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High-Spectral-Efficiency Optical
Modulation Formats
Peter J. Winzer
(Invited Paper)

AbstractAs 100-Gb/s coherent systems based on polarizationdivision multiplexed quadrature phase shift keying (PDM-QPSK),
with aggregate wavelength-division multiplexed (WDM) capacities close to 10 Tb/s, are getting widely deployed, the use of
high-spectral-efficiency quadrature amplitude modulation (QAM)
to increase both per-channel interface rates and aggregate WDM
capacities is the next evolutionary step. In this paper we review
high-spectral-efficiency optical modulation formats for use in
digital coherent systems. We look at fundamental as well as at
technological scaling trends and highlight important trade-offs
pertaining to the design and performance of coherent higher-order
QAM transponders.
Index TermsCoding, coherent detection, digital signal processing, DSP, FEC, modulation, PDM, QAM, QPSK, SDM, WDM.

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 (i.e., between 1.1 and 2 dB per
year1), depending on the nature and penetration of services offered by various network operators in different geographic regions [1], [2]. The increasing number of applications relying on
machine-to-machine traffic and cloud computing could accelerate this growth to levels typical within data-centers and highperformance computers [3], [4]: According to Amdahls rule of
thumb [5], [6], the interface bandwidth of a balanced computer
architecture is proportional to its processing power. Since cloud
services are increasingly letting the network take the role of a
distributed computer interface, the required network bandwidth
for such applications may scale with data processing capabilities, at close to 90% (or 2.8 dB) per year [7]. Non-cacheable
real-time multi-media applications will also drive the need for
more network bandwidth.
For over two decades, the demand for communication
bandwidth has been economically met by wavelength-division
multiplexed (WDM) optical transmission systems, researched,

Manuscript received June 12, 2012; revised August 02, 2012; accepted August 02, 2012. Date of publication August 23, 2012; date of current version
December 12, 2012.
The author is with Bell Labs, Alcatel-Lucent, Holmdel, NJ 07733 USA
(e-mail: peter.winzer@bell-labs.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/JLT.2012.2212180
1Following [1], we conveniently express traffic growth in decibels, i.e., a 30%
dB.
growth corresponds to a growth of

developed, and abundantly deployed since the early 1990s [8].

Fig. 1(a) 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 (WDM, PDM, SDM; triangles), as achieved in
various record research experiments; commercial products
follow similar trends, with a time delay of typically 5 years [1],
[8], [9].
As can be seen from Fig. 1(a), WDM was able to boost
the relatively slow progress in single-channel bit rates (at
0.5 dB/year) to 2.5 dB/year during the 1990s, which was
more than enough to satisfy the 2-dB/year traffic growth and
partly contributed to the telecom bubble around 2000 [1].
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 spacings, 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 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 binary
[10] and quaternary [11] phase shift keying (BPSK, QPSK)
using direct detection with differential demodulation (DPSK,
DQPSK) [12], [13], followed by commercial deployment at
40 Gb/s [14], [15]. With the drive towards per-channel bit
rates of 100 Gb/s in 2005 [16], 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 [17],
[18]. In this context, polarization-division multiplexed (PDM)
QPSK allowed for a reduction of symbol rates by a factor of
4 compared to the information bit rate, which brought 40 and
100-Gb/s optical signals at around 10 and 25 GBaud within
the reach of fast analog-to-digital converters (ADCs). This,
in turn, enabled the use of digital coherent detection using
robust digital signal processing (DSP) to perform all-electronic
chromatic- and polarization-mode dispersion compensation,

0733-8724/$31.00 2012 IEEE

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Fig. 1. (a) Evolution of experimentally achieved single-channel bit rates (single-carrier, single-polarization, electronically multiplexed; green circles), symbol
rates in digital coherent detection (purple squares), and aggregate per-fiber capacities (triangles) using wavelength-division multiplexing (WDM; red), polarization-division multiplexing (PDM; blue), and space-division multiplexing (SDM; yellow). (b) Evolution of experimentally achieved per-polarization spectral
efficiencies in single- (red) and dual-polarization (blue) experiments..

frequency- and phase locking, and polarization demultiplexing

[19][26]. Commercial coherent systems for fiber-optic networks were introduced at 40 and 100 Gb/s in 2008 and 2010,
using PDM-QPSK at 11.5 and 28 GBaud, based on custom-designed CMOS ASICs to handle the massive DSP functionality
[27], [9].
The adoption of advanced coherent communication concepts
widely used in radio-frequency systems allowed spectral efficiencies to continue their scaling at
dB/year using essentially unchanged optical line systems, cf. Fig. 1(b). Reduced to
this growth rate, however, WDM capacity growth slowed down
to
dB/year, and is expected to slow down even further as
systems are rapidly approaching the nonlinear Shannon limit
of the fiber-optic channel [28]. In 2011, space-division multiplexing (SDM) research experiments using multi-core fiber
started to beat single-mode aggregate per-fiber capacities [29],
[30], [112], promising to restore the aggregate per-fiber capacity
growth, as shown in Fig. 1(a).
In this paper, we discuss higher-order coherent optical modulation formats as the underlying technology that has fueled capacity growth over the past
years. In Section II, we review,
on an intuitive and basic level, the notions of symbol constellation, pulse shaping, multiplexing, and coding, which are key to
advanced transponder and systems design. We then apply these
concepts in Section III to illustrate important fundamental and
technological trade-offs that have to be made when choosing
a modulation format. We show that these trade-offs depend on
whether utmost per-channel interface rates, WDM capacities, or
transmission reach are desired.

