digital coherent receivers and advanced optical modulation ...€¦ · advanced optical modulation...

Advanced Communication Systems course, Technology and Communications Systems Master (ETSIT-UPM), Final Work 2014

Abstract—Recent advances in coherent optical receivers is

reviewed. Digital-Signal-Processing (DSP) based phase and

polarization management techniques make coherent detection

robust and feasible. With coherent detection, the complex field of

the received optical signal is fully recovered, allowing

compensation of linear and nonlinear optical impairments

including chromatic dispersion (CD) and polarization-mode

dispersion (PMD) using digital filters. Coherent detection and

advanced optical modulation formats have become a key

ingredient to the design of modern dense wavelength-division

multiplexed (DWDM) optical broadband networks. In this paper,

firstly we present the different subsystems of a digital coherent

optical receiver, and secondly, we will compare the performance

of some multi-level and multi-dimensional modulation formats in

some physical impairments and in high spectral-efficiency (SE)

and high-capacity DWDM transmissions, simulating the DSP

with Matlab and the optical network performance with

OptiSystem software.

Index Terms—Coherent Detection, DWDM, polarization

multiplexing, modulation formats, optical impairments.

I. INTRODUCTION

HE amount of traffic carried on backbone networks has

been growing exponentially over the past two decades, at

about 30 to 60% per year, depending on the nature and

penetration of services offered by various network operators in

different geographic regions [74], [9]. The increasing number

of applications relying on machine-to-machine traffic and

cloud computing could accelerate this growth the required

network bandwidth for such applications may scale with data

processing capabilities, at close to 90% per year [45]. Non-

cacheable real-time multi-media applications will also drive

the need for more network bandwidth.

The demand for communication bandwidth has been

economically met by wavelength-division multiplexed

(WDM) optical transmission systems, researched, developed,

A.Macho ( ) Departamento de Tecnología Fotónica y Bioingeniería

Escuela Técnica Superior de Ingenieros de Telecomunicación Universidad

Politécnica de Madrid, Avda. Complutense nº30

28040 Madrid, Spain

e-mail: macho.andres@tfo.upm.es

telephone: +34649994228

and abundantly deployed since the early 1990s. Figure 1

illustrates the evolution of single-channel bit rates (single-

carrier, single-polarization, electronically multiplexed;

circles), as well as of aggregate per-fiber capacities using

wavelength-, polarization-, and most recently space-division

multiplexing [41].

As can be seen from Fig. 1, WDM was able to boost the

relatively slow progress in single-channel bit rates [74].

Technologically, the steep initial growth of WDM capacities

reflects rapid advances in optical, electronic, and

optoelectronic device technologies, such as wide-band optical

amplifiers, frequency-stable lasers, and narrow-band optical

filtering components. By the early 2000s, lasers had reached

Gigahertz frequency stabilities, optical filters had bandwidths

allowing for 50-GHz WDM channel spacing, and

electronically generated and directly detected 40-Gb/s binary

optical signals started to fill these frequency slots. At this

remarkable point in time where “optical and electronic

bandwidths had met,” optical communications had to shift

from physics toward communications engineering to further

increase spectral efficiencies, i.e., to pack more information

Digital Coherent Receivers

and Advanced Optical Modulation Formats

in 100 and 200 Gb/s DWDM Systems

Andrés Macho, Student Member, IEEE

Fig. 1. Evolution of single-channel capacity during the last two decades and aggregate capacities using WDM (red), PDM (blue), and space-division

multiplexing (SDM; yellow). This figure has been inserted from reference

into the limited ( -THz) bandwidth of the commercially most

attractive class of single-band (C- or L-band) optical

amplifiers. Consequently, by 2002 high-speed fiber-optic

systems research had started to investigate new modulation

formats using direct detection.

With the drive towards per-channel bit rates of 100 Gb/s in

2005 [69], however, it became clear that additional techniques

were needed if 100-Gb/s channels were to be used on the by

then widely established 50-GHz WDM infrastructure,

supporting a spectral efficiency of 2 b/s/Hz [70], [75]. In this

context, polarization-division multiplexed (PDM) allowed for

a reduction of symbol rates, which brought 40 and 100-Gb/s

optical signals.

At this point coherent optical receivers emerged as the main

area of interest in broadband optical communications due to

the high receiver sensitivities which they can achieve. They

have since been combined with digital post-processing to

perform all-electronic CD and PMD compensation, frequency-

and phase locking, and polarization demultiplexing. The use

of coherent optical receivers with the combination of

advanced modulation formats has led to increase the long

transmission distances and high spectral efficiencies required

for the current commercial core optical networks.

In this paper, we discuss the operation of digital coherent

optical receivers considering each of the subsystems required

and we analyze higher-order coherent optical modulation

formats as the underlying technology that has fueled capacity

growth over the past years. The paper is organized as follows.

Section II focuses in the basics of coherent receiver structure

and DSP algorithms for CD and PMD equalization, and phase

recovery of the two main modulation formats employed in

high-capacity DWDM networks: PDM-QPSK and PDM-

16QAM. Section III reviews the main advanced modulation

formats, analyzes their tolerance to some physical

impairments and presents three high SE DWDM

transmissions. Finally, in Section IV the paper concludes with

a discussion of the main results obtained in this work.

II. SUBSYSTEMS OF A DIGITAL COHERENT RECEIVER AND

DIGITAL-SIGNAL-PROCESSING

In coherent optical communication, information is encoded

onto the electrical field of the lightwave; decoding entails

direct measurement of the complex electric field. To measure

the complex electric field of the lightwave, the incoming data

signal (after fiber transmission) interferes with a local

oscillator (LO) in an optical 90° hybrid as schematically

shown in Fig. 2. If the balanced detectors in the upper

branches measure the real part of the input data signal, the

lower branches, with the LO phase delayed by 90°, will

measure the imaginary part of the input data signal. For

reliable measurement of the complex field of the data signal,

the LO must be locked in both phase and polarization with the

incoming data.

Phase and polarization management turned out to be the

main obstacles for the practical implementation of coherent

receivers. The state of polarization of the lightwave is

scrambled in the fiber. Dynamic control of the state of

polarization of the incoming data signal is required so that it

matches that of the LO. Each dynamic polarization controller

is bulky and expensive [42]. For DWDM systems, each

channel needs a dedicated dynamic polarization controller.

The difficulty in polarization management alone severely

limits the practicality of coherent receivers. Phase locking is

challenging as well. All coherent modulation formats with

phase encoding are usually carrier suppressed. Therefore,

conventional techniques such as injection locking and optical

phase-locked loops cannot be directly used to lock the phase

of the LO. Instead, decision-directed phase-locked loops must

be employed. Both phase and polarization management can be

realized in the electrical domain by using DSP. Moreover,

coherent detection in conjunction with DSP enables

compensation of fiber-optic transmission impairment, opening

up new possibilities that will likely shape the future of optical

transmission technology.

In a digital coherent receiver, there are four key subsystems:

1) Optical front-end, which linearly maps the optical field

into a set of electrical signals.

2) ADC, which converts from the electrical signals into a set

of discrete-time-quantized signals at the sampling rate.

3) Digital demodulator, which converts the digital samples

into a set of signals at the symbol rate.

4) Outer receiver, which includes error correction and whose

functionality is to optimally decode the demodulated

signals in order to produce the best estimate of the

Fig. 2. Polarization and phase diverse coherent receiver composed by a pair

of optical of 90º hybrids and four pairs of balanced photodiodes. PBS (Polarization Beam Splitter). PC (Polarization Controller).

Fig. 3. Different subsystems of a digital coherent optical receiver. This figure has been inserted from reference [25].

sequence of bits, which were encoded by the transmitter.

We shall focus on the first three of these subsystems, which

form the inner receiver, whose functionality is to produce a

“synchronized channel,” which is as close as possible to the

information theoretic communication channel.

In order to discuss the DSP contained in the digital

demodulator, we begin by considering the structural level

design of the DSP, as can be seen in Fig. 3. While for a

particular digital coherent receiver, the subsystems employed

may differ slightly from those detailed in Fig. 3, they give

some indication as to the design choices, which can be made

at a structural level, such as the ordering of the subsystems.

Additional considerations at the structural level include the

combining or partitioning of subsystems, for example, the

carrier phase estimation may be separated into estimating the

frequency offset and the residual carrier phase. It is possible to

perform joint carrier phase and symbol synchronization [31].

We shall focus on the structural and algorithmic level rather

than the implementation level, where the finite resources, such

as machine precision and clock speed are considered. In order

to discuss performance of the digital coherent receiver at the

algorithmic level, we will restrict our discussion to one

possible realization, where the subsystems are arranged, as in

Fig. 3, including the “inner receiver” and the “outer receiver,”

which performs symbol estimation and decoding.

There are numerous feedback paths between the subsystems.

Some of these paths occur naturally, such as between the

phase estimation subsystem and frequency estimation

subsystem, however, other paths depend on the algorithms

employed. For example, feedback from the symbol estimation

and decoding subsystem is required for data-aided algorithms,

but not for blind algorithms. Likewise, for synchronous

sampling at the baud rate, feedback would be required from

the timing-recovery subsystem to the ADC subsystem, which

could be omitted for asynchronous sampling. In the

subsequent sections of this paper, we shall discuss each of

these subsystems independently, forming a basis for

understanding the operation of a digital coherent receiver

employing feedback between the subsystems.

