distorsioni dovute al canale
trasmissivo possono quindi essere compensate digitalmente prima della rivelazione dei
simboli con l'utilizzo di filtri FIR. Il recupero della fase e della frequenza della portante
vengono effetuati con uno stimatore FF il quale permette di de-ruotare il segnale ricevuto
in base alla stima effettuata. Infine, il segnale può essere decodificato (con l'aiuto di
correzione dell'errore FEC) applicando (nel caso delle costellazioni quadrate) una serie di
soglie di decisione separatamente per le componenti in-fase e in-quadratura.
La correzione FEC è un metodo di codifica del segnale originario con l'aggiunta di
un overhead contenente informazioni utili al ricevitore ottico, consentendo l'individuazione
e correzione degli errori che si verificano nel percorso di trasmissione. La correzione FEC
abbassa drasticamente il BER permettendo quindi l'aumento delle distanze che i segnali
ottici possono percorrere senza rigenerazione. Nei sistemi di comunicazione ottica
l'overhead tipico dovuto al FEC è del 7%.
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Sintesi in italiano
Infrastruttura Ottica
Un collegamento di trasmissione ottica può essere definito come il mezzo fisico
attraverso il quale un segnale si propaga tra un trasmettitore ed un ricevitore. Nel
trasmettitore una portante ottica, generalmente l'uscita di un laser, è modulata con una
sequenza di bit. Al ricevitore, il segnale ottico viene nuovamente convertito in un segnale
elettrico utilizzando uno o più fotodiodi. Dopo un'appropriata decisione, idealmente, la
sequenza di bit trasmessa è nuovamente ottenuta.
I rivelatori coerenti hanno il vantaggio di non necessitare di una gestione di
dispersione lungo la linea di trasmissione, risparmiando i relativi moduli di
compensazione, e consente amplificatori dalle strutture più semplici. Inoltre, le
funzionalità di monitoraggio delle prestazioni ottiche che un ricevitore digitale coerente
offre sono semplificate poiché viene ridotto il numero di misurazioni necessarie da
effetuare direttamente sul link.
Nei sistemi di trasmissione ottica a lungo raggio, l'amplificazione ottica è quasi
esclusivamente utilizzata per amplificare il segnale tra le varie tratte di fibra. Uno dei
principali vantaggi dell'amplificazione ottica, al contrario di quella ottica-elettrico-ottica, è
l'amplificazione indipendente dal formato di modulazione e dal bit-rate. Il tipo più comune
di amplificatori ottici è quello a fibra drogata di erbio (EDFA). Un valore tipico per la
potenza di uscita di un EDFA è circa 23 dBm, che è generalmente sufficiente per
amplificare fino a 80 canali WDM nella banda di lunghezza d'onda tra 1525 nm e 1570
nm.
La principale fonte di rumore ottico a livello trasmissivo è l'emissione spontanea
amplificata (ASE) che è il risultato di una transizione, appunto, spontanea da uno stato
eccitato ad uno stato energetico inferiore dei fotoni in un supporto fisico, accompagnata
dall'emissione dei relativi fotoni.
Multiplexer ottici riconfigurabili (ROADM) sono uno degli elementi chiave per le
reti ottiche di prossima generazione, riconfigurabili dinamicamente. I multiplexer ROADM
permetto il passaggio selettivo delle diverse lunghezze d'onda senza la necessità di costosi
convertitori ottico-elettrico-ottici (O-E-O). Mentre i ROADM di prima generazione sono in
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Sintesi in italiano
grado di operare con architetture lineari o ad anello, dai ROADM di ultima generazione ci
si aspetta che possano operare con nodi di rete di alto grado che sono essenziali per la
progettazione e l'implementazione delle future reti di trasporto ottico.
Trasmissione Ottica
Nei sistemi di trasmissione WDM a lungo raggio ci sono fondamentalmente cinque
limitazioni dominanti: OSNR, larghezza di banda ottica, dispersione cromatica, PMD e
distorsioni non lineari. La tolleranza rispetto a queste limitazioni dipende linearmente, o
anche quadraticamente, dal bit-rate. Quindi, tali parametri devono essere presi in
considerazione durante la progettazione di reti ottiche WDM. Questi sistemi sono
configurati perchè più canali a lunghezze d'onda diverse possano condividere la stessa fibra
ottica, aumentando la velocità effettiva di trasmissione su tale fibra. Ma con questa
tecnologia è nata una nuova sfida: i parametri che forniscono informazioni dirette sulle
prestazioni del sistema non possono essere misurati direttamente su un sistema multicanale
(che richiederebbe il demultiplexing spettrale prima di effettuare una valutazione
individuale delle prestazioni BER su ogni canale demultiplato). In alternativa, è possibile
ricavare il rapporto segnale-rumore ottico (OSNR) dalla valutazione dello spettro ottico per
ottenere informazioni indirette sulle prestazioni dei canali e quindi del sistema.
Come suggerisce il nome, la dispersione cromatica (CD) produce una diffusione nel
tempo dei vari componenti di frequenza di un segnale a causa della differenza di velocità di
gruppo registrato da ciascun componente di frequenza. Con l'accumularsi della CD,
simboli adiacenti iniziano a sovrapporsi nel tempo: in termini di teoria dell'informazione,
la CD introduce memoria nel canale.
La differenza principale tra la fibra ottica e altri mezzi di trasmissione è la presenza
di non linearità, cioè le proprietà di propagazione del mezzo variano con l'incremento di
potenza del segnale. Le principali distorsioni non lineari della fibra derivano dalla non-
linearità di Kerr, che provoca un cambiamento di indice di rifrazione proporzionale alla
intensità del segnale. Effetti non lineari includono componenti deterministiche e statistiche.
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Sintesi in italiano
La non linearità subita da un segnale dovuta alla propria intensità è detta self-phase
modulation (SPM). In sistemi WDM, un segnale subisce anche gli effetti non lineari dovuti
ai canali vicini: questi sono la cross-phase modulation (XPM) e il four-wave-mixing
(FWM). Nei sistemi a lungo raggio, l'interazione tra il rumore ASE e segnale affetto dala
non linearità di Kerr comporta il rumore di fase non lineare (NLPN). Quando questo è
causato dal rumore ASE e dal segnale nel canale di interesse, questo è chiamato SPM
indotta NLPN, quando, invece, è causato dal rumore ASE e dai segnali dei canali adiacenti,
è chiamato XPM indotta NLPN.
Per la realizzazione di sistemi ottici WDM a 100 Gbit/s ed oltre, gli effetti di
quantizzazione dovuti alla risoluzione limitata del convertitore analogico-digitale (ADC)
svolgono un ruolo importante. Nel lavoro di tesi ho studiato questi effetti sia teorici che
tramite simulazione. Attraverso le simulazioni effettuate durante la tesi ho verificato che il
modello teorico dell'errore di quantizzazione è un'approssimazione sufficiente dell'errore di
quantizzazione misurato durante le simulazioni dello stesso sistema di trasmissione ottica
(in questo caso senza considerare ulteriori fonti di rumore). Le simulazioni hanno anche
evidenziato l'impatto della risoluzione del ADC sul rate di errore del sistema studiato.
Nelle stesse simulazioni è evidente che le prestazioni di un ADC caratterizzato da 4, 5, 6
bit sono molto simili in termini di OSNR rispetto al pre-FEC richiesto BER (2 * 10 -3
).
In un sistema di trasmissione a lungo raggio, la dispersione cromatica interagisce con
la SPM e XPM. L'ammontare della dispersione lungo la linea di trasmissione può
provocare gravi distorsioni del segnale tali da non permetterne la ricostruzione. È quindi
importante progettare l'evoluzione della dispersione locale lungo il link, operazione nota
come mappa di dispersione.
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Sintesi in italiano
Reti ottiche
Il design di reti ottiche deve ottimizzare i vari parametri elettrici e ottici per garantire
il buon funzionamento della rete stessa. Una figura di merito utile è il rapporto segnale-
rumore ottico (OSNR), che specifica il rapporto della potenza del segnale netta rispetto alla
potenza di rumore. È un rapporto di due potenze, pertanto, se un segnale e rumore sono
entrambi amplificati, il rapporto OSNR rivela ancora la qualità del segnale.
La simulazione effettuata è mostrata in Figura 6.3. Si compone di un trasmettitore
112 Gb/s Pol-Mux 16QAM, una linea di trasmissione in cui non vengono considerate
distorsioni non lineari e un ricevitore coerente che comprende quattro ibridi a 90° (due per
ciascuna polarizzazione) e una unità DSP. Nella linea di trasmissione è inserita una
sorgente di rumore ASE (utile per impostare il rapporto OSNR desiderato). Dopo il
rilevamento e il campionamento, il segnale è passato all'unità DSP simulata off-line con
algoritmo proprietario Ericsson implementato in Matlab. La dispersione cromatica residua
viene compensata con un filtro FIR. Gli effetti di polarizzazione residua sono mitigati
attraverso una struttura MIMO. I coefficienti della struttura MIMO sono ottimizzati
utilizzando l'algoritmo a modulo costante (CMA).
Conclusioni
Il lavoro di ricerca descritto in questa tesi è incentrato sullo studio e sulla
simulazione dei sistemi di trasmissione ottica che potrebbero consentire un maggiore bit-
rate facendo fronte alla richiesta di maggiore capacità delle reti esistenti. I modi per
aumentare il bit-rate studiati sono la multiplazione di polarizzazione per reti WDM
utilizzando avanzati formati di modulazione (spettralmente più efficienti) e rilevamento
coerente del segnale. Questa tesi è focalizzata sullo studio di due principali formati di
modulazione avanzata, cioè la quadrature phase-shift keying (QPSK) e 16-quadrature
amplitude modulation (16-QAM), sulle prestazioni del convertitore AD e sul rilevamento
coerente del segnale trasmesso seguito da elaborazione digitale.
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Sintesi in italiano
La conclusione generale è che a 100Gbit/s l'uso di QPSK con rilevamento coerente è
una configurazione opportuna da sviluppare per sistemi ultra-long-haul. I sistemi di nuova
generazione possono essere basate su 400Gbit/s bit-rate (448Gbit/s con FEC), la cui
generazione ottimale è ancora argomento di dibattito. Tuttavia, con futuri progressi nella
progettazione e realizzazione dei componenti utili a trasmettitore e ricevitore, il formato di
modulazione PDM-16-QAM diventa un ottimo candidato per raggiungere il bit-rate di
400Gbit/s per portante.
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Contents
List of acronyms V
Introduction VIII
Sintesi in italiano X
1 Thesis goal 1
2 Foreword 3
2.1 Definition of the system 3
2.2 State of art 5
2.3 Tools 9
3 Detailed architectures for 100G DP-QPSK Tx and Rx 11
3.1 Tx: laser, modulators 12
3.1.1 Modulation formats 19
3.2 Rx: coherent receivers 23
3.2.1 Coherent detection 25
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Contents
3.2.2 ADC: general specifications and actual state of the art performaces 26
3.2.3 DSP: equalization 27
3.2.4 DSP: carrier frequency and phase recovery 28
3.2.5 DSP: symbol detection 29
3.2.6 FEC: hard and soft decision, foundamental limit 29
4 Infrastructure modelling 35
4.1 Coherent systems (uncompensated) 35
4.2 Amplifiers: general concepts and typical parameters 36
4.3 Photonic Switches: architectures (WSS), ROADM 38
5 Transmission modelling 42
5.1 OSNR calculation: launch power, amplifiers (noise figure), loss 42
5.2 Filtering effects (net bandwidth) 44
5.3 Nonlinearities: optimal channel power, single and WDM propagation 46
5.4 Penalties due to receiver nonideal behaviour (ADC quantization) 49
5.5 A note about dispersion maps and upgrade of legacy systems 50
6 Network design 53
6.1 Evaluation of signal quality 53
6.1.1 OSNR from span and equipment parameters 54
6.1.2 Effective OSNR (propagation penalties) 56
6.1.3 Pre-FEC BER evaluation and FEC correction 58
6.2 RWA problem 58
6.3 Network design exercise 60
7 Conclusions 64
Bibliography 65
XX