A. Digital Communications and the Structure of Language

in several ways [31], as illustrated in the left column of Table I

[32]. A finite set (or alphabet) of letters is used to form words
and sentences, whereby letters are written in series, one after
the other. The countably discrete nature of letters contained in
a (language-specific) alphabet motivates the term digital2. Note
that letters are abstract concepts that need to be mapped into the
physical reality of the analog world we live in. This is done by
representing each letter by some kind of analog waveform that
bears key features of the letter. For example, the letter A in the
26-ary Latin alphabet can be represented by the analog waveforms , , ,
,
, etc. As long as writer (transmitter)
and reader (receiver) use the same alphabet and are able to establish the correct mapping between the analog waveforms and
the set of letters, communication may take place.
On top of using a well-defined alphabet of letters, each language also uses a considerable amount of redundancy. This
is done by forming words and sentences from letters. By allowing a much smaller number of words and sentences than
what would be mathematically possible by arbitrarily arranging
letters within words and words within sentences, the receiver is
put in the position to correct for spelling errors. For example,
the words laguage or langyage are immediately identified as
misspelled versions of the correct code word language. Being
able to identify and correct these typos shows the ability of our
brain to act as an efficient error correction device. Language
redundancy in the form of synonyms can also be employed
by the transmitter to avoid the use of certain words that are
known to cause trouble in conveying a message. For example,
many non-native English speakers mispronounce a th as an
s, which can lead to uncorrectable confusion if both resulting
words are legitimate English words, such as the words think
and sink. Error correction may still be possible on a sentence
level by identifying a words most likely meaning within a given

The basic structure of digital communication signals (optical

and electronic alike) resembles the structure of many languages

2The word digital is derived from the Latin word digitus (finger) and alludes
to the basic way of counting members of discrete sets.

II. THE ANATOMY OF A MODULATION FORMAT

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TABLE I
THE STRUCTURE OF DIGITAL COMMUNICATIONS IN MANY WAYS RESEMBLES THE STRUCTURE OF LANGUAGE [31], [32]

context, but this kind of error correction is much more prone to

mistakes than the one on the individual word level. It may thus
prove advantageous to substitute words containing th by suitable synonyms to avoid likely errors in the first place rather than
having to correct for them after they have occurred.
B. Digital Symbol Constellations and Analog Pulse Shapes
The above outline of basic language structure illustrates
many important concepts used in advanced digital communication systems, as summarized in the right column of Table I.
In digital communications, the alphabet of letters becomes an
alphabet (also called a constellation) of discrete communication
symbols
. Importantly, these symbols can be viewed as an
abstraction that does not yet assign physical meaning. Before
transmitting symbols over a physical channel, a set of analog
waveforms
has to be chosen to map an abstract symbol
constellation onto physical reality. Once mapped to analog
waveform representations, the symbols are sequentially transmitted at rate
, one symbol per symbol period
,
resulting in the transmit waveform

two symbols by sending no pulse and sending a pulse,

respectively. The exact shape of the pulse adds detail to the
format and its transmission performance over the analog
channel, just as , , ,
,
show key similarities but
differ in their details. This simplest of all modulation formats is
called on/off keying (OOK) and is still the almost exclusively
deployed format at per-channel bit rates up to 10 Gb/s.
Another example is the binary orthogonal alphabet shown
second in Table I. The key feature of this alphabet is that the
two letters are orthogonal (in whatever physical dimension) and
that both letters have equal energy. In general, two analog waveforms
and
representing complex spatial optical
field distributions are orthogonal if their inner product vanishes
[33], [34], i.e., if 3
(3a)

(3b)

(1)
is measured in baud, where
The symbol rate
symbol/s. If all symbols in an -ary alphabet (i.e., an alphabet
of
letters) occur with equal probability, and if all symbols
carry user information, each symbol conveys
bits of information, and bit rate
and symbol rate
are related by
(2)
For example, the simple binary symbol constellation shown
first in Table I consists of two symbols, each conveying one
bit of information. The key feature of these two letters is that
one of them carries no energy and one of them does carry
energy (as measured by their distance from the origin in the
symbol constellation). One may then choose to represent the

where
, and denote time, frequency, and the transversal
spatial coordinates respectively, and
is the
Fourier transform of
. Important examples for (scalar) orthogonal waveforms in time and frequency domain are shown
in Fig. 2. In particular, waveforms that are non-overlapping either in time (cf. (3a)) or in frequency (cf. (3b)) are orthogonal,
irrespective of their shape. Further,
-time-shifted copies of
certain temporally overlapping pulses
are orthogonal if
has nulls at integer multiples of , which follows from (3b) with
. This condition is equivalent to Nyquists criterion for no inter-symbol
3Regarding spatial orthogonality, the overlap integrals in (3) are an approximation of a more general orthogonality condition involving the -component
of the propagating electromagnetic field [35].