A. Phase and Polarization Diverse Coherent Optical

Receiver

The functionality of the optical front-end, being both phase

and polarization diverse, is to linearly map the incoming

optical field into the electrical domain. To realize this

functionality, the architecture is shown in Fig. 2, is often

employed, which employs a pair of 90º hybrids, one for each

polarization [42]. The received signal interferes inside an

optical hybrid with a LO-signal provided by another CW-laser

converting both quadratures of X-and Y-polarization into the

electrical domain. Both the LO- and transmitter laser have

phase noise, which can be modeled as a random walk process

of the variance 𝜎2 = 2𝜋 ∙ ∆𝜗 ∙ 𝑑𝑡 with ∆𝜗 representing the

laser linewidth and 𝑑𝑡 is the time between two observations.

Typical laser linewidths range from ~100 kHz, corresponding

to commercially available external cavity lasers (ECL), up to a

few MHz for a conventional DFB laser. The LO-laser is

usually free running within ~1 GHz of the optical frequency of

the transmit laser, which is referred to as intradyne detection.

In this case, the remaining frequency offset is compensated

digitally, e.g., by applying a higher-order nonlinearity to the

signal and estimating the offset from the spectrum.

A four port phase- and polarization-diversity hybrid may be

used with single-ended detection, resulting in the four

photocurrents given in (1):

[ 𝑖𝐼𝑋(𝑡)𝑖𝑄𝑋(𝑡)

𝑖𝐼𝑌(𝑡)

𝑖𝑄𝑌(𝑡)]

[ 𝑅𝑒{𝐸𝑋𝐸𝐿𝑂

∗ } +1

2|𝐸𝑋|

4|𝐸𝐿𝑂|

𝐼𝑚{𝐸𝑋𝐸𝐿𝑂∗ } +

2|𝐸𝑋|

4|𝐸𝐿𝑂|

𝑅𝑒{𝐸𝑌𝐸𝐿𝑂∗ } +

2|𝐸𝑌|

4|𝐸𝐿𝑂|

𝐼𝑚{𝐸𝑌𝐸𝐿𝑂∗ } +

2|𝐸𝑌|

4|𝐸𝐿𝑂|

Each of the photocurrents consists of three terms: a coherent

detection term (leftmost), a signal complex envelope term

(center), and an LO complex envelope term (rightmost).

Although the LO complex envelope term is constant (and may

therefore be removed with AC coupling), the signal complex

envelope is time varying and must be minimized relative to

the coherent detection term by making the LO much more

powerful than the signal.

To overcome the constraints imposed on signal-LO power

ratios, balanced photo-detection is often employed for

coherent optical receivers. In this scenario, an 8 port optical

hybrid is used, with a 180º phase shift between each

quadrature pair. The pairs of outputs are then differentially

amplified to eliminate the direct-detection components in the

signal. The eight output ports of the hybrid are given by:

[ 𝑖𝐼𝑋+(𝑡)

𝑖𝐼𝑋−(𝑡)

𝑖𝑄𝑋+(𝑡)

𝑖𝑄𝑋−(𝑡)

𝑖𝐼𝑌+(𝑡)

𝑖𝐼𝑌−(𝑡)

𝑖𝑄𝑌+(𝑡)

𝑖𝑄𝑌−(𝑡)]

2𝑅𝑒{𝐸𝑋𝐸𝐿𝑂

∗ } +1

4|𝐸𝑋|

8|𝐸𝐿𝑂|

2𝑅𝑒{𝐸𝑋𝐸𝐿𝑂

∗ } +1

4|𝐸𝑋|

8|𝐸𝐿𝑂|

2𝐼𝑚{𝐸𝑋𝐸𝐿𝑂

∗ } +1

4|𝐸𝑋|

8|𝐸𝐿𝑂|

2𝐼𝑚{𝐸𝑋𝐸𝐿𝑂

∗ } +1

4|𝐸𝑋|

8|𝐸𝐿𝑂|

2𝑅𝑒{𝐸𝑌𝐸𝐿𝑂

∗ } +1

4|𝐸𝑌|

8|𝐸𝐿𝑂|

2𝑅𝑒{𝐸𝑌𝐸𝐿𝑂

∗ } +1

4|𝐸𝑌|

8|𝐸𝐿𝑂|

2𝐼𝑚{𝐸𝑌𝐸𝐿𝑂

∗ } +1

4|𝐸𝑌|

8|𝐸𝐿𝑂|

2𝐼𝑚{𝐸𝑌𝐸𝐿𝑂

∗ } +1

4|𝐸𝑌|

8|𝐸𝐿𝑂|

After differential amplification, this becomes the four-

dimensional signal given by:

[ 𝑖𝐼𝑋(𝑡)𝑖𝑄𝑋(𝑡)

𝑖𝐼𝑌(𝑡)

𝑖𝑄𝑌(𝑡)]

[ 𝑅𝑒{𝐸𝑋𝐸𝐿𝑂

𝐼𝑚{𝐸𝑋𝐸𝐿𝑂∗ }

𝑅𝑒{𝐸𝑌𝐸𝐿𝑂∗ }

𝐼𝑚{𝐸𝑌𝐸𝐿𝑂∗ }]

The received signal defined by (3) represents the ideal

coherently received optical field, which is: no direct-detection

terms, infinite common-mode rejection between differential

pairs and perfectly matched optical path lengths in the hybrid

resulting in an exact 90º difference between quadratures.

Ideally, the I and the Q channels of a quadrature

communication system are orthogonal to each other. However,

implementation imperfections (e.g., incorrect bias points

settings for the I, Q, and phase ports, imperfect splitting ratio

of couplers, photodiodes responsivity mismatch, and

misadjustment of the polarization controllers) can create

amplitude and phase imbalances that destroy the orthogonality

between the two received channels and degrade performance

of the quadrature system. Also, in practice, phase diversity

receivers are vulnerable to imperfections in the optical 90º

hybrid, which result in dc offsets and both amplitude and

phase errors in the received signals. These effects give rise to

quadrature imbalance in a communication system.

All of these imperfections, can in principle, be compensated

digitally, thereby relaxing the requirements on the optical

components. While blind source separation techniques, such

as independent component analysis could be used [25], it is

often possible to simplify this problem, reducing it to finding

two pairs of mutually orthogonal components 𝐸𝑥𝐼 , 𝐸𝑦

𝐼 , 𝐸𝑥𝑄 , 𝐸𝑦

In the field of DSP, there are numerous techniques to achieve

this for creating orthogonal components, such as the Gram–

Schmidt orthogonalization algorithm (see subsection II.C).

B. Analog-to-Digital Conversion

Having mapped the signal from the optical domain into the

electrical domain, the next stage is to convert the analog

signals into a set of digital signals. From a functional view, we

can consider the ADC to be made up of two subsystems, a

sampler, which samples the signal in time, converting the

continuous time analog signal into a discrete-time analog

signal, followed by a quantizer, which converts the discrete-

time analog signal into a finite set of values determined by the

bits of resolution in the ADC.

For a digital communication system, which transmits

symbols at a rate of Rs symbols per second, the minimum

sampling rate is Rs (in hertz). In general, however, for

asynchronous sampling a sampling rate of 2·Rs Hz, is

advantageous, giving rise to two samples per symbol, thereby

enabling digital timing recovery. While in practice, there may

be a slight difference between clocks of the transmitter and the

receiver, the signal may be resampled by interpolating of the

digital signal, which will be discussed in subsection II.F.

The receive-side ADC, usually specified in terms of its

effective number of bits (ENoB). As shown in [65], the

required ADC resolution at a 1-dB receiver sensitivity penalty

and at a pre-FEC bit error ratio (BER) typical of coded

systems (e.g., is approximately 3 bits more than what would

be needed to recover the √𝑀 amplitude levels of the two

signal quadratures if the constellation were received without

any distortions and phase rotations. The technological trade-

off between ADC resolution and bandwidth is analyzed in a

series of papers by Walden [56], [57], and reveals a reduction

of about 3.3 ENoB per decade of analog input bandwidth.

C. Orthogonalization: front-end imperfection compensation

The functionality of this subsystem is to recover the

orthogonality between the I and Q components in each

polarization transmitted. Ideally, the I and the Q channels of a

quadrature communication system are orthogonal to each

other.

However, as we can see in Fig. 4 (constellations simulated

with OptiSystem) the main optical impairments (chromatic

dispersion, polarization-mode dispersion and fiber Kerr

nonlinearities) and hardware imperfections (e.g., incorrect bias

points settings for the I, Q, and phase ports, imperfect splitting

ratio of couplers, photodiodes responsivity mismatch, and

misadjustment of the polarization controllers) can create

amplitude and phase imbalances that destroy the orthogonality

between the two received channels and degrade performance

of the multilevel modulation formats. Also, in practice, phase

diversity receivers are vulnerable to imperfections in the

optical 90º hybrid, which result in dc offsets and both

amplitude and phase errors in the received signals. These

effects give rise to quadrature imbalance in a digital

communication system.

