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Abstract—As fiber-optic transmission systems evolve toward
higher per-wavelength-channel data rates, the analog bandwidth
of digital-to-analog converters (DACs) has become a bottleneck.
Here, external analog multiplexing techniques utilizing multiple
DACs in each signaling dimension enable us to generate signals
with bandwidths exceeding the DACs’ capabilities. This tutorial
provides a comprehensive review of these techniques, including
electronic and optical ones. Moreover, it presents an analytical
model from the perspective of spectral image superposition as a
basis for a unified understanding of the principles of the various
schemes.
Index Terms—Optical transmitter, digital-to-analog converter
(DAC), bandwidth extension, digital signal processing,
intermediate-frequency-involved multiplexing, digital spectral
weaver.
I. I
NTRODUCTION
IGITAL
coherent transmission systems have been
deployed in a broad range of optical fiber networks, and
have become indispensable components in modern
communication infrastructure. Here, application-specific
integrated circuits (ASICs) for digital signal processing (DSP)
for such transceivers are interfaced with high-speed digital-to-
analog and analog-to-digital converters (DACs and ADCs) to
enable the use of spectrally efficient multilevel modulation
formats, pulse shaping, and pre/post-compensation for various
impairments [1]. While the data rates of digital coherent
transceivers have come to exceed 1 Tbps per wavelength
channel (Tbps/λ), the spread of bandwidth-intensive
applications such as the internet of things, 5G mobile
communications, and artificial intelligence is spurring demand
for even higher data rates. The data rate is the product of the
spectral efficiency (SE) in bps/Hz and the signal bandwidth in
Hz. Considering the constraint of the signal-to-noise ratio
Manuscript received *, 2024.
H. Yamazaki and M. Nagatani are concurrently with NTT Network
Innovation Laboratories, NTT Corporation, Kanagawa 239-0847, Japan, and
NTT Device Technology Laboratories, NTT Corporation, Kanagawa 243-0198,
Japan (e-mail: hrsh.yamazaki@ntt.com; munehiko.nagatani@ntt.com).
M. Nakamura, F. Hamaoka, T. Kobayashi and Y. Miyamoto are with NTT
Network Innovation Laboratories, NTT Corporation, Kanagawa 239-0847,
(SNR), the room for improving the already high SE seems to be
severely limited. On the other hand, the signal bandwidth is
mainly determined by the analog bandwidths of the DACs and
ADCs, but significant improvements in their analog bandwidths
appear challenging. This state of affairs also applies to
multilevel intensity-modulated direct-detection (IMDD)
systems, which have been widely studied for their application
to short-range high-capacity transmission.
The effective analog bandwidths of transceivers can be
extended by utilizing multiple sets of DAC/ADCs in parallel in
external analog electronic or optical
multiplexing/demultiplexing (or interleaving) architectures
having tailored digital pre- and post-processing algorithms [2].
Fig. 1 shows the concept of the bandwidth extension of
transmitters by this means. The currently deployed standard
transmitter for digital coherent systems (Fig. 1(a)) use four
DACs, one for each of the four signaling dimensions (in-phase,
I, and quadrature, Q, of the two orthogonal polarizations). The
DACs are fabricated using Si complementary metal oxide
semiconductor (CMOS) technology and monolithically
integrated on the DSP ASIC. Signals from the DACs are sent to
a frontend (FE) module consisting of driver amplifiers and an
optical modulator. The signal bandwidth of the final output
optical signal, B, on each side of the optical carrier frequency,
f
LD
, equals to that of the analog bandwidth of each DAC. Fig.
2(b) shows an electronically bandwidth-extending transmitter,
where an electronic multiplexer (MUX) is used in place of each
driver in the FE to convert two signals with a bandwidth of B
into one signal having a larger bandwidth, e.g., 2B. The MUXs
are fabricated using compound semiconductor technologies,
such as SiGe, InP, or GaAs, in order for them to provide a larger
bandwidth and output amplitude than those of CMOS DAC.
The modulator’s electro-optic (EO) bandwidth should also be
made larger. The DSP incorporates pre-processors designed
Japan (e-mail: msnr.nakamura@ntt.com; fukutaro.hamaoka@ntt.com;
tkyk.kobayashi@ntt.com; yutaka.miyamoto@ntt.com).