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construct a 4-dimensional signal constellation for high sensitivity at high spectral efficiency [37], [38], or a combination of
PPM and PDM-QPSK for highest sensitivities at reduced bandwidth expansion compared to a pure PPM or FSK approach
[39].
C. Multiplexing
If information is transmitted on parallel channels, the aggregate bit rate of the resulting multiplex is given by the singlechannel bit rate multiplied by the number of parallel channels,
(5)
Fig. 2. Examples for waveform orthogonality in time and frequency.

interference (ISI) [33]. An important class of pulse shapes satisfying this criterion are square-root raised cosine pulses [33].
By the same token,
-frequency-shifted copies of
are
orthogonal provided that
has nulls at integer multiples of
, as illustrated in Fig. 2. This condition is
at the heart of pulse shaping in orthogonal frequency division
multiplexing (OFDM) [36].
To transmit the binary orthogonal alphabet of Table I, one
could choose to map each letter onto (any) one of two orthogonal polarizations (polarization-shift keying, PolSK), one of
two orthogonal frequencies (frequency-shift keying, FSK), one
of two orthogonal time slots (pulse position modulation, PPM),
or one of two orthogonal spatial modes (mode-orthogonal
modulation). Obviously, a receiver built to detect PolSK will
be unable to detect FSK, and vice versa. This underlines the
importance of properly specifying both the symbol alphabet
and the set of corresponding analog physical waveform representations to make digital communications work.
An important set of orthogonal physical dimensions that
can be used to construct two-dimensional symbol alphabets
in digital communications is the quadrature space, composed
of real and imaginary components of a bandpass signal (also
called sine and cosine or in-phase (I) and quadrature (Q)
components). For example, the quaternary (4-ary) or the 16-ary
alphabets shown in Table I are usually mapped onto real and
imaginary parts of the complex optical field, where they are then
called quaternary (or quadrature) phase-shift keying (QPSK)
and 16-ary quadrature amplitude modulation (16-QAM), respectively. Table I visualizes one of many possible mappings
of 16-QAM to physical waveforms; here, the analog waveform
transitions along straight lines within the complex plane of the
optical field. QAM signals typically use the same analog pulse
shape for all symbols in the constellation, i.e.,
,
which lets the transmitted waveform take the form
(4)
Constellations in more than two dimensions can also be conorthogonal time slots ( -PPM) or
structed, e.g., by using
orthogonal frequencies ( -FSK) to improve sensitivity at
the expense of spectral efficiency [33]. Higher-dimensional
spaces can also be constructed by combining different physical
dimensions. Recent examples include polarization-switched
QPSK (PS-QPSK), combining quadrature and polarization to

Parallel channels can be established using the and polarization of the optical field
orthogonal frequencies, or
orthogonal spatial modes [34]. In optical communications, frequency-division multiplexing (FDM) comprises WDM as well
as optical superchannels and OFDM with orthogonal yet spectrally overlapping subcarriers [40]. Fig. 2 visualizes two important examples for the use of orthogonal subcarriers to form
Nyquist WDM (left) and OFDM (right). Importantly, the characteristics of a modulation format are largely independent of the
multiplexing strategy. In particular, and certain implementation
aspects aside, OFDM, optical superchannels, and single-carrier systems based on the same modulation format achieve the
same spectral efficiency and exhibit the same tolerance to noise
and other linear signal impairments; the tolerance to nonlinear
signal distortions is approximately the same for typical dispersion uncompensated system parameters [41][43].
D. Coding
Returning to our structural comparison in Table I, as with language, redundancy in digital communications can be introduced
either to avoid certain symbol combinations that are known to
cause trouble on a specific communication channel (line coding)
or to correct errors at the receiver (forward error correction,
FEC). Both techniques may introduce the required overhead in
a variety of ways. The most common physical dimensions to include coding overhead are the time domain (by transmitting at
a higher symbol rate than what would be required by the client
application), and the symbol constellation (by adding additional
symbols to carry redundancy as opposed to user information).
The gross channel bit rate, including all coding redundancy, is
usually referred to as the line rate.
An important quantity associated with codes is the code rate4
, defined as the ratio of information bit rate to line rate.
In optical communications, the term coding overhead (OH), i.e.,
the percentage of bits that are added to the information bits for
coding redundancy, is more commonly used. Coding overhead
and code rate are related by [28]
(6)
Overheads around 7% have been standard for fiber-optic communication systems for about a decade [44], and soft-decision
FECs with overheads around 20% are being developed for nextgeneration systems [45], [46].
4Note that the code rate is a dimensionless quantity as opposed to a bit rate
or a symbol rate, which carry units of per second.

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If overhead is added solely in the time domain, maintaining