Chapter 1
Thesis goal
With the increasing of global information exchange it’s becoming crucial to be able
to transmit information over longer distance. All the services which rely on wired
communications are in expansion, and the bandwidth demand is always increasing. This
fact represents one of the more critical issue from a technological point of view, because,
on one hand big efforts deal with the exploitation of the available technology; on the other
hand, new solutions to upgrade the existing data rates to higher capacities must be devised.
An answer to this issue are optical fibers that are already used for most of the voice
and data traffic all over the world. A lot of research activity is directing to coherent
detection techniques, already investigated in the early nineties, but then abandoned because
of intensity modulation direct detection (IM/DD) cost efficiency, and technological ease.
Coherent techniques require a more complex receiver architecture, but allow higher
receiver sensitivity and more spectrally efficient modulation formats, therefore it can be
guessed that these transmission schemes will probably represent the future of optical
communication systems.
Besides the considerations on the future of optical systems, today an important
research field is represented by the investigation of effective penalty reduction techniques
at the receiver end provided by electronic processing of the received signal. Signal
1

Chapter 1 - Thesis goal
processing in the electrical domain presents several advantages: it is simple to integrate in
the receiver electronics, it is cost effective, and a wide variety of solutions are already
known from theory and radio communications.
The aim of this thesis is to study 100 Gb/s optical coherent transmission systems and
ADC performances. The thesis is organized as follows:
• Detailed architectures for Tx and Rx focusing on advanced modulation formats in
combination with coherent detection and electronic distortion equalization to
increase spectral efficiency and to reduce long haul transmission system
complexity;
• Foundamentals of physical layer issues of optical transport networks focusing on
linear and non-linear transmission impairments;
• Introduction to optical network design concepts and standards with experimental
activity with VPItransmissionMaker and DSP algorithms implemented in Matlab.
2

Chapter 2
Foreword
The growing trend to ultra-high-speed transmission and high spectral efficiency
WDM systems has boosted new techniques such as polarization multiplexing (PolMux)
and multilevel modulation formats.
Initiated by the recent progress of high-speed electronics, great attention has recently
been paid to transmission systems combining coherent detection and digital signal
processing (DSP). This approach enables powerful mitigation of chromatic dispersion
(CD) and polarization-induced distortions (polarization cross-talk), and presents improved
noise characteristics compared to direct detection receivers.
2.1 Definition of the system
The setup of optical transmission system is shown in Fig. 2.1, and consists of an
array of lasers with different wavelengths to generate the optical carriers. Each laser is
modulated by an external modulator (e.g. a Mach–Zehnder modulator) to impress the data
signal. The next generation of optical transmission system operating at a line rate of 112
Gb/s (including FEC and Ethernet protocol overheads).
3

Chapter 2 - Foreword
Fig. 2.1 - Generic setup of a fiber optical wavelength division multiplexing transmission
system
As modulation format is used quadrature phase shift keying (QPSK) and polarization
multiplexing (PolMux) with coherent detection. QPSK polmux transmits a QPSK signal on
each of the two orthogonal polarization axes, thus doubling the spectral efficiency. After
the multiplexer an optical amplifier (erbium doped fiber amplifier, EDFA) is deployed to
increase the signal launch power. Potentially a dispersion pre-compensation fiber may be
used. To improve the performance (especially in long fiber links) contra-directional (in
some cases combined with co-directional) Raman pumping may be utilized in the
transmission fiber. Along the transmission line the signal is periodically amplified
(approximately every 80–100 km).
In most of today’s systems the accumulated group-velocity dispersion (GVD) is
compensated after each span by a lumped dispersion compensating fiber (DCF). An
alternative to DCFs are chirped fiber Bragg gratings (FBG). At a node, where several
different routes interconnect, an optical cross-connect (OXC) may be deployed. An OXC
allows to switch from one fiber to another dynamically. It is also possible to route
individual wavelengths in different directions.
At the receiver, the different wavelengths need to be demultiplexed. This can be
4

achieved by optical band pass filters. Novel modulation formats with coherent detection
make use of an additional laser at the receiver to generate a local oscillator signal. This
signal is mixed with the incoming signal using a so called 90°-hybrid. In PolMux systems
additionally a separation of the two polarization axes is needed, which is usually performed
by a polarization splitter. After conversion into the electrical domain performed by an
ADC, typically an electrical equalizer is employed. The equalizer is used to compensate for
distortions along the transmission line (especially linear effects such as accumulated
dispersion and polarization mode dispersion). Additionally the mismatch in phase and
frequency between the transmitter laser and the local oscillator at the receiver must be
compensated. This is also achieved by digital signal processors.
2.2 State of art
For millions of people around the world, surfing the Internet day to day to get
information, check e-mails, dispatch shopping comfortably from their desk and download
multimedia and data files has become a natural habit. However, for most of them, the
sophisticated technology they are using to connect to the central office over a simple
twisted copper pair with satisfactory transmission speed remains concealed. Originally laid
to transmit voice signals up to 4 kHz bandwidth, twisted pairs could be utilized to transmit
data signals up to 64 kbit/s with cable modems in the mid nineties. Today, digital
subscriber line (DSL) technology has captured the market. Several hundred millions of
subscribers worldwide have broadband access to the Internet via DSL, with transmission
speeds of up to several Mbit/s in the local loop.
The attraction of transmission over an optical fibre is mainly in its much larger
capacity compared to copper counterparts and immunity to electromagnetic interference
and other external influence. At present, optical fibre transmission is seen as a dominant
technology for both long-haul and short-haul broadband transmission.
In contrast to electrical systems, optical fiber communication systems are still distant
5