The Gram–Schmidt orthogonalization procedure (GSOP)

enables a set of nonorthogonal samples to be transformed into

a set of orthogonal samples. Given two nonorthogonal

components of the received signal, denoted by 𝑟𝐼(𝑡) and 𝑟𝑄(𝑡),

the GSOP results in a new pair of orthonormal signals,

denoted by 𝐼0(𝑡) and 𝑄0(𝑡), as follows:

Fig. 4. (a) QPSK constellation imbalanced due to the photodiodes responsivity mismatch at the quadrature receiver structure. (b) I and Q

channels imbalanced in a homodyne receiver due to misalignment between

the axes of the two PBS inside of the quadrature receiver. (c) I and Q channels imbalanced in a heterodyne receiver due to misalignment between

the axes of the two PBS inside of the quadrature receiver. (d) Correction of

nonorthogonality in the above case using GSOP in OptiSystem.

𝐼0(𝑡) =𝑟𝐼(𝑡)

√𝑃𝐼 (4)

𝑄′(𝑡) = 𝑟𝑄(𝑡) −𝜌 ∙ 𝑟𝐼(𝑡)

𝑃𝐼 (5)

𝑄0(𝑡) =𝑄′(𝑡)

√𝑃𝑄 (6)

Where 𝜌 = 𝐸{𝑟𝐼(𝑡) ∙ 𝑟𝑄(𝑡)} is the correlation coefficient,

𝑃𝐼 = 𝐸{𝑟𝐼2(𝑡)}, 𝑃𝑄 = 𝐸{𝑟𝑄

2(𝑡)}. Fig. 4(c)-(d) shows an

example where de GSOP has been applied to a nonorthogonal

set of data with quadrature imbalance and an intermediate

frequency (IF) of 100 MHz. The GSOP corrects the mismatch

and transforms the ellipse into a circle, with the thickness

determined by the amount of noise. The orthogonality for

received signals with quadrature imbalance can thus be

restored using (4)–(6) with the amplitudes of the recovered

signals normalized correctly [34].

D. Fixed Equalization

The main driver for coherent optical communication is the

possibility to compensate for transmission impairments by

using DSP. This is possible only when both the phase and the

magnitude of the complex field of light are detected. All linear

impairments in fiber-optic transmission systems can

potentially be compensated, in particular GVD and PMD.

While in principle equalization could be realized in one

subsystem, it is generally beneficial to partition the problem

into static and dynamic equalization.

GVD compensation requires static equalization with large

static filters. In contrast, dynamic equalization requires

adaptive equalization with a set of relatively short adaptive

filters to compensate the rotation of the state-of-polarization

(SOP) of the signal, which is essential to polarization

demultiplexing and to compensate de PMD effects.

D.1 GVD compensation

Dispersion in optical fiber is an all-pass filter on the electric

field of the lightwave, given by a complex transfer function in

the frequency domain [61], [70], [41, Ch. 5]:

𝐻𝑓(𝜔) ≈ 𝑒𝑥𝑝 {+𝑗𝐷 ∙ 𝐿 ∙ 𝜆0

4𝜋𝑐0𝜔2 − 𝑗

𝑆 ∙ 𝐿 ∙ 𝜆04

24𝜋2𝑐02 𝜔3} (7)

With coherent detection, the effect of dispersion can be

reversed or compensated by a filter with a transfer function

given by 𝐻𝑓∗(𝜔). Such a filter can be realized by using a FIR

filter, as shown in Fig. 5, with coefficients given by the

discrete inverse Fourier transform of:

𝑏𝑛 =1

𝑁∑𝐻𝑓

∗(𝜔𝑘)

𝑁−1

𝑘=0

∙ 𝑒𝑗𝜔𝑘𝑛 ; ∀ 𝑛 ∈ {0,1, … , 𝑁 − 1} (8)

In this expression, 𝑁 is the number of taps of the filter,

given by 𝑁 = 0,032 ∙ 𝐶𝐷 (𝑛𝑠/𝑛𝑚) ∙ 𝑅𝑠2 [25], where CD is

the accumulated chromatic dispersion in the lightpath and 𝑅𝑠 is the symbol rate. In Section III we will demonstrate with

Matlab&OptiSystem simulation the CD compensation for

112-Gb/s PDM-NRZ-QPSK after 1500 km of transmission.

Fig. 6 shows the constellation diagrams of one polarization

before and after CD compensation. In an uncompensated

optical coherent transmission link the signal launched to the

fiber loses its deterministic nature and becomes in a signal like

“Gaussian Noise” [1]. In this situation the initial QPSK

constellation becomes in a Gaussian constellation. After CD

compensation the ISI induced by CD is eliminated, but there

will still be ISI due to crosstalk between polarizations and

carrier frequency and phase offset (see subsection II.G). For

this reason after CD compensation the QPSK constellation

forms the shape of a ring.

Alternatively, the dispersion compensation filter in the

digital domain can be realized by using an infinite impulse

response (IIR) filter, which was shown to be more

computationally efficient but requires buffering.

D.2. Nonlinearities compensation

Nonlinear impairments can be compensated by using

electronics or DSP, because propagation in optical fiber is

well described mathematically by the Generalized Nonlinear

Schrödinger Equation (GNLSE) [5]. Nonlinear impairments

can be precompensated at the transmitter or postcompensated

at the receiver. Because of fiber dispersion and nonlinearity,

the received signal is different from the transmitted signal. To

ensure that the received signal is identical to the transmitted

signal, virtual fibers, with signs of dispersion and nonlinearity

opposite to those of the physical transmission fiber, must be

added in the DSP domain in the transmission system. In the

precompensation of nonlinear impairments, the virtual fiber is

placed between the input data stream and the external

modulator so that the signal is predistorted by the virtual fiber

while being compensated through the real transmission fiber.

Several electrical precompensation schemes have been

Fig. 5. Structure of a FIR filter for chromatic dispersion compensation in the time domain [Kaminow13, Ch. 5].

Fig. 6. QPSK constellation diagram for the ‘x polarization’ at the receiver

(a) before and (b) after CD compensation.

Fig. 5. Structure of a FIR filter for chromatic dispersion compensation in the (a) time domain and (b) in the frequency domain [41, Ch. 5].

Fig. 6. QPSK constellation diagram for the ‘x polarization’ at the receiver

(a) before and (b) after CD compensation.

demonstrated to compensate for chromatic dispersion or

nonlinearity in single-channel or WDM systems [48], [42],

[24]. In the postcompensation of nonlinear impairments, the

virtual fiber is placed after coherent detection so that the

signal is distorted in the real transmission fiber while being

compensated through the virtual fiber. Postcompensation

using coherent detection and DSP has been shown to be very

effective in chromatic dispersion compensation and

intrachannel nonlinearity compensation [42].

While the complexity may be reduced using wavelets [26],

nonlinear compensation based on one step per span may still

be prohibitive to implement in hardware. Nevertheless, it

provides a benchmark against which simpler compensation

schemes may be compared, such as the three block models

Hammerstein–Wiener (NLN), the Wiener-Hammerstein

(LNL) [18], with the challenge being to improve the nonlinear

tolerance of the system without making the DSP prohibitive to

implement.

E. Adaptive Equalization

The purpose of this subsystem is to compensate the PMD

degradation and to eliminate the crosstalk between the two

polarizations of the received PDM signal. This crosstalk arises

due to the misalignment between the SOP of the received

signal and the axes of the initial PBS in Fig. 2. The key is to

observe the analogy between dual-polarization optical systems

and multiple-input–multiple-output (MIMO) radiofrequency

wireless communications. As a result, algorithms for wireless

MIMO channel estimation can be readily applied to

polarization demultiplexing in optical polarization MIMO [7].

The schematic of an optical polarization MIMO system is

shown in Fig. 7. In the transmitter, two synchronous data are

modulated in orthogonal polarizations. The modulation format

can be amplitude and/or phase modulation. 𝐸𝑥 and 𝐸𝑦 are the

complex representation of the modulated signals in each

polarization. After transmission through the optical fiber, the

polarization of the lightwave is usually rotated due to the

anisotropic nature of the fiber. For an arbitrarily orientated

axes of the first PBS of the receptor, the received signal 𝐸𝑥′

and 𝐸𝑦′ , contains significant crosstalk between the original

SOP transmitted. The Jones vector at the transmitter and at the

receiver are related by the unitary Jones matrix of the optical

fiber:

(𝐸𝑥′

𝐸𝑦′ ) = 𝐿 ∙ (

𝐽𝑥𝑥 𝐽𝑥𝑦𝐽𝑦𝑥 𝐽𝑦𝑦

) ∙ (𝐸𝑥𝐸𝑦) (9)

Where 𝐿 is a real scalar describing the optical loss from the

input to the output, and the polarization change due to fiber is

described by the Jones matrix 𝑱. Equation (9) describes a 2x2

MIMO system, as shown in Fig. 7. Neglecting the polarization

dependent loss (PDL), this MIMO system, in theory, can

transmit two synchronous channels without any penalty [41,

Ch. 1], and consequently the Jones matrix 𝑱 is unitary. It

should be noted that PDL makes the channel polarization

matrix non-unitary, leading to penalties in electronic

polarization demultiplexing and complication in channel

polarization matrix estimation.

Because of environment variations, the polarization of the

lightwave in fiber generally drifts with time. The rate of this

polarization drift is generally much slower than the symbol

rate. Therefore, the system can be designed to estimate the

Jones matrix 𝑱 for the entire frame by using a training

sequence in the preamble of each frame to remove polarization

crosstalk.