a given information bit rate requires transmission at a proportionally higher symbol rate, which can lead to increased
implementation penalties due to band-limited transmitter and
receiver hardware. Furthermore, higher-bandwidth signals
passing through multiple reconfigurable optical add/drop
multiplexers (ROADMs) in an optically routed network may
experience more severe filter-induced spectral narrowing.
Obviously, for a code to prove in, all penalties arising from an
increased symbol rate must be compensated for by the codes
performance improvement, which leads to the notion of an
application-specific net coding gain. A way to avoid increased
symbol rates for increased FEC OH is to put redundancy into
the symbol constellation itself, by adding more symbols than
required for information transport at a target spectral efficiency.
This technique (sometimes referred to as coded modulation
[47]) is well studied in electronic and wireless communications
and is starting to enter optical communications as well [28],
[48][52]. We will discuss this technique further in the context
of Fig. 6(b).
For more details on the basics of digital communications and
coding, the interested reader is referred to classic textbooks such
as [33], [53][55]. Detailed tutorials on the basics of digital
optical communications can be found in, e.g., [13], [28], [34].
Recent reviews specific to optical communications include [9],
[12], [13], [28], [32], [56][58].
III. KEY TRADE-OFFS IN CHOOSING A MODULATION FORMAT
The question as to the best optical modulation format is frequently encountered in optical transmission system design. As
might be expected, there is no unique answer to this question.
Rather, the answer depends on system requirements such as:
Target per-channel interface rate
Available per-channel optical bandwidth
Target WDM capacity (or spectral efficiency)
Target transmission reach
Optical networking requirements
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. In
this section, we highlight some of the key trade-offs impacting
the selection of a modulation format for specific applications.
A. Symbol Rate versus Constellation SizeDAC Resolution
In order to increase per-channel interface rates (cf. green
circles in Fig. 1), one can increase the symbol rate
, the
constellation size , or the multiplexing factor . According
to (5), the resulting speed improvement is linear in
and
but only logarithmic in . As a consequence, increasing line
rates by means of larger symbol constellations becomes progressively harder as
is increased. Fig. 3 visualizes this situation, showing experimentally achieved combinations of symbol
rates (single-carrier-equivalent symbol rates for OFDM) and
bits per symbol,
. Red squares denote transmitters employing digital pulse shaping or OFDM, while blue circles represent transmitters whose pulse shapes
are inherently determined by the characteristics of the transmit electronics and

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Fig. 3. Summary of single-channel (single carrier, single polarization, electronically multiplexed) higher-order modulation experiments and contours of constant single-channel line rates. Inset: Maximum achieved single-channel line
rate versus constellation size. (Red squares: Digital pulse shaping or OFDM.
Blue circles: No digital pulse shaping.)

optics. (The role of digital pulse shaping in optical transmission systems is further discussed in Section III.F.) Contours of
constant single-channel (single carrier, single polarization, electronically multiplexed) line rates are also shown. The inset gives
the maximum single-channel line rate achieved in research experiments at a particular number of bits per symbol. Interestingly, the speed trade-off between
and
settles at
,
revealing 16-QAM as the modulation format that has so far allowed for the highest single-channel interface rate of 320 Gb/s at
80 GBaud, polarization multiplexed to a single-carrier 640-Gb/s
[59].
To generate a square -QAM constellation using a single
I/Q modulator (driven by two quadrature signals with
amplitude levels), one needs two digital-to-analog converters
(DACs), each with a minimum resolution of
bits, at
a sampling rate equal to the symbol rate. Having higher-resolution DACs allows for compensation of modulator or driver
nonlinearities [60]; having over-sampled DACs further allows for digital pulse shaping and OFDM, as discussed in
Section III.F. Commercial DACs built in CMOS technology
are currently available up to 65 GSamples/s with as much
as 8-bit resolution [61], capable of producing constellations
beyond 16-QAM. Compared to the inset of Fig. 3, this could
shift the optimum constellation size in terms of raw interface
rates to
for CMOS-integrated
ASIC
solutions. The state-of-the-art in high-speed DAC technologies
is further reviewed in [62], [63].
In order to go beyond technologically achievable
single-channel line rates using the best trade-off between
and
requires multiplexing in the polarization, frequency,
or spatial dimension, as discussed in Section II.C. For example,
spatial paths have been used for low-power
-Gb/s
short-reach interfaces [3], and optical superchannels with, e.g.,
orthogonal optical subcarriers have been used to achieve
aggregate line rates of 1.2 Tb/s, transmitted over long-haul
(7200-km) distances [40], [64]. All parallel approaches used to
scale interface rates ask for photonic integration in order to be
economically viable [3], [65], [66].

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TABLE II
APPROXIMATE ENOB REQUIREMENTS FOR ADCS
USED FOR DIGITAL COHERENT QAM DETECTION

B. Symbol Rate versus Constellation SizeADC Resolution

Related to the resolution of the transmit-side DAC is that of
the receive-side ADC, usually specified in terms of its effective
number of bits5 (ENoB). As shown in [67], 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
amplitude levels of the two signal quadratures if the
constellation were received without any distortions and phase
rotations (cf. Table II).
The technological trade-off between ADC resolution and
bandwidth is analyzed in a series of papers by Walden [68],
[69], and reveals a reduction of about 3.3 ENoB per decade
of analog input bandwidth. This reduction of available ENoB
with detection bandwidth is also frequently observed in optical
superchannel experiments [40]: The detection of a single optical subcarrier (isolated by optical or analog electronic filtering
prior to digitization) typically shows better performance than
the simultaneous detection of multiple subcarriers followed by
digital filtering after the ADC. The reason for this observation
is that in the latter case the amplitude resolution of the ADC
is shared among all detected subcarriers, which accordingly
reduces the ENoB available for each individual subcarrier.
According to Waldens studies, converters improve at a rate
of
ENoB per year at fixed bandwidth, or at 27% (1 dB)
per year in bandwidth at fixed ENoB, which matches the evolution of symbol rates in digital coherent detection experiments,
represented by purple squares in Fig. 1(a). Commercial CMOS
based ADCs achieve up to 65 GSamples/s at close to 6 ENoB
across a
-GHz bandwidth [61], [70]. Using 28-nm CMOS
technology, ADC bandwidths of
GHz at sampling rates
between 80 and 100 GSamples/s at
ENoB are expected to
be available soon [71]. The state-of-the-art in high-speed ADC
technologies is further reviewed in [62], [63].
Looking at the speed versus converter resolution trade-off
in terms of a combined transmitter/receiver sensitivity penalty,
Fig. 4 displays back-to-back implementation penalties (i.e., the
gap between experimentally achieved and theoretically possible
signal-to-noise ratios at a reference BER of
) for recent research experiments. The black curves are contours of constant
single-channel (single carrier, single polarization) line rates, as
in Fig. 3. The gray lines represent a linear least-squares fit to
the reported experimental implementation penalties, revealing a
slope close to 4 bits/decade. Within reasonable limits reflecting
the significant scatter of the penalty data, this suggests that it is
equally hard to build, e.g., an 8-GBaud 256-QAM system [72]
5Although ENoB is the most commonly used performance metric for highspeed DACs and ADCs, a clear relationship between ENoB and the BER performance of a digital coherent receiver has not yet been established.