from a commercial practical implementation of high-order modulation formats. The
difficult-to-handle optical phase and technological difficulties with cost-effectively
manufacturing more complex high-speed electronic devices restrict the presently installed
optical systems almost exclusively to a simple deployment of intensity modulation (IM) on
the transmitter side and direct detection (DD) at the receiver end. For optical systems, all
system concepts beyond IM-DD can still be qualified as advanced. However, favored by
the very low fiber attenuation of about 0.2 dB/km across several THz of bandwidth, optical
fiber communication is superior to other wireline or wireless communication technologies
and can support very high capacities of several Tbit/s over many thousand kilometers, even
when advanced modulation formats are not employed.
With the objective of reducing costs per information bit in optical communication
networks, per fiber capacities and optical transparent transmission lengths have been
stepped up by the introduction of new technology in recent years. A crucial innovation was
the Erbium-doped fiber amplifier (EDFA) at the beginning of the nineties. Using EDFAs,
long distances can be bridged without electro–optical conversion. Furthermore, the
wavelength division multiplex (WDM) technology which allows a lot of wavelength
channels to be simultaneously transmitted over one fiber, has benefited from the high
bandwidth of the EDFA, since several WDM channels can be amplified using only one
EDFA. During the nineties, the capacity-distance product was further enhanced by
employing other optical key technologies such as optical dispersion compensation, Raman
amplification and advanced optical fibers, as well as through electronic means such as
forward error correction (FEC) and the adaptive compensation of chromatic dispersion
(CD) and polarization mode dispersion (PMD).
6

Fig. 2.2 - Enhancement of capacity · distance/cost through innovative technology in
optical communication networks
Two emerging optical key technologies which are seen as a possible further step
towards even more cost effective optical networks, are advanced optical modulation and
coherent detection. Through the adoption of high-order modulation formats, higher spectral
efficiency (which is defined as the ratio of the data rate per channel to the WDM channel
spacing) can be reached through the reduced symbol rate and the spectral narrowing
therewith aligned. Furthermore only coherent detection permits convergence to the
ultimate limits of spectral efficiency. Several bit/s/Hz per polarization can be transmitted
with unconstrained coherent detection, even considering the impact of fiber nonlinearity.
On the other hand, when employing these new technologies, the complexity of the
transmitters and receivers increases, so that cost reduction due to higher spectral efficiency
has to be weighed up against higher hardware costs. Continuing research and future
investigations will help judge the economic potential of high- order modulation and
coherent detection.
7

Fig. 2.3 - Economical issues for the introduction of advanced modulation and coherent
detection
The electrical field in single mode fibers (SMF) exhibits three physical parameters
that can be used to carry information. Besides amplitude and phase, polarization can also
be exploited for modulation. Plenty of different modulation formats based on the
modulation of all the quadratures of the optical field were proposed in the early nineties,
primarily in association with coherent detection. However, these investigations received
relatively little attention because the necessary complex high-speed electronics were rarely
available. Moreover, the emergence of the EDFA offered completely new perspectives for
simple IM-DD systems so that there was enough potential to increase capacity even
without high-order modulation. Thus, the investigation of high-order modulation formats
remained mainly confined to the description of some transmitter and receiver structures
and the calculation of theoretical bit error ratio (BER) noise performances.
Having optimized optical systems with binary intensity modulation (also denoted as
on–off keying, OOK) and direct detection over the years using the technologies described
above, a new interest in alternative optical modulation formats emerged in the late nineties.
At first, there was interest in obtaining higher robustness against fiber propagation effects
and extending transmission reach, rather than the pursuit of higher spectral efficiencies.
With the emergence of the EDFA, the former advantage of a higher receiver
sensitivity - compared to direct detection - disappeared. Comparable sensitivities could be
achieved by direct detection receivers with optical preamplifiers . Thus, as it had for the
8

high-order modulation formats, research into this area ceased, the more so as the
components were complex and costly.
Nowadays however, coherent optical systems are reappearing as an area of interest.
More recently, the high-speed digital signal processing available allows for the
implementation of critical operations like phase locking, frequency synchronization and
polarization control in the electronic domain through digital means. Thus, under the new
circumstances, the chances of cost effectively manufacturing stable coherent receivers are
increasing.
2.3 Tools
One of the most important tools for designing and optimizing networks is simulation.
Simulation uses interconnected mathematical models of components to predict the
performance system as a whole. By incorporating a simulation within an optimization loop,
the system's performance can be optimized for a particular scenario.
VPItransmissionMaker
VPIphotonics has created applications for WDM systems simulation, in particulary,
VPItransmissionMaker is used in this thesis work. VPItransmissionMaker is designed for
almost all physical layer simulation tasks. This software has libraries of modules that you
can place on a schematic and link together to fully describe an optical system or network.
Each module has a set of parameters to describe its physical characteristics, although you
can also use behavioral parameters. The hierarchy is supported by having subsystem
modules that each have a schematic to describe their contents.
The combination of a powerful graphical interface, a sophisticated and robust
simulation scheduler together with flexible optical signal representations enables and
9

efficient modelling of any transmission system.
MATLAB
MATLAB it's a MathWorks product that provides a range of numerical computation
methods for analyzing data, developing algorithms, and creating models. The MATLAB
language includes mathematical functions that support common engineering and science
operations. Core math functions use processor-optimized libraries to provide fast execution
of vector and matrix calculations. All these caracteristics were useful to test DSP algorithm
implementation.
10

Chapter 3
Detailed architectures for 100G DP-QPSK Tx and Rx
An important goal of a long-haul optical fiber system is to transmit the highest data
throughput over the longest distance without signal regeneration. Given constraints on the
bandwidth imposed by optical amplifiers and ultimately by the fiber itself, it is important
to maximize spectral efficiency, measured in bit/s/Hz. But given constraints on signal
power imposed by fiber nonlinearity, it is also important to maximize power (or OSNR)
efficiency. The most promising detection technique for achieving high spectral efficiency
while maximizing power (or OSNR) efficiency, is coherent detection with polarization
multiplexing, as symbol decisions are made using the in-phase (I) and quadrature (Q)
signals in the two field polarizations, allowing information to be encoded in all the
available degrees of freedom. When the outputs of an optoelectronic downconverter are
sampled at Nyquist rate, the digitized waveform retains full information of the electric
field, which enables compensation of transmission impairments by digital signal
processing (DSP). A DSP-based receiver is highly advantageous because adaptive
algorithms can be used to compensate time-varying transmission impairments. Advanced
forward error-correction coding can also be implemented.
11

Chapter 3 - Detailed architectures for 100G DP-QPSK Tx and Rx
3.1 Tx: laser, modulators
Optical modulation is the conversion of a signal from the electrical into the optical
domain. This can be achieved by a variety of modulation technologies, which include
directly modulated lasers (DML), electro-absorption modulators (EAM) and Mach-
Zehnder modulators (MZM). In order to realize high-speed modulation an optical
modulator should have a high electro-optical bandwidth, low optical insertion loss, not
induce undesired frequency chirp in the signal and have a high enough extinction ratio
(defined as the ratio of the energy in the ’0’ compared to the energy in the ’1’s).
POLMUX-QPSK transmitter
A POLMUX-QPSK transmitter consists of two quadrature (e.g. DQPSK) modulators
and a polarization beam splitter (PBS) to multiplex the two outputs on orthogonal
polarizations. The use of a 2 bits/symbol modulation format and polarization multiplexing
results in a low symbol rate 28 Gbaud (112-Gb/s line rate). The lower symbol rate
improves the tolerance to linear transmission impairments as well as making it possible to
use lower-frequency electrical components. In addition, the combination of POLMUX-
QPSK modulation and coherent detection allows for an OSNR requirement close to the
theoretical optimum.
Fig. 3.1 - 4-dimensional signal constellation diagram for POLMUX-DQPSK modulation
12