T. Hashimoto is with NTT Device Technology Laboratories, NTT
Corporation, Kanagawa 243–0198, Japan (e-mail:
toshikazu.hashimoto@ntt.com).
Analog Electronic and Optical Multiplexing
Techniques for Transmitter Bandwidth
Extension
Hiroshi Yamazaki, Member, IEEE, Munehiko Nagatani, Member, IEEE, Masanori Nakamura,
Member, IEEE, Fukutaro Hamaoka, Member, IEEE, Takayuki Kobayashi, Member, IEEE, Toshikazu
Hashimoto, and Yutaka Miyamoto, Member, IEEE
(Invited Tutorial)
D
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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2
based on the configuration of the MUX. This configuration
allows the final signal bandwidth to be extended without
increasing the DAC’s bandwidth and without increasing the
required bandwidth of the wiring between the DSP ASIC and
the FE. Fig. 1(c) shows a bandwidth-extending transmitter
utilizing an optical MUX, which typically includes a clock-
driven modulator for generating optical subcarriers (or electro-
optic comb) around f
LD
. Various schemes are possible, as will
be discussed later, but as an intuitive example, here, by feeding
two 2B-spaced subcarriers separately to the two modulators and
combining their outputs, we can generate a doubled-bandwidth
optical signal. This configuration allows the bandwidth to be
extended without increasing bandwidth requirements for all the
electronics and modulators, at the cost of additional optical
complexity.
Before the advent of digital coherent transmission
technology, parallel DAC/ADC architectures have long been
studied in the field of electronics [3], [4], [5], [6], [7]. Several
techniques underlie the development of electronic test and
measurement instruments, such as arbitrary waveform
generators (AWGs) and digital storage oscilloscopes (DSOs)
[8], [9], [10], [11]. The idea of utilizing such electronic
parallelization to extend the bandwidth of optical transceivers
first appeared in the literature in 2014 [12], and the first
experimental demonstration was reported in 2015 with an
different approach [13], [14]. Subsequently, there were various
proposals and demonstrations of electronically bandwidth-
extending optical transmitters as detailed later. On the other
hand, optical multiplexing/demultiplexing techniques for
transceiver bandwidth extension trace their roots to “static”
optical arbitrary waveform generation (OAWG), which is a
spectrally resolved (line-by-line) pulse shaping for repetitive
optical pulses [15], [16]. By introducing DAC-driven high-
speed modulators in place of the static amplitude and phase
adjusters, a “dynamic” OAWG, which can be used as a
bandwidth-extending transmitter, was first experimentally
demonstrated in 2010 [17]. Its receiver-side counterpart, optical
arbitrary waveform measurement (OAWM), was also
demonstrated [18]. Since then, there has been extensive
research into optical-domain bandwidth-extending techniques,
as also detailed later. Although the electronic and optical
bandwidth extension techniques appear to have distinct origins,
their underlying principles are similar and the same analytical
framework can be applied to them.
In this tutorial paper, as an extension from a tutorial talk at
the Optical Fiber Communication Conference 2024 [19], we
focus on transmitter-side bandwidth extension technologies in
the aforementioned context. We categorize the multiplexing
techniques into baseband multiplexing (BB-MUX), which is
briefly reviewed in Section II, and intermediate-frequency-
involved multiplexing (IFI-MUX), which is described in detail
in subsequent sections and is the central topic of this paper. In
Section III, we explain the operation principles and designs of
electronic IFI-MUX systems. We first intuitively describe
several examples of IFI-MUX systems, and then provide a
general analytical model that provides a systematic method to
design digital pre-processors for various IFI-MUX systems. In
Section IV, we discuss the operation principles of optical IFI-
MUX systems. By applying the same analytical model as those
for the electronic ones, several approaches other than the
OAWG are derived. Section V provides a review of the state-
of-the-art experimental demonstrations, and Section VI
concludes the paper by summarizing the previous sections and
considering open challenges in this field.
Listed below are the common assumptions and notation used
in this paper:
● All DACs connected to the same MUX component
operate at the same sampling rate, f
s
.
● The cutoff frequency, f
cutoff
, is used without a strict
definition. The intensity-response threshold for f
cutoff
is
typically between −3 and −10 dB from the response at
a low frequency but is supposed to be selected on a
case-by-case basis.
● The unit bandwidth, B, corresponds to the bandwidth
of the baseband sub-signal output from each DAC, and
supposed to be equal to or smaller than both f
cutoff
and
f
s
/2.