Fig. 4. Summary of experimentally achieved implementation penalties at

for single-channel (single carrier, single polarization, electronically multiplexed) higher-order modulation formats. Gray lines represent a
linear fit to the penalty data, revealing a slope of 3.9 bits/symbol per decade
of symbol rate. Black lines represent contours of constant single-channel line
rates. (Red squares: Digital pulse shaping or OFDM. Blue circles: No digital
pulse shaping.).

as it is to build an 80-GBaud 16-QAM system [59], at least in a

research context.
C. Symbol Rate versus Constellation SizeDigital Filter Sizes
Since digital coherent receivers have the entire optical field
information available in digital form, linear optical impairments
can be readily compensated for by digital filters within the receivers DSP. The most important such impairments are chromatic dispersion (CD), polarization-mode dispersion (PMD),
and filtering impairments as they arise from a signals multiple passes through ROADMs in an optically routed network.
Todays DSP ASICs are capable of handling the CD of more
than 2000 km of standard single-mode fiber (SSMF, 17 ps/km
nm), equivalent to a CD compensation capability of
ns/nm,
at
GBaud [73].
Chromatic dispersion represents an all-pass filter with
quadratic phase [74], which can be compensated using a filter
with the inverse phase profile [75]. The length of such a filters
impulse response (in terms of
spaced filter taps) is
approximately given by
[75],
which amounts to
taps for the above parameters. As
adjacent-pulse overlap due to dispersive pulse broadening
scales quadratically with symbol rate, doubling
results in
a quadrupled number of filter taps to compensate for the same
fiber lengths worth of CD; other linear impairments such as
PMD or concatenated filtering scale linear with symbol rate.
On the other hand, keeping the symbol rate fixed and scaling
the transponders interface rate by going to higher-order constellations keeps the required filter lengths unchanged (but may
limit the reach due other factors discussed in this section).
D. Symbol Rate versus Constellation SizeLaser Phase Noise
In addition to the above considerations, the trade-off between
symbol rate and constellation size is also impacted by phase
noise. Random phase fluctuations of signal and/or local oscillator (LO) light as well as pattern-dependent phase perturbations
induced by fiber nonlinearities [76] translate into angular noise
that ultimately degrades detection performance. The tolerance

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Fig. 5. Local oscillator phase noise induced pulse distortions from digital coherent detection.

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a 0.5-dB sensitivity penalty and for a CD compensation capability of 30 ns/nm (

-km SSMF) drops from 3 MHz to less
than 500 kHz (instead of increasing to 16 MHz) when going
from 10.7 GBaud to 56 GBaud. Experiments at 107 Gbaud confirm this observation [83]. This trade-off suggests an optimum
symbol rate with respect to laser phase noise in digitally CD
compensated coherent systems.
E. Spectral Efficiency versus Noise and Transmission Reach

to phase noise depends substantially on the underlying detection

algorithm and its hardware implementation [67], [77], [78]. In
general, higher-order modulation formats become progressively
more sensitive to phase noise. Since it is the phase noise accumulation across a modulation symbol (or multiples thereof) that
determines the impact of phase noise on detection performance,
the tolerance to laser phase noise for a given detection algorithm
and modulation format depends on the ratio of the combined
signal and LO laser linewidth
to the symbol rate,
(or, equivalently, on the product of laser linewidth and symbol
duration,
). For small (
-dB) penalties and at typical pre-FEC BERs between
and
, QPSK tolerates
values of
on the order of
, 16-QAM on the order
of
, and 64-QAM on the order of
[67], [77], [79].
Hence, a
-kHz linewidth external cavity laser (ECL) is an
appropriate light source down to symbol rates of several GBaud
for QPSK and down to
GBaud for 16-QAM. Significantly
higher-order constellations at
GBaud or below require narrower-linewidth lasers [72] or particularly phase-noise tolerant
DSP algorithms [80] to avoid sensitivity penalties from laser
phase noise. On the other hand, going to higher symbol rates
proportionally relaxes laser phase noise requirements. For example, 64-QAM at 21.4 GBaud has been demonstrated using a
-kHz ECL [81], 16-QAM at 14 GBaud has been shown
to tolerate
MHz of laser linewidth [82], and QPSK at
GBaud was demonstrated using linewidths of about 10 MHz,
which allowed for distributed feedback (DFB) lasers at negligible phase noise penalties [83].
Another important aspect related to laser phase noise in digital coherent receivers is the conversion of laser phase noise to
intensity noise within the CD filter [84], [85]. This effect can
also be understood as signal decoherence induced by LO phase
noise, as visualized in Fig. 5: The fibers CD spreads the signal
(together with all the signal lasers phase fluctuations) over a
large number of symbols (
for a 2000-km SSMF link at
30 GBaud). An ideal digital coherent receiver compensates for
this temporal spreading by applying the inverse CD in the digital domain, where the digital CD compensation filter restores
the transmit signal by coherently superimposing the dispersed
received signal components within a range of, e.g.,
symbols. However, if the phase of these samples exhibits random
fluctuations (generated by the LO lasers phase noise, cf. Fig. 5),
far-apart samples of the received signal that need to be superimposed by the CD compensation filter are no longer coherent,
which inevitably degrades the digital superposition process. As
a consequence, high-speed signals become less tolerant to LO
laser phase noise in the presence of long digital filters such
as needed for significant CD compensation. For example, [85]
shows that the LO laser linewidth tolerance for PDM-QPSK at