A DQPSK transmitter is most conveniently implemented by two nested MZMs
operated as phase modulators. Fig. 3.2 shows the corresponding transmitter setup,
consisting of a continuously operating laser source, a splitter to divide the light into two
paths of equal intensity, two MZMs operated as phase modulators, an optical π/2-phase
shifter in one of the paths, and a combiner to produce a single output signal. The symbol
constellations of the upper and lower paths as well as at the modulator output are also
shown, together with the symbol transitions. Using this transmitter structure, one first takes
advantage of the exact π-phase shifts produced by MZMs, independent of drive signal
over-shoot and ringing. Second, this transmitter structure requires only binary electronic
drive signals, which are much easier to generate at high speeds than multilevel drive
waveforms.
Fig. 3.2 - Structure of a DQPSK transmitter. Two MZMs are used as phase modulators,
and the two separately modulated fields are combined with a π/2 phase shift
The actual transmitted signal bit rate (112 Gbit/s) is the sum of the payload data rate
plus additional overhead for data encoding, transmission management and forward error
correction (FEC). Dividing the data among two optical polarizations allows each
polarization to operate at half the data rate that would be required for a single polarization.
Cutting the modulation rate in half reduces the optical bandwidth required to carry the
signal, allowing more tightly spaced channels. This contributes to maintaining a 50 GHz
channel spacing for 100G channels.
13

Mach-Zehnder modulators
Mach-Zehnder modulators (a metal-oxide-semiconductor (MOS) capacitors
embedded in Si rib waveguides) encode data symbols onto an optical carrier and perform
pulse shaping. When polarization multiplexing is used, the TX laser output is split into two
orthogonal polarization components, which are modulated separately and combined in a
polarization beam splitter (PBS).
In particular, MZMs work by the principle of interference, controlled by modulating
the optical phase. The incoming light is split into two paths at an input coupler (Fig. 3.3).
Fig. 3.3 - Transfer function of an optical fibre coupler
One (or both) paths are equipped with phase modulators that let the two optical fields
acquire some phase difference relative to each other, controlled by the applied phase
modulation voltages V1;2. Finally, the two fields interfere at an output coupler. Depending
on the applied electrical voltage, the interference varies from destructive to constructive,
thereby producing intensity modulation. The optical field transfer function TE(V1;V2) of the
MZM reads
(3.1)
where Φ(V1;2) are the voltage-modulated optical phases of the two MZM arms, and ψ is an
additional, temporally constant phase shift in one of the arms, referred to as the modulator
14

bias. If the phase modulation depends linearly on the drive voltage (Φ
= kV) which is true for most materials used for MZMs, the MZM power transfer function
depends only on the drive voltage difference (ΔV) : TP(V1;V2) = |TE(V1;V2)|2
= TP(ΔV) =
cos2
(kΔV/2 + kVbias/2). The modulation voltage that is required to change the phase in one
modulator arm by π, thereby letting the MZM switch from full transmission to full
extinction, is called switching voltage Vπ. For a given drive voltage difference ΔV
according to the desired modulated intensity, the additional degree of freedom in choosing
V1(t)+V2(t) can be exploited to imprint phase modulation (chirp) on the signal. If chirp is
not desired (which is often the case), the two modulator arms are driven by the same
amount, but in opposite directions V1(t)= -V2(t) and the phase term in (3.1) vanishes. This
driving condition is known as balanced driving or push–pull operation. Due to their well-
controllable modulation performance and the possibility of independently modulating
intensity and phase of the optical field, MZMs form the basis of many advanced optical
modulation formats.
16-QAM transmitter
16-QAM modulation signal can be generated either from an intensity modulator
followed by a phase modulator or from an IQ-modulator composed of two arms with two
orthogonal carriers, where the in-phase component of the complex envelope modulates the
optical carrier in the I-arm and quadrature component modulates the 90° phase-shifted
optical carrier in the Q- arm. In the latter case only an amplitude modulation (which can be
realized with a single-drive MZM driven by bipolar driving signals at a DC bias point at
-π) has to be performed in each arm and the electrical driving signals have a smaller
number of states. A further reduction of the number of states can be reached by replacing
the amplitude modulation in each arm by separate intensity and phase modulations. Then,
the intensity modulator is driven by an unipolar RF driving signal at a DC bias point at -π
and the phase modulator changes the phase between 0 and π for positive and negative
values of ik and qk respectively. Furthermore it is possible to save two modulators
15

compared and to realize the intensity and phase modulation with only one component,
using a dual drive MZM. The dual drive MZM can be simultaneously driven in the push-
pull-mode for intensity modulation and in the push-push-mode for phase modulation, and
the RF driving signals for intensity and phase modulation have to be electrically combined
before being injected into the MZM inputs.
Fig. 3.4 - Optical multi-level modulation transmitters, (a) Serial configuration, (b) IQ-
configuration with single- drive MZM, (c) IQ-configuration with MZM und PM, (d) IQ-
configuration with dual-drive MZM [20]
16

Every transmitter structure has its own advantages and drawbacks. The serial
configuration (a) features a simple optical part, but the electrical driving signals have a
high number of states (e.g. 12-ary signals are required for phase modulation for Square-16-
QAM). The IQ-transmitters are composed of two arms, leading to a bigger optical
complexity and necessitating integration, but the electrical driving signals have less
number of states. For example for Square-16-QAM 4-ary electrical signals are required for
the single-drive MZM configuration (b), whereas only 2-ary signals for the configuration
with separate intensity and phase modulation (c). For the dual-drive MZM configuration
(d) two modulators can be saved compared to configuration (c), but electrical combining of
the driving signals is necessary.
Fig. 3.5 - Eye diagrams of the squared envelope and IQ-plots for serial configuration
transmitters and Square-16-QAM modulation [20]
17

Fig. 3.6 - Eye diagrams of the squared envelope and IQ-plots for different transmitters and
Square-16-QAM modulation [20]
Polarization Beam Splitter
An optical polarization beam splitter cube, made by coating of interferential thin
films, is composed of two cemented prisms, one of them having on the hypotenuse a thin
films package with indices and thickness so chosen to maximize the effect of polarization
in the spectral range of interest. Figure 3.6 represents such a beam splitter that transmit
radiation polarized type "p" (electric field intensity vector is parallel with the plane of
incidence) and will reflect “s” polarized radiation (electric field intensity vector is
perpendicular to the plane of incidence). The advantages of this type of polarizers are they
have a very good efficiency (negligible absorption), resistance and reliability, negligible
18

diffusion. Because of these qualities, beam splitters obtained by thin layers coating are
commonly used in complex optical systems for image processing as well as in optical
systems with laser radiation.
Fig. 3.7 - Principle of operation of Polarizing Beam Splitter Cubes
3.1.1 Modulation formats
Advanced optical modulation formats have become a key ingredient to the design of
modern wavelength-division multiplexed (WDM) optically routed networks.
At the beginning, in this thesis the modulation format adopted was dual polarization
quadrature phase shift keying (DP-QPSK) with a coherent receiver, as suggested by OIF
[6]. Then 16-QAM is adopted to test digital signal processing algorithm developed in
Ericsson.
19

Fig. 3.8 - Polarization of electromagnetic wave
DP/PM-QPSK
The electromagnetic field has two quadratures in two polarization components; thus,
in total, 4 DOFs, which span a 4-D signal space. The electric field amplitude of the optical
wave can be written as
(3.2)
where indexes x and y denote the polarization components, and r and i the real and
imaginary parts of the field, respectively.
The phase φx and φy are by definition in the interval (-π; π]. The electric field may be
equivalently described in terms of its phase, amplitude, and polarization state (the latter
being the relative phase and amplitude between the x and y field components) as
(3.3)
where ||E||2
= |Ex|2
+ |Ey|2
, θ = sin-1
(|Ey| / ||E||) and J denotes the Jones vector, which is
usually normalized to unity, i.e., J+
J = |J|2
= 1.
A final way of expressing the signal is as a 4-D vector with real components
20