Various channel estimation algorithms can be used to

estimate 𝑱. Considering the high data rate used in optical

communications, the least-mean-squares (LMS) algorithm

based in the minimum-mean-square error (MMSE) criteria

was widely used initially. The Jones Matrix of the optical

system can be estimated by using the following iterative

algorithm:

𝑱𝑖 = 𝑱𝑖−1 + 𝜇 [(𝐸𝑥′

𝐸𝑦′ )⌋

− 𝐿 ∙ 𝑱𝑖−1 ∙ (𝐸𝑥𝐸𝑦)⌋𝑖

] ∙ 𝐿 ∙ (𝐸𝑥𝐸𝑦)⌋𝑖

⏟ 𝑖≥0 𝑎𝑛𝑑 𝑱−1𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑜𝑛

Where 𝜇 is a positive step size, 𝑖 is the iteration index, and

𝐿 are the optical losses in the lightpath. The inverse of

estimated matrix 𝑱 can then be applied to the received signals

to recover the transmitted data 𝐼𝑋, 𝑄𝑋, 𝐼𝑌 and 𝑄𝑌 with a set of

filters in a butterfly structure with adaptive taps (Fig. 8). Since

𝑱 is a unitary matrix, its inversion and conjugate transpose are

identical. In optical polarization MIMO systems, the received

signal polarization estimation and tracking are performed by

Fig. 7. Analogy between wireless MIMO and optical PDM [41, Ch. 5].

Fig. 8. Butterfly structure for polarization demultiplexing and polarization-

mode dispersion compensation.

DSP algorithms, and no optical dynamic polarization control

is required at the receiver.

However, it is possible to estimate the Jones matrix of the

optical channel without relying on a training sequence if there

exist statistical properties of the transmitted symbols that can

be exploited. In particular, for PDM systems using constant-

intensity modulation formats such as M-(D)PSK, the Jones

matrix can be estimated using the fact that the modulus of the

received signal should be constant [3]. Without loss of

generality, let us assume that the constant modulus is unity.

An estimate of the Jones matrix is obtained by minimizing the

mean squared errors ⟨휀𝑥,𝑦2 ⟩ of the quantities 휀𝑥,𝑦 = 1 −

|𝐸′𝑥,𝑦|2. In order to do so, the gradient of the mean squared

error with respect to the appropriate elements of the Jones

matrix should vanish, i.e.:

𝜕휀𝑥2

𝜕𝐽𝑥𝑥= 0,

𝜕휀𝑥2

𝜕𝐽𝑥𝑦= 0,

𝜕휀𝑦2

𝜕𝐽𝑦𝑥= 0,

𝜕휀𝑦2

𝜕𝐽𝑦𝑦= 0 (11)

To obtain the estimate of the channel Jones matrix, it is

initialized as an identity matrix. Subsequently, the matrix

elements are updated by using the stochastic gradient

algorithm of [16] as follows:

𝐽𝑥𝑥 ⟶ 𝐽𝑥𝑥 + 𝛿 ∙ 휀𝑥 ∙ 𝐸𝑥 ∙ 𝐸𝑥′ ∗ (12)

𝐽𝑥𝑦 ⟶ 𝐽𝑥𝑦 + 𝛿 ∙ 휀𝑥 ∙ 𝐸𝑥 ∙ 𝐸𝑦′ ∗ (13)

𝐽𝑦𝑥 ⟶ 𝐽𝑦𝑥 + 𝛿 ∙ 휀𝑦 ∙ 𝐸𝑦 ∙ 𝐸𝑥′ ∗ (14)

𝐽𝑦𝑦 ⟶ 𝐽𝑦𝑦 + 𝛿 ∙ 휀𝑦 ∙ 𝐸𝑦 ∙ 𝐸𝑦′ ∗ (15)

Where * denotes complex conjugate, (𝐸𝑥 , 𝐸𝑦) is the

demultiplexed optical field and 𝛿 is the positive convergence

parameter. This algorithm is known as Constant Modulus

Algorithm (CMA). The CMA was proposed by Godard in

[16], as a means of blind equalization for QPSK signals in the

1980s. In M-QAM systems it is found that the classic CMA

becomes much less effective and therefore can no longer be

used as a stand-alone equalization algorithm. This is because

an M-QAM signal does not present constant symbol

amplitude. As a result, the CMA error signal will not approach

zero even for an ideal M-QAM signal, resulting in extra noise

after equalization. To address this issue, we can use in the

DSP the multi-modulus algorithm (CMMA). Due to the limit

extension of this work we cannot go into details, but the reader

can obtain more information in [75].

In connection with Fig. 6, after CD compensation, the two

polarizations of 112-Gb/s PDM-NRZ-QPSK have been

demultiplexed with Matlab and the PMD degradation has been

compensated as well. Figure 9 (a)-(b) shows the constellation

diagrams of ‘x-polarization’ before and after adaptive MIMO

equalization. The ISI due to crosstalk between the two

polarizations of the signal is eliminated, so the thickness of the

ring constellation is reduced. Besides, we have simulated 220-

Gb/s PDM-RZ-16QAM with OptiSystem (see Section III) and

we have processed the received signal after 1000 km (in this

case the CMMA is implemented in OptiSystem software). The

results before and after MIMO equalization are shown in Fig.

9 (c) and (d) for ‘x-polarization’.

F. Interpolation and Timing Recovery

Having equalized for the channel impairments, it becomes

possible to compensate for the difference between the symbol

clock and the ADC sampling rate. In principle, it is entirely

possible to operate the entire ASIC using only the ADC

sampling rate, however, an alternative is to consider

partitioning the ASIC, such that one part operates using the

ADC clock and the second part uses a derived symbol clock.

For synchronous sampling at the baud rate, feedback would be

required from the timing-recovery subsystem to the ADC

subsystem, which could be omitted for asynchronous

sampling. The task of the interpolating subsystem is to obtain

samples 𝑦[𝑘]at time 𝑡 = 𝑡0 + 𝑘𝑇𝑠𝑦𝑚 given samples 𝑥[𝑖] at 𝑡 =

𝑖 ∙ 𝑇𝐴𝐷𝐶 .

F.1 Interpolation

Interpolation draws on the mathematical theory of

approximation theory, using Lagrange polynomials or splines

to interpolate a sampled function. To illustrate the principle, if

𝑥[𝑖] are our samples at 𝑡 = 𝑖 ∙ 𝑇𝐴𝐷𝐶 + 𝜇 ∙ 𝑇𝐴𝐷𝐶 , where 𝑖 is an

integer and 0 ≤ 𝜇 < 1, then it is possible to create a

continuous-time approximation of the form:

𝑦(𝑡) = ∑𝑥[𝑖]𝜑𝑖(𝑡 − [𝑖 ∙ 𝑇𝐴𝐷𝐶 + 𝜇 ∙ 𝑇𝐴𝐷𝐶])

where 𝜑𝑖(𝑡) are a set of interpolation functions Hence, if we

resample this signal at a time 𝑡 = 𝑘 ∙ 𝑇𝑠𝑦𝑚 + 휀 ∙ 𝑇𝑠𝑦𝑚, where 𝑘

Fig. 9. QPSK constellation diagram for the ‘x polarization’ at the receiver (a)

before and (b) after polarization demultiplexing and PMD compensation. 16-

QAM constellation -‘x polarization’- (c) before and (d) after polarization

demultiplexing and PMD compensation.

is an integer and 0 ≤ 휀 < 1, then the samples 𝑦[𝑘] will be

given by:

𝑦[𝑘] = ∑𝑥[𝑖]𝜑𝑖(𝑘𝑇𝑠𝑦𝑚 + 휀𝑇𝑠𝑦𝑚 − [𝑖𝑇𝐴𝐷𝐶 + 𝜇𝑇𝐴𝐷𝐶])

such that the output is a linear combination of the inputs, and

hence, may be realized as an FIR filter. For the case of linear

interpolation, the samples 𝑦[𝑘] will be a linear combination of

𝑥[𝑖] and 𝑥[𝑖 + 1]. Linear interpolation forms the basis of

higher order approximations, such as cubic interpolation or

step interpolation. Nevertheless, as the degree of the

approximation is increased, it does not necessarily follow that

the quality of the approximation improves, indicating that step

interpolation outperforms linear or cubic interpolation [23],

[44], [58].

F.2 Timing Recovery

The timing recovery has been a topic of extensive research

[31] with both non-data-aided and data-aided [37] algorithms

being employed. One such algorithm aims to maximize the

squared modulus |𝑦(𝑚𝑘, 𝜇𝑘)|2 of the interpolated signal

𝑦[𝑘] = 𝑦(𝑚𝑘, 𝜇𝑘) [31]. Differentiating |𝑦(𝑚𝑘 , 𝜇𝑘)|2 with

respect to time gives the error signal as follows:

𝑒(𝑚𝑘) =𝑑

𝑑𝑡(|𝑦(𝑚𝑘, 𝜇𝑘)|

≈ 2𝑅𝑒 {𝑦(𝑚𝑘, 𝜇𝑘)[𝑦(𝑚𝑘 + 1, 𝜇𝑘) − 𝑦(𝑚𝑘 − 1, 𝜇𝑘)]

2𝑇𝑠𝑦𝑚} (18)

with this error signal going to zero when the signal is

synchronized. We may use this error signal 𝑒(𝑚𝑘) to update

𝑤𝑘, our estimate of 𝑇𝑠𝑦𝑚/𝑇𝐴𝐷𝐶 , such that:

𝑤𝑘+1 = 𝑤𝑘 +∑ 𝑐[𝑖] ∙

𝑁−1

𝑖=0

𝑒(𝑚𝑘−𝑖) (19)

where the error signal is filtered by an FIR filter of length N with coefficients 𝑐[𝑖], which incorporate the convergence

factor for this stochastic gradient method.