While our above considerations were all linked to trade-offs

involving per-channel interface rates, one of the most important
trade-offs in advanced system design is largely independent
of single-channel interface rates or the number of sub-carriers
in an OFDM or optical superchannel multiplex. This independence is exact in the linear regime and in the presence of fiber
nonlinearities is approximately valid for typical dispersion
uncompensated system parameters [41][43]: The trade-off
between spectral efficiency and system 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. Fig. 6(a) visualizes this trade-off in
the linear regime, showing the achievable (single-polarization) spectral efficiency as a function of the received SNR
per bit [28], [33]. The Shannon limit for a linear, additive
white Gaussian noise channel [31] is shown together with the
theoretical performance of various higher-order square QAM
constellations (blue circles) assuming Gray-coded symbol
mapping and state-of-the-art 7% overhead hard-decision FEC
capable of correcting an input BER of
to values
below
[44]. Representative experiments are denoted
by red squares. Performance will shift towards the Shannon
limit as more advanced coding [45], [46] and/or non-square
QAM constellation shaping [47], [86] are being used. The
impact of advanced coding on (linear) system performance
is quantified in Fig. 6(b), where the blue circles represent
the performance of the 7% hard-decision FEC underlying
Fig. 6(a) and the Shannon bounds for the respective square
QAM formats with ideal soft-decision FEC are shown as blue
curves. The asymptotic gap between square QAM performance
and the modulation unconstrained Shannon limit (black curve)
amounts to 1.53 dB and can be tapped into by proper constellation shaping, especially for large constellation sizes [47], [86].
Note that the Shannon limit is relatively steep in the low-spectral-efficiency regime but asymptotically flattens out to a slope
of 1 b/s/Hz for every 3-dB of higher SNR per bit at high spectral
efficiencies. With reference to Fig. 6(a), starting with QPSK as
a baseline, doubling system capacity asks for 16-QAM, which
comes at the expense of a 3.7-dB higher SNR per bit, or 6.7-dB
higher optical SNR (OSNR) [28] at fixed symbol rate, plus a
-dB higher expected implementation penalty (cf. Fig. 4). To
retain approximately the QPSK transmission reach at 16-QAM,
this SNR gap may be closed through techniques such as:
(i) stronger (soft-decision) FEC or coded modulation [45],
[46], [86] to lower the receivers SNR requirements and
move both theoretical and experimental points in Fig. 6(a)
closer to their Shannon bounds. In the spirit of coded
modulation, as indicated in Fig. 6(b), one may choose

WINZER: HIGH-SPECTRAL-EFFICIENCY OPTICAL MODULATION FORMATS

3831

Fig. 7. Trade-off between dual-polarization spectral efficiency and transmission reach, showing the nonlinear Shannon limit of [28] together with experimentally achieved results (circles). The ellipse indicates a range into which
commercial systems might fall, and the asterisk represents Alcatel-Lucents
commercially deployed optical transmission platform [73].

Fig. 6. Dependence of (single-polarization) spectral efficiency on the received SNR per bit. The Shannon limit for a linear, additive white Gaussian
noise channel is shown together with the theoretical performance of various
square QAM formats (blue circles), assuming Gray-coded symbol mapping
and state-of-the-art 7% overhead hard-decision FEC. Also shown in (a) are
representative experimental results (red squares); numbers indicate QAM
constellation sizes. In (b), the Shannon limits for various square QAM constellations are shown, and the effects of constellation shaping, coded modulation,
and signal over-filtering are indicated.