(3.4)
The transmitted optical power is P = ||s||2
= ||E||2
= Ex,r
2
+ Ex,i
2
+ Ey,r
2
+ Ey,i
2
.
The DP-QPSK modulation format uses QPSK modulation in both polarization
components, i.e., φx = mπ/4 and φy = nπ/4, where m, n {-3, -1, 1, 3}, while∈ |Ex| and |Ey|
remain the same for all phases. Thus, the polarization of DP-QPSK varies between four
states: linear in + 45° direction for φr = 0, linear in - 45° direction for φr = ∓ π/2, left-hand
circular (LHC) for φr = π/4 or φr = -3π/4, and right-hand circular (RHC) for φr = -π/4 or φr
= 3π/4.
16-QAM modulation format
16-QAM modulation offers twice higher spectral efficiency than QPSK and further
reduces the required symbol rate to obtain the equivalent overall bit-rate, although, at the
expense of an increased required OSNR, and worse performance in the linear and
nonlinear transmission regime. A QPSK signal has 6.8dB lower required OSNR than 16-
QAM signal for the same symbol rate of 28Gbaud, and also 3.8dB lower required OSNR
for the same bit rate of 112Gbit/s. 16-QAM will also have reduced tolerance towards
nonlinearity than QPSK because of the presence of 3 intensity levels and, hence, higher
peak-to-mean ratio. The DSP for 16-QAM signals is more complicated than for QPSK, in
particular, adaptive equalisation and carrier phase estimation.
A note about OFDM versus QPSK
In order to increase the robustness and spectral efficiency of high-data rate fiber-
optic transmission systems coherent detection in combination with digital signal processing
21

has been proposed so that equalization of these linear distortions can be done at the
receiver in the digital domain. The first modulation format that was investigated with such
DSP based equalization at the receiver is polarization division multiplexed quadrature
phase shift keying (PDM-QPSK). This single carrier modulation format transmits two
QPSK modulated signals over the two polarizations that exist in single-mode fiber.
A multi-carrier modulation format called PDM–OFDM could be seen as an
alternative to PDM-QPSK showing similar tolerances to CD and PMD. OFDM is a multi-
carrier transmission technique where a data stream is carried with many lower-rate
subcarrier tones. It has emerged as the leading physical-layer interface in wireless
communications in the last decade.
(a) (b)
Fig. 3.9 – a) OFDM Sub-carriers in frequency domain;
b) OFDM Sub-carriers in time domain
CO-OFDM combines the advantages of ‘coherent detection’ and ‘OFDM
modulation’ and posses many merits that are critical for future high-speed fiber
transmission systems. First, the chromatic dispersion and polarization mode dispersion
(PMD) of the transmission system can be effectively estimated and mitigated. Second, the
spectra of OFDM subcarriers are partially overlapped, resulting in high optical spectral
efficiency. Third, by using direct up/down conversion, the electrical bandwidth
requirement can be greatly reduced for the CO-OFDM transceiver, which is extremely
attractive for the high-speed circuit design, where electrical signal bandwidth dictates the
22

cost. At last, the signal processing in the OFDM transceiver can take advantage of the
efficient algorithm of Fast Fourier Transform (FFT)/Inverse Fast Fourier Transform
(IFFT), which suggests that OFDM has superior scalability over the channel dispersion and
data rate.
PDM–OFDM can be easily scaled to higher constellation sizes and allows for
flexible oversampling rates, but at the cost of a more complex transmitter (DAC required).
Because of its high peak to average power ratio (PAPR), the nonlinear tolerance OFDM
requires pre- and post-compensation in links with periodic dispersion compensation. This
adds additional complexity to the system. Still, the over-all complexity of OFDM is lower
than that of QPSK, not because of the modulation format but to the equalization algorithm.
As long as QPSK is used as modulation format, PDM-QPSK has the great benefit
that no DACs are required at the transmitter and, therefore, for the first generation of
100Gb transmission systems it is most likely that this modulation format is used despite the
more complex receiver. For higher constellation sizes, however, the complexity of both the
modulation at the transmitter as well as equalization at the receiver is significantly
increased in the case of single carrier, whereas it remains the same for OFDM. Therefore, it
is expected that for these systems OFDM will be used.
3.2 Rx: coherent receivers
Future dynamically reconfigurable all-optical networks add more flexibility with
adaptive routing of optical paths and switching optical wavelengths, which requires an
adaptive equalizer to compensate for the residual deterministic distortions. Both flexibility
and bandwidth efficiency can be met by digital coherent receivers, which apply optical
intradyne demodulation with subsequent digital equalization and data recovery in the
electrical domain. The digital coherent receiver not only compensates for all deterministic
linear channel impairments, namely chromatic dispersion (CD) and all-order polarization-
mode dispersion (PMD), but also enables a systematic parameter estimation and a
23

comprehensive optical performance monitoring, which allows to measure the signal
quality, extend the fault management, and judge the quality-of-service. Cost-efficient
systems with digital coherent receivers are typically operated in the linear or weakly
nonlinear regime. Increasing the launch power increases the optical signal-to-noise ratio
(OSNR) but also increases the influence of fiber nonlinearities which are typically
interpreted as noise by the linear equalizer. The weakly nonlinear regime defines a tradeoff
between the requirements for a high OSNR and a relatively low impact of nonlinearities
leading to a bit error rate (BER) around 10-3
. Under this assumption, the channel transfer
function can be described by a linear concatenation of all deterministic linear channel
impairments. By polarization-diverse coherent demodulation and analog-to-digital
conversion (ADC), all properties of the optical field are transferred from the optical
domain into the electrical domain. With digital processing, the data can be recovered
mitigating noise and compensating for channel impairments. The core element of this data
recovery comprises the equalizer with several blocks of finite impulse response (FIR)
filters.
Intradyne receivers
The digital coherent receiver uses polarization-diversity intradyne detection to
convert the full optical field (i.e. amplitude, phase and polarization information) to the
electrical domain. This requires the detection of both the in-phase and quadrature
components for two arbitrary, but orthogonal, polarization states - a total of four signals.
Because the full (base-band) optical field is transferred to the electrical domain, a digital
coherent receiver can operate with any kind of optical modulation format.
First, a PBS splits up the signal into two arbitrary, but orthogonal, polarization
components X and Y. The polarization components X and Y are therefore an arbitrary
rotation of the two polarization components at the transmitter. Each of the polarization
components is then fed into a 90° hybrid and mixed with the output of a LO laser. The LO
is free-running and should be aligned with the transmitter laser within an approximate
24

frequency range of several hundred megahertz.
Fig. 3.10 - Schematic diagram of a digital coherent receiver
The allowable frequency range depends on the signal processing algorithms that are
used for carrier phase estimation. The LO can be fixed within this frequency range using a
slow feedback signal generated through signal processing. The mixing of the received
signal and LO in the 90° hybrids gives the in-phase and quadrature components, then
detected with 4 photodiodes (either balanced or single-ended) and converted to the digital
domain using high-speed analog-to-digital converters (ADCs). Compared to direct-
detection receivers, coherent detection and the associated digital signal processing imply a
significant shift in system complexity from the optical to the electrical domain. In
particular the ADCs are a key component for any digital coherent receiver implementation.
3.2.1 Coherent detection
The most advanced detection method is coherent detection, where the receiver
computes decision variables based on the recovery of the full electric field, which contains
both amplitude and phase information. Coherent detection thus allows the greatest
flexibility in modulation formats, as information can be encoded in amplitude and phase,
or alternatively in both in-phase (I) and quadrature (Q) components of a carrier. Coherent
detection requires the receiver to have knowledge of the carrier phase, as the received
25

signal is demodulated by a LO that serves as an absolute phase reference.
3.2.2 ADC: general specifications and actual state of the art performaces
At a receiver it's possible to capture all the information in a noisy bandlimited signal
by filtering the signal to reject noise and interference outside the band of interest, and
subsequently sampling the signal at its Nyquist rate. Then, the amplitude of the signal
samples at detection is usually quantized to a discrete and finite set of values that are
represented by sampling bits. This is done by an analog-to-digital converter (ADC).
Consider a transmitted waveform and suppose that each symbol transmitted takes on
one of M (quantization levels) complex values. The combination of an ADC and
demodulator that puts out more values per sample is called a soft-decision detector and
than it leads to two scenarios for the digital demodulator and subsequent decoder. In the
first scenario, called hard-decision decoding, the demodulator decides which modulation
symbol was transmitted and passes its decision to the decoder; the decoder operates on
these hard decisions. In the second scenario, called soft-decision decoding, some or all of
the sampling bits are passed to the decoder and the decoder uses this soft information to
decode. In other words, the digital demodulator is effectively removed. Obviously, using
soft-decision decoding with many quantization levels is preferable for performance, while
using hard-decision decoding with few quantization levels reduces complexity.
ADC implementation has been shown in different semiconductor technologies.
Particulary BiCMOS technology allows for the realization of high speed ADCs. The most
promising architecture is a full-flash topology where 2Q
−1 parallel comparators are used to
convert the signal with a resolution of Q bits in a single step. ADCs can also be made with
CMOS technology, but this requires the use of a number of slower converters which are
then time interleaved to achieve a high total sampling rate. Realizing the ADCs in CMOS
technology has the important advantage that they can be combined on a single chip with
the subsequent digital signal processing. And as the digital signal processing has an
26