G. Carrier Frequency and Phase Estimation

Given the structural design of the DSP, we have elected to

separate the bulk frequency estimation from the carrier

recovery. We can model the received signal such a:

𝑥𝑖𝑛[𝑘] = 𝑥𝑠𝑦𝑚[𝑘]𝑒𝑥𝑝 (𝑗(𝜃𝑠[𝑘] + 𝜃𝑒[𝑘] + 2𝜋∆𝑓 ∙ 𝑘 ∙ 𝑇𝑠𝑦𝑚)) (20)

The phase ambiguity generated due to the linear and

nonlinear impairments induces a rotation of the symbols in the

constellation. This rotation in the symbol phase can be

classified in a carrier phase offset much slower than symbol

rate (less than ~10 MHz due to CD, PMD and fiber Kerr

nonlinearities) and in a faster phase rotation due to laser

frequency mismatch (less than ~5 GHz due to phase and

frequency laser noise). With the separation of the frequency

estimation and carrier recovery subsystems we can not only

reduce the amount of phase, which the carrier recovery

subsystem has to track, but also it improves the efficacy of the

carrier recovery, since many phase estimation schemes are

only unbiased in the presence of zero frequency offset. The

task of the frequency estimation subsystem is to estimate ∆𝑓,

while the phase recovery module obtains 𝜃𝑠[𝑘].

G.1 Frequency Recovery

There are many algorithms to estimate the frequency offset

in the received signal, which can be classified in two main

groups: differential phase-based methods and spectral

methods. In this paper we only mention the frequency

estimation proposed by the spectral methods but the reader can

obtain more information about differential phase-based

methods in [30], [2], [59]. For QPSK and M-QAM symbols

∆𝑓 may be estimated by:

∆𝑓 = argmax∆𝑓

∑𝑥𝑖𝑛4 [𝑘]𝑒𝑥𝑝(−𝑗8𝜋𝑘∆𝑓𝑇𝑠𝑦𝑚)

𝑘=1

which may be implemented by observing the peak in the

spectrum of 𝑥𝑖𝑛4 . In practice, the number of frequency points

may be insufficient to give an accurate estimate of the

frequency, however, an iterative method may be used to

improve this estimate in QAM formats [50]. While these are

essentially feed-forward techniques, feedback techniques

employing a frequency-controlled loop may also be used,

having the advantage that they are agnostic to the modulation

format [31], [38].

However, it is interesting to remark that in transmissions

when the symbol rate is faster than 5 GHz we can estimate ∆𝑓

constant in the symbol period. In this case we can rewrite (20)

𝑥𝑖𝑛[𝑘] = 𝑥𝑠𝑦𝑚[𝑘]𝑒𝑥𝑝(𝑗(𝜃𝑠[𝑘] + 𝜃𝑐[𝑘])) (22)

𝜃𝑐[𝑘] = 𝜃𝑒[𝑘] + 2𝜋∆𝑓 ∙ 𝑘 ∙ 𝑇𝑠𝑦𝑚 (23)

and consequently, the estimation of the carrier frequency can

be realized with the estimation of the carrier phase offset.

G.2 Phase Recovery

Phase locking in the hardware domain can be replaced by

phase estimation in the software–DSP domain. In order to

estimate the residual carrier phase, feed-forward techniques

are often preferable [25]. As with many of the frequency-

estimation algorithms, the carrier phase in QPSK may be

Fig. 10. Representation of phase ambiguity in QPSK constellation due to

frequency and phase offset.

estimated using the fourth-power carrier phase recovery

algorithm [25] (Fig. 11). With 𝑥𝑖𝑛[𝑘] = 𝐴 ∙ 𝑒𝑥𝑝(𝑗(𝜃𝑠[𝑘] +

𝜃𝑐[𝑘])) and 𝜃𝑠[𝑘] = 0,± 𝜋/2, 𝜋 radians. To estimate the

carrier phase θc[k] by using DSP, the received signal is raised

to the fourth power as shown in Fig. 11, we obtain:

𝐴4 ∙ 𝑒𝑥𝑝(𝑗(4𝜃𝑠[𝑘] + 4𝜃𝑐[𝑘])) = 𝐴4 ∙ 𝑒𝑥𝑝(𝑗4𝜃𝑐[𝑘]) (24)

because 𝑒𝑥𝑝(𝑗4𝜃𝑠[𝑘]) = 1, i.e., the power operation strips off

the data phase. The carrier phase can then be computed and

subtracted from the phase of the received signal to recover the

data phase. Such a feed-forward phase estimation scheme

lends itself well to real-time digital implementation. Figure 11,

however, is an idealization where no additive noise is present

in the received signal. In realistic systems, the received signal

will contain noise dominated by either ASE–LO beat noise or

shot noise of the LO. In the presence of these additive noises,

digital carrier-phase estimation must be adapted to manage

these noises. The generalization of fourth-power carrier phase

recovery algorithm for QPSK signals gives the estimate of the

phase as follows [20]:

𝜙[𝑘] = 𝑎𝑟𝑔 {1

2𝑁 + 1∑ 𝑤[𝑛]𝑥𝑖𝑛

4 [𝑘 + 𝑛]

𝑛=−𝑁

} (25)

where w[n] is a weighting function, which depends on the

ratio of the additive white Gaussian noise to the laser phase

noise. The result of the weighting function is to apply a

Wiener filter to estimate the phase noise [20], [47], which can

approach the performance of an ideal maximum a priori

(MAP) estimator of the phase. Using this approach for a 1-dB

penalty, a linewidth up to 28 MHz may be tracked for 28

GBaud PDM-QPSK [47].

As modulation formats move beyond QPSK to M-QAM,

the requirements on the laser linewidth become increasingly

stringent because the symbol period is longer for the same bit

rate and consequently more phase laser fluctuations will take

place due to spontaneous emissions [42], [55]. Later, in

section III.C we will analyze the tolerance of 100G-PDM-

QPSK and 200G-PDM-16QAM to frequency and phase laser

noise.

Nevertheless using conventional wireless approaches such

as decision-directed phase locked loops, have enabled a

linewidth of 1 MHz to be tracked digitally for 14 GBaud

PDM-16-QAM [54]. Furthermore, for differential 16-QAM

and 64-QAM, it has been shown that a digital phase-locked

loop can compensate for a residual frequency offset of 1% of

the symbol rate [33]. While the digital phase-locked loop

presents challenges for CMOS-based parallel implementation,

hardware efficient carrier-recovery schemes have also been

proposed with similar performance [65].

In addition to the errors due to the residual phase noise,

there is also the possibility of a cycle slip, which can have a

catastrophic effect on the performance. As discussed by

Taylor [47], in order to reduce the probability of a cycle slip to

that of the corrected the BER=10-18, the laser linewidth may

need to be reduced by two orders of magnitude, e.g., 600 kHz

for 28 GBaud PDM-QPSK. In order to minimize the impact of

phase ambiguity differential decoding has been proposed.

While this has the effect of increasing the BER by as much as

a factor of two, and hence, incurring a modest penalty (<1

dB), this often outweighs advantage of relaxed linewidth

requirements and simplified symbol decoding.

To close this subsection, we include in Fig.12 the

constellation diagrams of 112-Gb/s PDM-NRZ-QPSK and

220-Gb/s PDM-RZ-16QAM obtained at the output of the DSP

after a transmission of 1500 km and 1000 km, respectively (in

the former case the signal is processed with Matlab and in the

latter case with OptiSystem). We show the comparison before

and after carrier frequency and phase recovery in both cases.

H. Symbol Estimation and Decoding

Following carrier recovery, the symbols may be decided by

the outer receiver. This could take the form of a soft-decision

forward error correction (SD-FEC) using a Galois field

corresponding to the symbol alphabet, or symbol estimation

followed by hard-decision FEC (HD-FEC). In current systems,

which are based on hard decision decoding of binary data,

Fig. 11. Mth power carrier phase recovery algorithm. Symbol phase is

recovered by digital cancellation of carrier phase and frequency offset [25].

Fig. 12. QPSK constellation diagrams for the ‘x polarization’ at the receiver

(a) before and (b) after carrier frequency and phase recovery. 16-QAM

constellation -‘x polarization’- (c) before and (d) after carrier frequency and

phase recovery.

symbol estimation and bit decoding is required. For

rectangular constellations, such as QAM, 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, by using

nonrectangular decision boundaries, it is possible to improve

the performance for systems limited by linear and nonlinear

optical impairments, which is a line of research for improve

the performance in superchannels transmissions [10], [41, Ch.

III. ADVANCED OPTICAL MODULATION FORMATS IN 100 AND

200-Gb/s DWDM TRANSMISSIONS

Digital coherent detection technology described in the

above section allows the use of a universal receiver front-end

for different advanced optical modulation formats. It moves

the complexity of phase and polarization tracking into the

digital domain [42].