to transmit, e.g., 64-QAM instead of 16-QAM at a fixed

spectral efficiency of 3.73 b/s/Hz, thereby increasing the
available coding OH from 7% to 60%. Obviously, the
increased coding gain has to offset additional implementation penalties for the higher constellation size;
(ii) lower-loss fiber or (potentially higher-order) distributed Raman amplification [87] to improve the OSNR
delivered to the receiver;
(iii) lower-nonlinearity fiber or more powerful, nonlinear
distortion compensating DSP to allow for higher optical
signal launch powers [28], [88].
A further doubling in capacity, from 16-QAM to 256-QAM,
however, comes at the expense of an additional 8.8 dB in SNR
per bit (cf. Fig. 6(a)), which is impossible to accommodate
without reducing system reach.
The trade-off between spectral efficiency and system reach,
including noise, fiber nonlinearities, as well as current technological shortfalls, is further summarized in Fig. 7, showing
the PDM spectral efficiency as a function of transmission
distance. Record experimental results (circles) are shown
together with the nonlinear Shannon limit of [28]. Both
curves trace straight lines on a logarithmic scale for the transmission distance , since the delivered SNR is inversely
proportional to , and the spectral efficiency is given by
in the high-SNR
regime [89], [90]. The ellipse indicates a range into which

commercial systems working over installed legacy fiber with

appropriate OSNR margins might fall. The asterisk represents
Alcatel-Lucents commercially deployed 1830 optical transmission platform [73]. Importantly, we note that experimental
records have approached the nonlinear Shannon limit to within
a factor of less than two, which at an annual 2-dB traffic
growth rate corresponds to
months. Realizing that WDM
capacities are no longer scalable, alternative solutions have to
be speedily developed. Since shortening the regeneration distance is neither a cost- nor an energy-efficient option [89], the
exploitation of space as the last remaining physical dimension
is mandatory, leading to the notion of now heavily researched
SDM systems [91], [92], with the hope to get per-fiber capacities back onto a solid growth track, cf. Fig. 1(a).
F. Spectral Efficiency and Pulse Shaping
In our above considerations we were mostly concerned with
constellation size and symbol rate. However, from Section II
we know that the choice of analog transmit waveforms is
another important aspect of digital communication signals. Traditionally, high-speed optical communication transmitters have
used electronic multiplexers to generate binary drive signals,
whose exact pulse shape is determined by the multiplexers
output stage and hence depends on the characteristics of the
underlying high-speed electronics. Fig. 8(a) shows a typical
electronic non-return-to-zero (NRZ) drive waveform, measured
at 56 Gb/s. Note that high-speed electronic drive signals like
this contain a significant amount of non-linear ISI with memory,
i.e., they cannot generally be represented as a linearly filtered
version of an ideal QAM signal according to (4). Hence, linear
equalization cannot entirely remove ISI from signals based on
such waveforms, which inherently results in an ISI-induced
implementation penalty, even after linear equalization within
the coherent receiver.
Starting with high-speed electronic drive waveforms, higherorder QAM signals can either be generated in the optical domain
by means of parallel, binary-driven modulator structures [11],
[40], or in the electrical domain by first synthesizing high-speed
multi-level electrical drive signals that are then imprinted onto

3832

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 30, NO. 24, DECEMBER 15, 2012

Fig. 8. (a) Electronically multiplexed measured 56-Gb/s NRZ waveform,

(b) Ideal sinc pulse and corresponding waveform representing the same bit
pattern, and (c) measured and ideal optical spectra.

Fig. 9. The role of raised-cosine and square-root raised cosine pulses with
in a basic digital communication link according to (4).

the two quadratures of the optical field using an I/Q modulator

[82]. Both methods generate optical signals whose analog pulse
shapes contain non-linear ISI with memory and whose spectral
shapes are determined by the characteristics of the electronics.
Fig. 8(c) shows a typical resulting spectrum with its wide main
lobe and its pronounced sidelobes. Both spectral features generate crosstalk among tightly spaced WDM channels and are
hence of concern for high-spectral-efficiency systems. One partial mitigation option is the use of pre-modulation electronic filters or post-modulation optical filters to truncate the spectrum
in an analog manner [82].
Recently, researchers have also applied faster-than-Nyquist
signaling [93], [94] by over-filtering the transmit signal, i.e.,
the transmit filter is chosen so narrow that it induces substantial (linear) ISI onto the transmit waveform [95], [96], [111].
While this technique allows WDM channels to be spaced closer
together, the induced ISI needs to be compensated at the receiver by sequence detection (as opposed to the much simpler
symbol-by-symbol detection) [33], such as maximum a-posteriori (MAP) detection or maximum likelihood sequence estimation (MLSE) [95], [96], [111]. This way, it is possible to transmit
at spectral efficiencies exceeding the number of bits/symbol of
the underlying modulation format, e.g., at sufficiently high received SNR one can transmit at or above 4 b/s/Hz using PDMQPSK, as shown in Fig. 6(b). Note, however, that the same spectral efficiencies can be achieved by using richer symbol constellations at the transmitter and simpler symbol-by-symbol detection at the receiver. This leads to a trade-off between transmit
constellation size, analog pulse shaping, and receive DSP complexity. Importantly, all techniques are upper-bounded by the
corresponding Shannon capacity at the respective received SNR
(cf. Fig. 6(b)).
Optimum spectral and temporal pulse shaping to generate
ISI-free QAM signals is best done using an oversampled