inherently parallel architecture this fits well with the parallel ADC architecture required for
CMOS implementation. At the time of writing, a 50-Gsample/s ADC design has only been
realized for digital storage oscilloscopes, where the power dissipation requirements are less
strict than for a transponder. The required vertical resolution of the ADCs to have a
negligible penalty resulting from quantization distortions is 5-6 bits. In order to use
available vertical resolution as effectively as possible the dynamic range of the ADC
should be fully used. This requires an automatic gain control in front of the ADCs to adapt
to changes in the received optical power, for example resulting from optical transients or
component aging. Finally, also the electrical bandwidth of the ADCs is an important design
parameter. Generally, an electrical 3-dB bandwidth of 0.5 times the baudrate is sufficient.
3.2.3 DSP: equalization
Digital (electrical) signal processing (DSP) has been emerging as a practical solution
for long-haul optical communications for some years. DSP are used for the compensation
of (linear) transmission impairments and polarization demultiplexing. One of the main
challenges is that the algorithms have to be as simple as possible to enable high-speed real
time processing.
The first stage of a coherent receiver is a dual-polarization optoelectronic
downconverter that recovers the baseband modulated signal. In a digital implementation,
the analog outputs of a dual-polarization downconverter are passed through anti-aliasing
filters with impulse responses p(t) and then sampled synchronously at a rate of 1/T =
M/KTs, where M/K is a rational oversampling ratio. Channel impairments can then be
compensated digitally before symbol detection. The LO laser is polarized at 45° relative to
the PBS, and the received signal is separately demodulated by each LO component using
two single-polarization downconverters in parallel. The four outputs are the I and Q of the
two polarizations, which has the full information of Es(t). CD and PMD are linear
distortions that can be compensated quasi-exactly in the electronic domain after
27

photodetection using a finite impulse response (FIR) filter. In theory, the use of a matched
filter in conjunction with symbol rate sampling is optimal. In practice however, symbol-
rate sampling is susceptible to sampling time errors. Fractionally spaced sampling can
overcome this.
3.2.4 DSP: carrier frequency and phase recovery
Consider the system model shown in Fig. 3.11(a), where we assume all other channel
impairments have been compensated by the digital coherent receiver, whose outputs are yk
= xk ejφk + nk, where xk is the transmitted symbol, and φk and nk are the carrier phase and
AWGN, respectively (Fig. 3.110(b)).
Fig. 3.11 - Feedforward carrier phase estimation. (a) System model, (b) soft phase
estimation, (c) analytical model
A FF phase estimator directly estimates the carrier phase and then de-rotates the
received signal by this estimate so symbol decisions can be made at low BER. The FF
phase estimator has a soft phase estimator that first computes a symbol-by-symbol estimate
ψk of φk, followed by a MMSE filter Wp(z). The symbol-by-symbol estimate is corrupted by
AWGN so that ψk = φk + n'k, where n'k is the projection of nk onto a vector orthogonal to xk
ejφk. Since φk is correlated by the Wiener process, we use a linear filter to compute an
28

MMSE estimate φ^k−Δ. Using the analytical model shown in Fig. 3.11(c), whose input is the
discrete frequency noise process vk with zero mean and variance σ2
p = 2πΔνTs, it can be
shown that the MMSE filter for Δ = 0 has coefficients:
(3.5)
where r = σ2
p / σ2
n' > 0 is the ratio between the magnitudes of frequency noise and AWGN,
and α = (1 + r/2 ) − √ [(1 + r 2)2
− 1].
3.2.5 DSP: symbol detection
Following carrier recovery, the signal may be decoded by the outer receiver. This
could take the form of a soft-decision forward error correction (FEC) using a finite field
corresponding to the symbol alphabet, or symbol estimation followed by hard-decision
FEC. In current systems, which are based on hard- decision decoding of binary data,
symbol estimation and bit decoding is required. For rectangular constellations, such as
QAM o QPSK, this may be achieved by applying a series of decision thresholds to the in-
phase and quadrature components separately. While this corresponds to the maximum
likelihood symbol estimation for a system limited by additive white Gaussian noise
(AWGN), by using nonrectangular decision boundaries, it is possible to improve the
performance for systems limited by phase noise, both linear and nonlinear.
3.2.6 FEC: hard and soft decision, foundamental limit
FEC is a method of encoding the original signal with additional error detection and
correction overhead information (i.e., parity bytes), so that optical receivers can detect and
29

correct errors that occur in the transmission path. In optical communication systems the
typical FEC overhead is 7%.
At 100G rates, leading optical suppliers are implementing third- generation FEC
capabilities to extend performance and overall optical distances even further. These third-
generation FECs are based on even more powerful encoding and decoding algorithms,
iterative coding, and something referred to as “soft-decision” FEC. In a hard-decision FEC
implementation the decoding block makes a firm decision based upon the incoming signal,
and provides a single bit of information (1 or 0) to the FEC decoder. A signal is received
and compared to a threshold; anything above the threshold is a “1” and anything below the
threshold is a “0.”
A soft-decision decoder uses additional data bits to provide a finer, more granular
indication of the incoming signal. In other words, the decoder not only determines whether
the incoming signal is a “1” or a “0” based on the threshold, but also provides a
“confidence” factor in the decision. This provides an indication of how far the signal is
from the threshold crossing. These additional “confidence” or “probability” bits are used
by the soft-decision FEC decoder, along with the stronger, more complex third-generation
FEC coding algorithms, to provide 1–2 dB of additional net coding gain. In practice, a 3-
bit confidence estimation normally provides most of the theoretically achievable
performance improvement. While 1–2 dB coding gain doesn’t sound like much, it can
translate into 20–40% improvement in overall achievable distances, which is a very
substantial improvement at 100G.
One trade-off with these more advanced, third-generation FECs is they require ~20%
overhead for the FEC bytes, compared to first- and second-generation FECs, which only
require ~7% overhead. The higher 20% FEC overhead translates to slightly higher optical
data rates, which are already operating at the edges of currently available technology at
100G.
30

Fig. 3.12 - Net Coding Gain vs Overhead
Shannon limit
For every combination of code rate, code word length, modulation format, channel
type, and received noise power, there is a theoretical lower limit on the amount of energy
that must be expended to convey one bit of information. This limit is called the channel
capacity or Shannon capacity, named after Claude Shannon, whose 1948 derivation of
channel capacity is considered to have started the applied mathematical field that has come
to be known as information theory.
Shannon proved that reliable communication over a discrete memory-less channel is
possible if the communication rate R satisfies R < C, where C is the channel capacity, and
is given by
(3.6)
where Pave is the average signal power and equals C*Eb, where Eb is the average energy
per bit, N0 the noise spectral density and B the channel bandwidth. For a linear channel
degraded by additive white Gaussian noise, the optimum constellation in phase and
quadrature components of the optical field may be calculated. To calculate the performance
31

of each constellation, it's necessary to determine the impact of noise on each constellation
point. For a system using coherent detection, the noise and signal are combined as a vector
addition and the noise is independent of the signal amplitude. It's possible to calculate the
bit error rate (BER) performance of a given constellation assuming hard decision detection,
by calculating the probability that a given transmitted bit crosses an imaginary boundary
(the decision threshold) between it and its nearest neighbour. The performance of each
format may then be compared to the Shannon capacity limit by calculating the required
SNR for a given BER and error correction code, and calculating the net information
spectral density (number of transmitted bits per hertz), taking the symbol rate and the
number of bits per symbol into account.
Current technologies to achieve the maximum possible information throughput
involve WDM where the available optical bandwidth is split into frequency bands, each of
which is modulated separately. In this case, the information spectral density C/B also
depends on the combined width of the guard bands between WDM channels.
Strong forward error correction (FEC) is essential to enable operation close to the
fundamental Shannon limit. The use of higher order modulation formats suggests that the
capacity increase is only obtained at the expense of requiring higher SNR and
implementation complexity. As the number of bits per symbol is increased, the BER
degradation increases, requiring larger FEC overheads.
Third FEC generation
A major advancement in coding theory occurred in 1993, when a group of
researchers working in France developed turbo codes. The initial results showed that turbo
codes could achieve energy efficiencies within only a half decibel of the Shannon capacity.
One of the most interesting characteristics of a turbo code is that it is not just a single
code. It is, in fact, a combination of two codes that work together to achieve a synergy that
would not be possible by merely using one code by itself. In particular, a turbo code is
formed from the parallel concatenation of two constituent codes separated by an
32