With the rapid growth of capacity demand on carrier’s

transport networks, spectrally-efficient modulation and

detection technology have become increasingly important due

to their potential to reduce cost per transmitted bit by sharing

fiber and optical components over more capacity. Modulation

and detection technologies capable of achieving even higher

SE might be needed for 100-Gb/s and above DWDM systems

[6], [10]. Therefore, high-spectral-efficiency multi-level

modulation formats have been proposed to increase spectral

utilization: PDM-QPSK, PDM-QDB, PDM-8-PSK, and PDM-

M-QAM [70], [75], [41, Ch. 7].

The question as to the ‘best’ modulation format there is no

unique answer to this question. Rather, the answer depends on

system requirements such as [41, Ch. 7], [72]: target per-

channel interface rate, available per-channel optical

bandwidth, spectral efficiency, target transmission reach,

optical networking requirements and transponder integration

and power consumption. Each of the above boundary

conditions implies a certain set of trade-offs that help to

determine the ‘best’ modulation format:

Symbol Rate vs Constellation Size: affecting to DAC and

ADC resolution, digital filters size in DSP (proportional

to Rs2 [60]) to compensate the linear and nonlinear optical

impairments and the tolerance to laser phase noise (the

higher the symbol rate the more sensitive to laser phase

noise and consequently, narrower-linewidth lasers are

required [49]).

Spectral Efficiency vs Noise and Transmission Reach:

depends predominantly on the underlying modulation

format and FEC, and determines the maximum WDM

capacity that can be transmitted over a given distance

within a practical optical amplification bandwidth.

Figure 14 visualizes this trade-off in the linear regime,

showing the achievable BER as a function of the

required OSNR (0.1-nm resolution). The smaller

constellation size the more tolerant the modulation

format to ASE noise.

Spectral Efficiency vs Crosstalk Tolerance: The tolerance

of above modulation formats to in-band and out-band

crosstalk closely follows their tolerance to ASE noise.

Therefore, analyzing exclusively the Euclidean distance

between symbols in the constellation (Fig. 13), QPSK

will be the high-order modulation format with the most

tolerance to in-band and out-band crosstalk. This

consideration reveal yet another trade-off that limits the

constellation size (and with it the spectral efficiency) in

mesh networks, regardless of reach and delivered OSNR.

The resulting trade-offs, which include fundamental as well

as technological components, point at PDM-QPSK and PDM-

16-QAM as a promising sweet spot that represents a good

Fig. 13. Bit Error Rate versus SNR per bit in one polarization.

Fig. 14. Bit Error Rate vs OSNR (0.1-resolution) sensitivity trade-off.

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

0 2 4 6 8 10 12 14 16 18 20 22 24 26

Eb/No (dB)

QPSK QDB 8-PSK

8-QAM 16-QAM 64-QAM

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

10 12 14 16 18 20 22 24 26 28 30

OSNR (dB - 0.1 nm/res)

100G-PDM-QPSK 100G-PDM-QDB

150G-PDM-8-PSK 150G-PDM-8-QAM

200G-PDM-16-QAM 400G-PDM-64-QAM

compromise between various limiting effects but still enables

high-performance in 100-Gb/s transmissions with PDM-QPSK

and in 200-Gb/s transmissions with PDM-16QAM. In the next

subsections we review and investigate the tolerance of 112G-

PDM-QPSK (12% overhead for FEC) and 220G-PDM-

16QAM (20% overhead for FEC) to some physical

impairments: optical filtering, crosstalk and laser phase noise.

The analysis of both formats to GVD, PMD and fiber Kerr

nonlinearities degradation remains outstanding for future

works due to space restrictions of this document. Finally, we

present three high-spectral-efficiency and high-speed DWDM

transmission experiments implementing these formats and the

optical coherent receiver presented in Section II.

A. Optical Filtering Tolerance

The 112G-PDM-QPSK system equipped with the proposed

receiver has a high tolerance to narrowband optical filtering,

which also implies high achievable spectral efficiency. Fig. 15

shows the Q-penalty at dB as a function of the bandwidth of

commercially available optical Gaussian bandpass filters for

both signals. It can be observed that the 112-Gb/s PDM-QPSK

signal equipped with the proposed receiver can tolerate 28

GHz optical filtering with 2.3-dB Q-penalty (i.e., Nyquist

filtering). However, 220-Gb/s PDM-16QAM signal suffers

more penalization at the same filter bandwidth (~9 dB).

Consequently, the former signal is more tolerant to ISI

induced by optical filtering due to digital symbols have a

higher Euclidean distance in the constellation diagram.

The PDM-16QAM modulation format shows a poor

tolerance to narrowband optical filtering, which is the main

cause that high-capacity core optical networks based on this

modulation format cannot achieve long-haul transmissions

without additional ISI equalization in the DSP.

B. Crosstalk Tolerance

In-band crosstalk, may arise within multi-degree mesh

ROADMs, imperfect splices and connectors, or in the form of

multi-path interference in Raman amplified systems. In-band

crosstalk acts in a similar way as ASE noise, the difference

being that it is not typically Gaussian distributed (but has the

amplitude distribution of the underlying modulation) and is

not typically white (but has the spectral shape of the signal

itself). Figure 16 (a) and (b) illustrates the impact of in-band

crosstalk on 16-QAM modulation format. It shows a 16-QAM

signal constellation (open circles) onto which another 16-

QAM constellation (filled circles) with the same phase (a) or

with a 45º-rotation relative to the signal (b) is added as an

interferer. Since the minimum distance between symbols is

most strongly affected by the rotated interferer, we expect the

strongest impact of crosstalk for that case [39].

We analyze the in-band crosstalk tolerance of 112G-PDM-

QPSK and 220G-PDM-QPSK, with approximately the same

symbol period. The experimental setup used to verify the

results is shown in Fig. 16 (c). Using a 50/50 optical coupler,

the optical signal was split into two paths with a differential

delay of ~10 ns. Each path included a variable optical

attenuator (VOA) with power monitoring and a polarization

controller (PC). The lower-power path (the interfering signal)

optionally included dispersion-compensating fiber (DCF) with

-600 ps/nm dispersion at 1550 nm to study the impact of an

interferer with a substantially different dispersion from the

signal. The two signal copies were recombined in a final 50/50

optical coupler with random symbol alignment. The

corresponding crosstalk penalties at a BER of 10-3 are shown

in Fig. 17. The circles represent the case of an undispersed

Fig. 15. Q factor degradation due to ISI induced by second-order Gaussian

bandpass filter in 112G-PDM-QPSK and 220G-PDM-16QAM systems.

0 20 40 60 80 100 120 140 160 180 200

Optical Filter Bandwidth (GHz)

112G-PDM-QPSK

220G-PDM-16-QAM

Fig. 16. Impact of in-band crosstalk on 16QAM format; (a, b): crosstalk

models; (c) simulation setup; PC: Polarization controller; DCF: Dispersion-

Compensating Fiber. These figures have been inserted from reference [73].

Fig. 17. OSNR penalty at BER=10-3 versus crosstalk for the two measured

modulation formats with undispersed (solid lines) and dispersed (dashed lines) interferer.

-50-40-30-20-100

Crosstalk (dB)

interferer (with a random phase relative to the signal), while

the squares are for the 600-ps/nm dispersed interferer. As

expected, introducing dispersion onto the interferer increases

crosstalk penalties due to the larger peak-to-average power

(PAPR) of the interfering signal, resulting in more severe

crosstalk-induced reductions of the minimum symbol distance

compared to a well-confined, undispersed interfering

constellation. Hence, the expansion of the symbols into sizable

clouds due to ISI leaves less room for further degradations by

crosstalk. For a 1-dB crosstalk penalty, our simulations allow

for average crosstalk levels of about –15 dB and –24 dB for

112G-PDM-QPSK and 220G-PDM-16-QAM, respectively.

C. Tolerance to Combined Laser Linewidth and Frequency

Offset of 112-Gb/s PDM-QPSK and 220-Gb/s PDM-16QAM

formats

The trade-off between symbol rate and constellation size is

also impacted by laser phase noise. Random phase fluctuations

of LO light translate into angular noise that ultimately

degrades detection performance. The tolerance to phase noise

depends substantially on the underlying modulation format

and the carrier phase recovery algorithm In general, higher-

level modulation formats become progressively more sensitive

to phase noise. The tolerance to laser phase noise for a given

detection algorithm and modulation format depends on the

ratio of the combined TX and LO laser linewidth ∆𝜐𝑇𝑋−𝐿𝑂 to

the symbol period (∆𝜐𝑇𝑋−𝐿𝑂 ∙ 𝑇𝑠). The higher the combined

laser linewidth or the symbol period, the more phase

fluctuations disturb the correspondent digital symbol due to

spontaneous emissions of both lasers.

We have analyzed the tolerance of 112G-PDM-QPSK and

220G-PDM-16QAM to combined laser linewidth and

frequency offset. Figures 18, 19 and 20 shows the tolerance of

these formats and the robustness of our carrier phase recovery

algorithm implemented with Matlab in the previous section.

The simulations have been realized with OptiSystem in a

back-to-back (B2B) scheme, varying the combined laser

linewidth (without frequency offset in LO for the first

measurement and with a 1-GHz of frequency offset for the

second measurement). Given a 0.5 dB Q-penalty, a 112G-

PDM-QPSK system with the proposed receiver can tolerate up

to 2 MHz combined laser linewidth and 1 GHz frequency

offset, which further verifies the carrier recovery capability.