transmit DAC that simultaneously performs the task of generating the QAM symbols and shaping the pulse waveform
according to (4). To achieve ISI-free performance, as discussed
in the context of signal orthogonality in Section II.B, it is well
known in digital communications that pulse shapes meeting
the Nyquist criterion need to be established at the sampling
point within the receiver [33]. The most important class of
Nyquist pulses has a raised-cosine (RC) shaped spectrum,
where a shape parameter varies the roll-off from infinitely
steep (rectangular spectrum,
) to gradual (cosine-shaped
spectrum,
), as visualized in Fig. 9. The corresponding
time-domain waveform for
has
(sinc) characteristics, with a long lasting oscillatory behavior; larger
values of
induce stronger damping and hence shorten the
filter length needed to digitally shape the transmit pulses, albeit
at the expense of a weaker spectral confinement. Note that
the optimum receive filter in a digital communication link
should match the transmitted pulse spectrum6 (matched filter)
[33], which implies that root raised cosine (RRC) pulses
should be transmitted, i.e., pulses whose spectrum
is the
square-root of a RC spectrum [33]. In fact, it is these pulses
that obey the orthogonality relations of (3). While RRC pulses
by themselves contain ISI, the matched receive filter produces
and hence turns RRC pulses back
into ISI-free RC pulses (cf. Fig. 9).
Fig. 8(b) shows the waveform corresponding to the bit
pattern of Fig. 8(a) but using sinc pulses (i.e., RRC pulses with
). As can be seen by comparing the two waveforms in (a)
and (b), the peak-to-average power ratio (PAPR) is increased
when going from a standard binary drive waveform to RRC
pulses. As with OFDM transmit waveforms, this increase in
PAPR may pose practical problems, since the transmit DAC
6Strictly speaking, the aggregate filter function after the addition of white
noise needs to be matched to the aggregate pulse shape prior to the addition of
white noise for maximum SNR at the decision gate [33].

WINZER: HIGH-SPECTRAL-EFFICIENCY OPTICAL MODULATION FORMATS

Fig. 10. Tolerance of various higher-order modulation formats to in-band

crosstalk. (Solid curves: theory; circles and squares: experiments at 21.4 GBaud
without and with CD, respectively) [110].

has to be able to faithfully generate the entire waveform

without much amplitude clipping. Hence, a trade-off between
spectral confinement, pulse shaping, filter impulse response
length, PAPR, appropriately oversampled DAC resolution, and
ultra-dense WDM or optical superchannel system performance
has to be made [97], [98]. Nyquist pulse shaping forms the
basis for many recent high-spectral-efficiency single-carrier
and multi-carrier optical communication experiments [40],
[72], [99][101]. Pulse shapes with increased tolerance to fiber
nonlinearities are also being explored [102].
G. Spectral Efficiency versus Crosstalk Tolerance
In addition to noise from optical amplifiers and linear and
nonlinear distortions from fiber propagation and networking
elements, signals in optical networks may suffer from crosstalk
among neighboring WDM channels as well as from crosstalk
originating from spurious signals within the same wavelength
slot. The former, referred to as WDM crosstalk [97], [98], [103],
results in trade-offs between spectral confinement (i.e., pulse
shaping), permissible overheads for pilots and FEC, and WDM
channel spacing. The latter, generally referred to as in-band
crosstalk, may arise within multi-degree mesh ROADMs [104],
[105], imperfect splices and connectors [106], or in the form
of multi-path interference in Raman amplified systems [107],
[108]. In-band crosstalk acts in a similar way as amplifier noise
[87], [108][110], 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). Hence, the tolerance of
various higher-order modulation formats to crosstalk closely
follows their tolerance to optical amplifier noise. Fig. 10 shows
the crosstalk induced OSNR penalty at a BER of
for
(single-polarization) QPSK, 16-QAM, and 64-QAM [110].
The solid black curves represent a simple theoretical model,
circles denote the case of an interferer having the same CD
as the signal, and squares represent a substantially dispersed
interferer (see [110] for details). Introducing dispersion onto
the interferer slightly increases crosstalk penalties due to the
larger PAPR of the dispersed interfering signal, resulting in
larger peak excursions of the crosstalk induced perturbations

3833

compared to a well-confined, undispersed interfering constellation. As the back-to-back implementation penalty in this
21.4-GBaud experiment increases from 0.9 dB (QPSK) to 1.8
dB (16-QAM) and 4.0 dB (64-QAM), the crosstalk tolerance
also shrinks compared to theory. For a 1-dB crosstalk penalty,
QPSK shows a tolerance of about 16 dB, while 64-QAM
requires less than about 32 dB of crosstalk, which can become
challenging in practical systems with multiple mesh ROADMs;
the required 24 dB of crosstalk for 16-QAM is much more
manageable in deployed networks. These considerations 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.
IV. CONCLUSION
We have discussed the general structure of advanced optical
modulation formats for digital coherent detection systems
with respect to their digital (constellation) and analog (pulse
shaping) properties. We have shown how symbol rate, constellation size, and pulse shaping impact the scaling of per-channel
interface rates and WDM spectral efficiencies in various optical
networking contexts. The resulting trade-offs, which include
fundamental as well as technological components, point at
16-QAM as a promising sweet spot that represents a good
compromise between various limiting effects but still enables
high-speed, high-capacity long-haul optical networking.
ACKNOWLEDGMENT
The author would like to thank S. Chandrasekhar,
A. Chraplyvy, I. Dedic, R.-J. Essiambre, G. Foschini,
A. Gnauck, S. Korotky, G. Kramer, A. Leven, X. Liu, T. Pfau,
J. Sinsky, S. Randel, G. Raybon, R. Ryf, R. Tkach, and C. Xie
for insightful discussions.
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Author biography not included by author request due to space constraints.