interleaver. Each constituent code may be any type of FEC code used for conventional data
communications. Although the two constituent encoders may be different, in practice they
are normally identical.
The input data stream and the parity outputs of the two parallel encoders are then
serialized into a single turbo code word.
The interleaver is a critical part of the turbo code. It is a simple device that rearranges
the order of the data bits in a prescribed, but irregular, manner. Although the same set of
data bits is present at the output of the interleaver, the order of these bits has been changed,
much like a shuffled deck of cards (although each input word is shuffled in exactly the
same way). Without the interleaver, the two constituent encoders would receive the data in
the exact same order and thus—assuming identical constituent encoders—their outputs
would be the same. This would not make for a very interesting (or powerful) code.
However, by using an interleaver, the data {Xi} is rearranged so that the second encoder
receives it in a different order, denoted {Xi'}. Thus, the output of the second encoder will
almost surely be different than the output of the first encoder .
After encoding, the entire n-bit turbo code word is assembled into a frame,
modulated, transmitted over the channel, and decoded. Let Ui represent a modulating code
bit (which could be either a systematic or parity bit) and Yi represent the corresponding
received signal. Note that while Ui can only be 0 or 1, Yi can take on any value. In other
words, while Ui is a hard value, Yi is a soft value. The turbo decoder requires its input to be
in the following form:
(3.7)
where P(Yi | Ui = j) is the conditional probability of receiving signal Yi given that the code
bit Ui = j was transmitted. Probabilistic expressions such as the one shown in the above
equation are called log-likelihood ratios (LLR) and are used throughout the decoding
process. Calculation of the above equation requires not only the received signal sample Yi,
but also some knowledge of the statistics of the channel.
For each data bit Xi, the turbo decoder must compute the following LLR:
33

(3.8)
This LLR compares the probability that the particular data bit was a one versus the
probability that it was a zero, given the entire received code word (Y1, …, Yn). Once this
LLR is computed, a hard decision on Xi can be performed by simply comparing the LLR to
zero, that is, when Λ(Xi) > 0 the hard bit estimate is X'i = 1 and when Λ(Xi) < 0, X'i = 0.
The turbo decoder uses the received code word along with knowledge of the code
structure to compute Λ(Xi). However, because the interleaver greatly complicates the
structure of the code, it is not feasible to compute Λ(Xi) simply by using a single
probabilistic processor. Instead, the turbo decoder breaks the job of achieving a global LLR
estimate Λ(Xi) into two estimation steps. In the first step, the decoder attempts to compute
equation (3.8) using only the structure of the upper encoder, while during the second step,
the decoder computes it using just the structure of the lower encoder. The LLR estimate
computed using the structure of the upper encoder is denoted Λ1(Xi) and that computed
using the structure of the lower encoder is denoted Λ2(Xi). Each of these two LLR estimates
is computed using a soft-input soft-output (SISO) processor.
34

Chapter 4
Infrastructure modelling
An optical transmission link can be defined as the physical medium over which an
information carrying optical signal propagates between a transmitter and a receiver. In the
transmitter an optical carrier, generally the output of a laser, is modulated with a bit
sequence. At the receiver, the optical signal is again converted into an electrical signal
using one or more photodiodes. After a properly decision, ideally, the transmitted bit
sequence is again obtained.
4.1 Coherent systems (uncompensated)
The rapid shift away from direct-detection receivers and towards digital coherent
receivers is fuelled by a number of technology drivers. Among others, digital coherent
receivers have spurred the use of higher-order modulation formats (e.g. quadrature phase
shift keying [QPSK]), polarization-multiplexing, the compensation of linear transmission
impairments such as chromatic and polarization-mode dispersion (PMD) as well as
improved possibilities for optical performance monitoring. On newly deployed
transmission link simplicity of the transmission link is the most important advantage of
35

Chapter 4 - Infrastructure modelling
using digital coherent receivers. It negates the need for dispersion management along the
transmission link, which in turn offers advantages in transmission latency, sparing of
dispersion compensation modules, and allows for simpler amplifier structures. In addition,
the optical performance monitoring capabilities that a digital coherent receiver offers
reduces the number of required measurements on the installed fiber base and simplifies
monitoring of transmission performance.
4.2 Amplifiers: general concepts and typical parameters
In long-haul optical transmission systems, optical amplification is nearly exclusively
used to amplify the signal in between fiber spans. One of the main advantages of optical
amplification over optical-electrical-optical conversion is that it can amplify the optical
signal independently of modulation format and bit rate. The most common type of optical
amplifiers is Erbium doped fiber amplifiers (EDFA). EDFAs are constructed by doping a
single mode fiber with Erbium (Er3+ ) ions and pumping the fiber with one or more pump
lasers. The actual optical amplification takes place in the Erbium-doped fiber with a typical
length of 10 meters, which is pumped with light from one or more laser diodes. The∼
input signal and output of the pump lasers is combined using a pump combiner, which
allows for a low insertion loss. Optical isolators are normally required in optical amplifiers
to prevent backreflections. The input isolator prevents light from the counter-directional
pump or amplified spontaneous emission (ASE) to propagate backwards out of the
amplifier input. The gain equalizing filter is necessary to ensure that all WDM channels are
amplified uniformly and that a flat output spectrum is obtained. The wavelength of the
pump signal is either around 980 nm or 1480 nm. The typical gain of an EDFA can
therefore be in excess of 40 dB. The output power of an EDFA strongly depends on the
number of pump lasers and their respective pump powers. A typical value for the EDFA
output power is 23 dBm, which is generally sufficient to amplify up to 80 WDM channels∼
in the wavelength band between roughly 1525 nm and 1570 nm.
36

Fig 4.1 - schematic of an EDFA
Amplified spontaneous emission
The most important optical noise field related to fiber-optic transmission is ASE
(Amplified Spontaneous Emission): the loss coefficient αdB of optical fibers is ~0.2 dB/km
in the 1550-nm wavelength region. Transmission over a distance L at such wavelengths
experiences αdB L dB of loss. For 2000 km, the accumulated loss is ~400 dB, an incredibly
large power attenuation of 1040
. Clearly, such an enormous attenuation cannot be bridged at
a reasonable transmit power (even when leaving aside the detrimental impact of fiber
nonlinearities) using modulation formats with a reasonable spectral efficiency in optical
fiber. Therefore optical amplification is required along the optical path if frequent opto-
electronic regenerations are to be avoided. On the downside, optical amplifiers produce
ASE together with signal amplification. One may therefore understand ASE generation in
the fiber channel from the fundamental fact that the optical fiber is a lossy transmission
medium. Spontaneous emission is the result of a spontaneous transition from an excited
state to a lower energy state in a physical medium, accompanied by the emission of a
photon. At the same time, stimulated emission is responsible for amplifying a photon
within an optical amplifier. Since stimulated emission itself takes place at random, each
signal photon passing through an optical amplifier will experience a random multiplication
factor, in addition to being accompanied by a number of randomly multiplied
spontaneously emitted photons. The resulting quantum-mechanical optical field
37

fluctuations are summarized under the term ASE. ASE can be well represented by a
random classical optical field that has the statistical properties of additive Gaussian noise.
4.3 Photonic Switches: architectures (WSS), ROADM
Reconfigurable optical add/drop multiplexers (ROADMs) are one of the key
elements in building the next-generation, dynamically reconfigurable optical networks.
ROADMs enable dynamic add/drop or express passthrough of individual wavelength
division multiplexed (WDM) channels or group of channels at network nodes without the
need for costly optical–electrical–optical (O– E–O) conversions. While the first generation
ROADMs were of degree two and supported ring or line architectures, new ROADMs are
expected to support high-degree nodes which are essential for the design and deployment
of future optical transport networks. Over time, to accommodate large topologies the
networks will evolve from several interconnected rings to large meshes, hence requiring
the intersecting node degree to increase.
For a given network, the choice of ROADM architecture and underlying technology
depends on how effectively one can address present network needs and manage unforeseen
changes. Common issues to consider are control and management plane to properly
configure the node and to perform essential signaling and switching functions as well as
mitigation of transient effects induced by optical amplifiers. Transient effects induced by
optical amplifiers play an important role in determining the ability to cascade the
ROADMs in optical networks. An optical transient is a short-time deviation from a static
power level of some of the network channels. In WDM networks, the transient may be
caused by dynamic adding or dropping of optical channels or by performing protection,
provisioning or reconfiguration in the optical layer. When even a small transient is
generated at the beginning of a chain of optical amplifiers, it accumulates in the chain and
increases in amplitude. The accumulation process is nonlinear and could grow rapidly after
passing though several amplifiers. Transient conditions of the network are directly
38