On the other hand, 220G-PDM-16QAM can tolerate up to 1

MHz combined laser linewidth and 1 GHz frequency offset. It

shows that the former system is more tolerant to laser phase

noise for approximately the same symbol period (35,7 ps ~

36,3 ps). Based on Fig. 20, it is clear that for a low combined

laser linewidth both carrier recovery algorithms have the same

performance. However, with more than 6 MHz in ∆𝜐𝑇𝑋−𝐿𝑂,

fourth-power carrier phase recovery algorithm presents better

performance than 16th- power carrier phase recovery algorithm

for the same number of taps in digital filters of DSP. It shows

that 16QAM-DSP needs a high number of taps to recover the

phase with the same efficiency as fourth-power carrier phase

recovery algorithm.

D. High-SE DWDM Transmission Simulations

Finally, in this subsection we present three high-spectral-

efficiency and high-speed DWDM transmission simulations

implementing these modulation formats and using lumped

amplification (EDFA) and distributed Raman amplification.

Additionally, we use the coherent optical receiver analyzed in

Section II.

Fig. 18. 112G-PDM-QPSK tolerance to combined laser linewidth at different

frequency offsets.

Fig. 19. 220G-PDM-16QAM tolerance to combined laser linewidth at

different frequency offsets.

Fig. 20. Tolerance to laser phase noise comparison between 112G-PDM-

QPSK and 220G-PDM-16QAM without laser frequency mismatch.

0 1 2 3 4 5 6 7 8 9

Combined Laser Linewidth Δυ (MHz)

Frequency Offset=0GHz

0 1 2 3 4 5 6 7 8 9 10 11

0 1 2 3 4 5 6 7 8 9

112G-PDM-QPSK

220G-PDM-16-QAM

2.24 Bit/s/Hz, 1500 km, 40 x 112-Gb/s PDM-NRZ-QPSK

Figure 21 shows the simulation scenario. At the transmitter,

40 wavelengths (1550–1565.64 nm [35]) are modulated by

two 112-Gb/s PDM-NRZ-QPSK modulators (for odd and even

channels), each modulating twenty 100 GHz-spaced

wavelengths. The odd and the even channels are combined by

using an optical adder (ideal multiplexer). The 40 channels

originate from an external cavity laser (ECL) array, with a

linewidth of 50 kHz to reduce the laser phase noise at the

receiver. Even and odd channels are individually modulated

using a conventional quadrature modulator for each

polarization [42] and polarization-division multiplexed by a

polarization beam combiner (PBC). The quadrature

modulators are composed by two parallel double-nested

Mach-Zehnder modulator (DN-MZM) [42], [41, Ch. 7] with a

bandwidth greater than 30-GHz and a phase-shifter in the

lower branch. In order to emulate a random data modulation,

data signal was obtained using a 112-Gb/s pseudo-random bit

sequence (PRBS) generator, with 12% overhead for Soft-

Decision (SD) FEC.

The transmission line consists of 15 spans of 100 km of

SSMF (average span loss of 20 dB) and EDFA-lumped optical

amplification. The EDFAs were pumped at 980 nm to reduce

the accumulated ASE noise peak occurring in the 1560–1566

nm region. The average fiber input power per channel is about

+1.5 dBm/carrier. No optical fiber dispersion compensation

was used in the lightpath. At the receiver side, the measured

channel is selected by one tunable optical filter (TOF) with a

bandwidth of 0.4 nm @1550 nm. The test channel is processed

by the hardware and DSP software that we described in

Section II. The hardware implements polarization-and phase-

diverse coherent detection with a polarization-diversity 90-

degree hybrid, a tunable ECL LO (~50 kHz linewidth) and

four single-ended photodetectors. The sampling and

digitization was achieved by using a four ADC’s with 50

GSamples/s and 20-GHz electrical bandwidth. For the DSP,

we use the CMA for polarization recovery. In Fig. 22, we

show the measured average BER of the two polarizations as a

function of wavelength. One can see that all 40 channels have

a BER below the enhanced FEC threshold of 2·10-3 [41, Ch.

4.28 Bit/s/Hz, 600 km, 40x214-Gb/s PDM-CSRZ-QPSK

In the Final Degree Project (FDP) of Andrés Macho, a high-

capacity DWDM system was designed between Madrid and

Barcelona cities. In that work a full capacity of 8-Tb/s was

achieved over 76 wavelengths with 107-Gb/s PDM-33%RZ-

DQPSK modulation format, using coherent detection and

optical dispersion compensation implemented by a hybrid

dispersion map with double periodicity (pre-comp of -480

ps/nm, residual dispersion per span of 160 ps/nm and net

residual dispersion of 0 ps/nm at 1555 nm) [51].

Now, we propose to redesign this network with

uncompensated transmission (UT) dispersion map and using

the PDM-CSRZ-DQPSK modulation format with 214-Gb/s

per wavelength (14% overhead for SD-FEC) over DWDM 50-

GHz grid. Our proposal is to achieve a SE of 4 b/s/Hz in 200-

Gb/s DWDM transmissions without the necessity of Nyquist

filtering. We achieve this high SE using commercial third-

order Super-Gaussian filters and PDM-QPSK modulation

format, which has a great tolerance to narrowband optical

filtering.

Figure 23 shows the simulation scenario. At the transmitter,

the architecture employed is the same as the first simulation.

However, we use now a pulse carver at the output of each

conventional quadrature modulator, previous of polarization

multiplexing, to convert NRZ pulses to Carrier-Suppressed

Return-to-Zero (CSRZ) pulses [51]. The advantages of this

PDM-QPSK version is further analyzed in [52]. On each

polarization, the 110-Gb/s QPSK signals were then pulse-

carved with one MZM driven by 27.5-GHz clock.

Additionally, a random data sequence of 65536 bits was

obtained using a PRBS generator with a fixed bit rate of 214-

Gb/s. The lightpath consists of 6 spans of Vascade EX2000

[15] (average span loss of 16.2 dB) with a ROADM inserted

in Zaragoza. Maintaining the original design of [51], the

power losses are recovered by P-EDFA amplifiers (EDFA

codoped with phosphorous to increase the amplification

bandwidth) pumped at 1480 nm. However, no optical fiber

dispersion compensation was used in the network. Due to the

high-effective area of Vascade EX2000 (112 µm2) and a low

Kerr nonlinear refractive index (21·10-21 m2/W), we can

increase the power launched to the first span from +1 to +2

dBm/wavelength. At the receiver side, the measured channel

is selected by one TOF with a bandwidth of 50 GHz. The

ADC’s employed have 80 GSamples/s and 40-GHz electrical

bandwidth. Finally, we measured the channel performance

with our DSP (CMA). Fig. 24 shows the BER performance

Fig. 21. Simulation scenario setup for 40 x 112-Gb/s PDM-NRZ-QPSK

transmission. This figure is a modification of an illustration of [75].

Fig. 22. BER parameter after 1500 km of transmission. Optical spectrum and

the constellation diagrams of 1550 nm channel at the receiver.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1549 1554 1559 1564

Wavelength (nm)

x-pol y-pol

measured before transmission in Barcelona. The BER for all

40 x 214-Gb/s signals [35] were in the range from 1.9·10-5 to

9.4·10-4, under the enhanced FEC limitation (~2·10-3) [41, Ch.

6], [19].

4.4 Bit/s/Hz, 1000 km, 10x220-Gb/s PDM-RZ-16-QAM

In the final simulation we demonstrate transmission of 11 x

224-Gb/s POLMUX-RZ-16QAM over 1000 km with a

channel spacing of 50 GHz.

The experimental setup is depicted in Fig. 25. As shown in

the figure, ten external cavity laser (ECL) with wavelengths

on the 50 GHz ITU grid, and ranging from 1548.5 nm and

1552.5 nm [35] are grouped into odd and even channels using

two multiplexers. After the multiplexers, the two channels

groups are first pulse carved using two MZMs driven with a

27.5-GHz clock signal (50% duty cycle RZ pulses).

Subsequently, the two wavelength combs are modulated with

27.5-GBaud PDM-16QAM modulators. In order to generate

the 28-GBaud 16QAM optical signal, the IQ modulator is

driven with two 4 level pulse amplitude modulated (PAM)

signals, which are generated using a 16QAM sequence

generator. The amplitude of the 4-PAM signals is ~3 Vp-p. In

order to alleviate the intrachannel nonlinearities impact we

applied RZ pulse carving to the signal (Fig. 26). The two

polarizations per channel are multiplexed using a PBC.

Finally, the odd and even channels are combined on a 50-GHz

channel grid using a wavelength selective switch (WSS)

which is used to reduce the WDM crosstalk as well to equalize

the channels powers. Fig. 25.c illustrates the optical spectrum

of the ten PDM-RZ-16QAM channels, at the transmitter side.

The optical transmission link consists of ten spans of 100

km SMF built in a re-circulating loop. Each span in the loop is

composed from 75 km of Vascade EX2000 fiber (ULAF) [15]

followed by 25 km of SSMF [14]. Hybrid EDFA/Raman

amplification scheme has been employed in this link to

improve the received OSNR. We stimulate the SRS using

three pump wavelengths per span (ranging from 1470 to 1510

Fig. 23. DWDM optical network between Madrid and Barcelona cities. Simulation scheme proposed for 40 x 214-Gb/s PDM-CSRZ-QPSK

transmission. This figure is a modification of an illustration of [75].