dependent on the network architecture, while the transient response of the optical amplifier
is crucial to the mitigation technology . The response is measured by gain over- and under-
shoots, settling time, gain offset, and steady state optical power fluctuations before and
after the transients. Especially, the amplifier response depends on wavelength patterns and
power of both surviving and add/drop channels, and on the rise and fall time of the
add/drop event.
ROADM architecture and technology influences cost, optical performance, and
configuration flexibility.
Wavelength selective switches (WSSs) are the latest generation of wavelength
routing devices that promise to build flexible and degree upgradeable fully functional
ROADMs. High level of integration, excellent spectral filtering properties and the ability
to support node degree upgrades have favored the WSSs over other ROADM technologies
such as wavelength blockers and integrated planar lightwave circuits. Nonetheless, in cost-
sensitive network deployments and where node upgrades are not needed the latter two
technologies are still preferred because of lower cost. Rational design of add/drop nodes
would attempt to arrive at cost-reducing solutions without compromising optical
performance and flexibility.
While providing optical transparency at network nodes, ROADMs and wavelength
cross connects (WXCs) introduce network design constraints due to the accumulation of
physical impairments. One of the critical physical impairments is in-band crosstalk, which
is considered as a serious limitation to network scaling. The in-band crosstalk is defined as
any unwanted power additions at the wavelength of the main signal of interest.
A next generation WSS is is a path reversible 1:N wavelength routing module
constructed by integrating demultiplexers (DeMUXs), optical switches based on micro-
electro-mechanical systems (MEMS), and multiplexers (MUXs). The switch provides
wavelength independent (colorless) ports, i.e., any incoming wavelength or set of
wavelengths from the incoming ports can be switched to any of the outgoing ports.
Incoming wavelengths can also be blocked or attenuated individually. A fully functional
ROADM module is constructed by using a pair of WSSs, one for the add function and one
for the drop function, as illustrated in Fig. 4.2.
39

Fig. 4.2 - 2-deg ROADM module constructed using two WSS, each for add and drop [21]
A one-directional signal flow is considered. The ports can support any number of
wavelengths, therefore a 2-deg ROADM can be upgraded up to a N - 1-deg ROADM, or to
a WXC with add and drop functionality. As shown in Fig. 4.3a, among the N service ports
of the WSS, one is dedicated to local add/drop and the remaining (N - 1) are used as cross-
connecting ports to (N - 1) ROADM modules in the node. As an alternative solution, Figs.
4.3b and c show ways of implementing ROADM modules with a reduced number of
switches, where instead of a pair of WSSs for each add and drop, one uses a combination
of a WSS and an optical splitter or combiner. Both (b) and (c) simplify the design while
maintaining the same level of flexibility in upgrading nodes of degree up to N - 1 with the
property of colorless add/drop at the local node.
Fig. 4.3 a - b - Multiple-degree ROADM architectures: (a) WSSs for add and drop; (b)
splitters for drop and WSSs for add [21]
40

Fig. 4.3 c - Multiple-degree ROADM architectures: (c) WSSs for drop and combiners for
add [21]
However, splitters and combiners introduce additional node loss, which can be
compensated by fiber amplifiers. The advantage of the configuration in Fig. 4.3a is that
cascaded WSSs provide very good overall (port-to-port) isolation, thus potentially leading
to a very low signal crosstalk. Note, however, that option (b) has the advantage of
supporting broadcasting functionality while the options (a) and (c) cannot.
It is noted that the impact of in-band crosstalk in a WSS-based ROADM varies
considerably depending on how the WSS is configured in the ROADM.
41

Chapter 5
Transmission modelling
In long-haul WDM transmission systems there are basically five dominant
limitations: OSNR, optical bandwidth, chromatic dispersion, PMD and nonlinear
impairments. The tolerance with respect to these limitations scales linearly, or even
quadratically, with the bit rate. Hence, to build robust long-haul transmission systems at
high bit rates these transmission impairments should be considered and, if possible,
compensated.
5.1 OSNR calculation: launch power, amplifiers (noise figure), loss
In the last few years, we have witnessed the extensive deployment of wavelength-
division multiplexed (WDM) networks. These systems are configured to allow multiple
channels at different wavelengths to share the same optical fiber, increasing the effective
transmission rate on that fiber. But with this new technology arose a new challenge: the
parameters providing direct information on system performance (such as the bit error rate
(BER) and BER estimation techniques like Q-factor or eye analysis) cannot be measured
directly on a multichannel system. These key parameters require spectral demultiplexing
42

Chapter 5 - Transmission modelling
prior to making an individual evaluation of the BER performance on each demultiplexed
channel. Alternatively, optical signal-to-noise ratio (OSNR) can be derived, for each
individual channel, from an optical spectrum measurement to obtain indirect information
about the performance of these channels and hence of the system.
The OSNR is defined as
OSNR = P / [2 Bref * Nase] (5.1)
where P is the average signal power (in both polarizations for polarization-multiplexed
systems), Bref is an optical reference bandwidth (typically chosen as 0.1 nm, or 12.5 GHz
at 1550 nm), and Nase is the power spectral density of the ASE in each polarization.
OSNR can be directly correlated to the BER using the following equation which
justifies the fitting function used when performing BER vs. received power:
(5.2)
A poor OSNR leads to a degraded BER: its correlation to the BER makes OSNR a
key parameter to extract from the spectrum in order to provide a preliminary performance
diagnosis of a multichannel system or to monitor the system and obtain advance warning
of a possible BER degradation on a given channel.
The IEC standard defines optical signal-to-noise ratio as the ratio of the signal power
at the peak of a channel to the noise power interpolated at the position of the peak and is
described by the following equation:
OSNR = 10log10 (Pi / Ni) + 10log10 (Bm / Bref) (5.3)
where:
• Pi is the optical signal power in watts at the ith channel;
• Bm is the resolution bandwith of the measurement;
• Ni is the interpolated value of noise power in watts measured in the resolution
bandwidth of the measurement (Bm) derived from the noise measured at the mid-
channel spacing point;
43

• Bref is the reference optical bandwidth, and the second term of the equation is used
to provide an OSNR value that is independent of the instrument’s resolution
bandwidth (Bm) for the measurement so that results obtained with different
instruments can be compared.
Fig. 5.1 - Graphical description of parameters required to measure OSNR on a
multichannel system
5.2 Filtering effects (net bandwidth)
There are two classes of “optical filters” that enter the problem of establishing a fiber
channel capacity: all-pass and bandpass filters. The first class is represented by chromatic
dispersion (CD), originating from the dispersive nature of optical fibers. The second class
is represented by the presence of optical bandpass filters at ROADMs to separate and route
individual WDM channels in an ORN. These two classes of filters are very different in
nature and impact capacity differently.
44

Fiber Chromatic Dispersion
There are two distinct origins to the dispersive nature of single-mode optical fibers:
material and waveguide. Optical fibers are made of fused silica, a material that exhibits
inherent CD. Standard single-mode fibers (SSMFs) have a waveguide dispersion smaller
than the material dispersion with a combined dispersion ≈ 17 ps/(nm * km). The CD of
fibers can be altered dramatically by designing advanced waveguide structures, with
waveguide dispersion largely exceeding material dispersion. Independent of the origins of
dispersion, the equation describing dispersive propagation in fibers can be written as
(5.4)
where β2 is the group-velocity dispersion (GVD) parameter. As its name suggests, CD
produces a spread in time of the various frequency components of a signal due to the
difference in group velocity experienced by each frequency component. As CD
accumulates, neighboring symbols start to overlap in time, with the number of symbols
overlapping increasing with the accumulation of CD. In terms of information theory, CD
introduces memory to the channel.
ROADM Filtering
Routing individual WDM channels in an ORN requires optical bandpass filters in
ROADMs. The number of ROADMs needed to route the signal from a transmitter to a
receiver can vary widely in an ORN. In order to accommodate a varying number of
ROADMs in the various optical paths, optical filters should be cascadable in their
amplitude response. Concatenating optical filters with smooth amplitude roll-off can result
in considerable spectral narrowing. In contrast, an idealized rectangular optical filter can be
concatenated an arbitrary number of times without any spectral narrowing (provided that
45

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