Fig. 24. Measured BER of 50-GHz spaced, 40 x 214-Gb/s PDM-CSRZ-

QPSK signals after 600 km transmission.

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1549 1554 1559 1564

Wavelength (nm)

Fig. 25. (a) Simulation setup; (b) Re-circulating loop lightpath; (c) 16-QAM eye diagrams and 10 x 220-Gb/s PDM-RZ-16QAM optical spectrum. This

figure is a modification of an illustration of [75].

Fig. 26. BER results for the central channel versus transmission distance.

0 250 500 750 1000 1250 1500 1750

Transmission Distance (Km)

“Eye post-filtering”

“x-pol” “y-pol”

nm), with an average ON/OFF Raman gain of ~10 dB. ULAF

allows for higher launch powers as we have previously

mentioned. Therefore ULAF fiber is used directly after the

EDFA amplifiers. However, this large core size results in a

reduction in the Raman gain for the fiber. Consequently, we

use a 25 km section of SSMF at the end of each span to

enhance the gain from the backward pumping Raman

amplifier.

At the receiver a coherent detection is realized using an

ECL local oscillator, and a phase and polarization diversity

IQ-mixer with balanced photodiodes. The four outputs from

the coherent receiver are sampled at a sampling rate of 50

GSamples/s. Afterwards, the signal is processed in the DSP

with the algorithms and subsystems described in Section II (in

this case we use the DSP of OptiSystem library for PDM-16-

QAM signals).

The launch power for the 10 x 220-Gb/s PDM-RZ-16QAM

channels is varied between -4 dBm/ch and +4 dBm/ch, and the

optimum launch power is found to be around 0 dBm per

channel, which will be used for all of the following

measurements. The BER of the received signal at a

wavelength of 1550.52 nm is calculated at different

transmission distances and reported in Fig. 26. The figure

illustrates that a maximum transmission distance of ~1300 km

is feasible with a BER below the FEC limit (~5·10-3) [19], [41,

Ch. 6]. Note that in this case the FEC limit is lower than the

first and second simulations due a higher FEC overhead

(20%). The BER for the 10 channels has been measured after

a transmission distance of 1000 km with the optimum launch

power of 0 dBm (Fig. 27). The BER of all measured WDM

channels is below the FEC threshold. Finally, the constellation

diagrams for the POLMUX-RZ-16QAM signal are shown in

Fig. 28 both in the single channel and multi-channel B2B

configuration, as well as after 1000 km of transmission. The

constellation diagram for the multi-channel B2B configuration

shows the degradation of the signal quality due to WDM

crosstalk.

IV. CONCLUSIONS

In this paper, we have attempted to outline the subsystems

and algorithms, which are required to realize a digital coherent

optical receiver. As systems move beyond PDM-QPSK

toward higher level modulation formats or to multicarrier

techniques, a natural evolution will be for DSP to be employed

at both the transmitter and receiver, such that the structural

design of the DSP may differ from that presented.

Nevertheless, many of the subsystems outlined herein, such as

channel equalization and carrier recovery are likely to be

present in future photonic digital modems. While the

commercialization of photonic digital receivers has begun, it is

clear that there remain much research to be done in order to

allow a digital coherent optical communication system to

achieve the information theoretic channel capacity in super-

channel transmissions and future space-division multiplexing

systems.

In the second part of this work, we have demonstrated the

use of the CD, PMD compensation and phase recovery

algorithms in combination with advanced optical modulation

formats. Firstly, we have presented the main modulation

formats proposed in high-capacity optical networks. Secondly,

we have analyzed the tolerance of 112G-PDM-QPSK and

220G-PDM-16QAM signals to some physical impairments:

narrowband optical filtering, crosstalk and laser phase noise.

In the three impairments PDM-QPSK shows better tolerance

than PDM-16QAM at the same symbol rate. Finally, we have

presented three high-SE and high-speed DWDM transmission

simulations using 112G-PDM-QPSK, 214G-PDM-QPSK and

220G-PDM-16QAM multi-level modulation formats.

APPENDIX: THEORETICAL LIMIT OF BIT ERROR RATE FOR

ADVANCED OPTICAL MODULATION FORMATS

This appendix is an overview of [36] and [22] showing the

expressions employed to calculate the figures 13 and 14. The

relations between bit error rate (𝑃𝑏) and signal-to-noise ratio

per bit (𝐸𝑏/𝑁0) for M-QAM and M-PSK modulation formats

are given by [36]:

𝑃𝑏⏟𝑀−𝑄𝐴𝑀

=√𝑀 − 1

√𝑀 ∙ log2 √𝑀∙ 𝑒𝑟𝑓𝑐√(

3 log2𝑀

2(𝑀 − 1)) ∙𝐸𝑏𝑁0 (26)

𝑃𝑏⏟𝑀−𝑃𝑆𝐾

log2𝑀∙ 𝑒𝑟𝑓𝑐 [𝑠𝑖𝑛 (

𝑀)√log2𝑀 ∙

𝐸𝑏𝑁0] (27)

Fig. 27. Measured BER of 50-GHz spaced, 10 x 220-Gb/s PDM-RZ-16QAM signals after 1000 km transmission.

Fig. 28. PDM-RZ-16QAM constellation diagrams.

1548.2 1549.2 1550.2 1551.2 1552.2

Wavelength (nm)

To rewrite these expressions as a function of optical signal-

to-noise ratio (OSNR), in a first step, we need to develop the

electrical and optical signal-to-noise ratio definitions (Fig. 29):

𝑆𝑁𝑅 =𝐸𝑠𝑁0=

𝑃𝑠𝑁0 ∙ 𝑅𝑠

𝑂𝑆𝑁𝑅 =𝑃𝑠

2𝑁𝐴𝑆𝐸𝐵𝑟𝑒𝑓 (29)

where 𝑁0 is the power spectral density noise (Watts/Hz),

supposing it is a White Gaussian Noise random process. 𝑁𝐴𝑆𝐸

is the power spectral density of ASE noise in one polarization

and the reference bandwidth 𝐵𝑟𝑒𝑓 is commonly taken to be

12.5 GHz, corresponding to a 0.1 nm resolution bandwidth of

optical spectrum analyzers at 1550 nm carrier wavelength. In

PDM systems we have power signal in the two polarizations

of the optical fiber, and consequently, OSNR definition takes

the form:

𝑂𝑆𝑁𝑅⏟ 𝑃𝐷𝑀

=2𝑃𝑠

2𝑁𝐴𝑆𝐸𝐵𝑟𝑒𝑓=

𝑃𝑠𝑁𝐴𝑆𝐸𝐵𝑟𝑒𝑓

The definition of OSNR differs from SNR by a normalization

factor based on the particular choice for the fixed reference

noise bandwidth as well as by how one accounts for signal and

noise polarization modes. Assuming that 𝑁0 and 𝑁𝐴𝑆𝐸 are

equivalent, we can relate SNR and OSNR in PDM systems

directly as:

=𝑅𝑠𝐵𝑟𝑒𝑓

𝑆𝑁𝑅 (31)

Knowing the relations between 𝑆𝑁𝑅, 𝐸𝑏/𝑁0, 𝑅𝑠 and 𝑅𝑏 given

by [36], [69] and [22]:

𝑆𝑁𝑅 =𝐸𝑏𝑁0log2𝑀 (32)

𝑅𝑠 =𝑅𝑏

2 ∙ log2𝑀 (33)

we can rewrite the signal-to noise ratio per bit 𝐸𝑏/𝑁0 as a

function of OSNR in PDM systems:

=𝑅𝑏2𝐵𝑟𝑒𝑓

𝐸𝑏𝑁0 (34)

Finally, replacing in (26) and (27) we obtain the expressions

employed to calculate Fig. 14:

𝑃𝑏⏟𝑃𝐷𝑀−𝑀−𝑄𝐴𝑀

=√𝑀 − 1

√𝑀 ∙ log2 √𝑀∙ 𝑒𝑟𝑓𝑐√(

3 log2𝑀

𝑀 − 1)𝐵𝑟𝑒𝑓

𝑅𝑏𝑂𝑆𝑁𝑅 (35)

𝑃𝑏⏟𝑃𝐷𝑀−𝑀−𝑃𝑆𝐾

log2𝑀∙ 𝑒𝑟𝑓𝑐 [𝑠𝑖𝑛 (

𝑀)√log2𝑀 ∙

2𝐵𝑟𝑒𝑓

𝑅𝑏𝑂𝑆𝑁𝑅] (36)

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Andrés Macho received the

Telecommunication Engineering

degree (M.S.) from the ETSIT-

Universidad Politécnica de Madrid in

2013. Currently, he is working

towards his Ph.D. degree at

Nanophotonics Technology Center

Universidad Politécnica de Valencia

(Spain). His professional interest

includes high-capacity wavelength-

division multiplexed systems (WDM),

advanced optical modulation formats

and space-division multiplexing for

optical networks. He worked in 2013

at Telefonica R&D Corporation in the

Core Network Evolution group involved in some R&D European projects

(INSPACE, STRAUSS and DISCUS).

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