● Although it is not shown in the figures for simplicity,
adjacent spectral slices actually overlap due to the
finite roll-offs of the slicing filters.
● Superscript asterisk denotes conjugation, and tilde
denotes spectral flipping (conjugation and frequency
reversal) around B/2;
.
● In schematic spectra, dark-colored components (with
the fill color matching the edge color) represent the
flipped copies of the light-colored components. For
Fig. 1. Concept of transmitter bandwidth extension. Configurations of (a) a current standard digital coherent transmitter, (b) an electronically bandwidth-
extending
transmitter, and (c) an optically bandwidth-extending transmitter. Drv: driver, Mod: optical modulator, LD: laser diode.
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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3
example, when the signal in the first Nyquist zone is
considered as the original signal, its alias in the second
Nyquist zone and lower sidebands (LSBs) of the
intermediate-frequency (IF) images are dark-colored
according to this rule.
● Unless otherwise specified, the configuration of the
MUX system shown in each figure corresponds to an
electronic MUX system for one signaling dimension.
For a digital coherent transmitter, four sets of such
systems are required.
● The terms multiplexing and interleaving will be used
interchangeably, but interleaving will only be used to
cite literature.
II. O
PERATION PRINCIPLE OF
BB-MUX
Fig. 2 shows the configuration and operation principle of a
BB-MUX system. Here, the outputs from two DACs are simply
combined with a relative time shift corresponding to half the
sampling cycle of each. This type of multiplexing has been
called by several different names: pseudo-interleaving [6],
time-interleaving [3], [8], or non-clocked MUX [20]. In this
paper, we call it BB-MUX to emphasize that no intermediate-
frequency (IF) components are involved in the signal
generation process.
In the spectrum of the output from the DAC, components
with frequencies above the Nyquist frequency of f
s
/2 are aliases
of the original baseband signal below f
s
/2. If the DAC has a f
cutoff
smaller than f
s
/2, the aliases are naturally cut off. Otherwise, the
alias should be filtered out externally unless the DAC is used at
1 sample per symbol (sps); at 1sps, the alias is a part of the
signal. By using BB-MUX, we can double the effective
sampling rate from f
s
to 2f
s
, thereby doubling the effective
Nyquist frequency from f
s
/2 to f
s
. Therefore, if each DAC has a
f
cutoff
greater than f
s
/2, BB-MUX effectively extends the upper
bound of the signal bandwidth from f
s
/2 to f
cutoff
. In other words,
it “unlocks” the alias band above f
s
/2 for use as a part of
arbitrary signals. On the other hand, if f
cutoff
is smaller than f
s
/2
and the power of the alias is negligible, BB-MUX does not
provide any merits in terms of the signal bandwidth. As such, it
is valid only for those DACs having a f
cutoff
greater than f
s
/2.
In the BB-MUX system, digital data sent to the two DACs
are basically defined by alternately selecting the samples in the
virtual target signal, which is defined by sampling the target
analog signal at a sampling rate of 2f
s
. In other words, the data
to be sent to one DAC is sampled from the target analog signal
at f
s
with a sample timing difference of 1/(2f
s
) from that of
sampling for the other DAC. Accordingly, the output spectra of
the two DACs, X
1
(f) and X
2
(f), can be expressed as:
!"
"
#
$
%
where S(f) is the spectrum of the arbitrary target analog signal,
R(f) is the analog frequency response of each DAC, the asterisk
represents convolution, and δ(f) denotes the Dirac delta
function. The term
!" "
#
&
represents the timing difference of
1/(2f
s
). Since |R(f)| is negligibly small at f≥f
s
in most high-speed
DACs suitable for use in optical transmission, the terms for
|k|≥2 can be omitted. Assuming an ideal combiner, the final
output of the system, X(f), is given as:
'
This holds true even when S(f) extends beyond f
s
/2, representing
the operation of the BB-MUX system described in the
preceding paragraph. The response R(f) can be compensated by
applying a digital filter. Non-uniformity of the responses and/or
timing-difference errors between the two DACs can also be
compensated digitally.
BB-MUX has recently been employed in high-end bench-top
AWGs, where each channel consists of two 128-GS/s SiGe
DACs and an external combiner [21], [22]. This type of AWG
has been used in a variety of high-speed optical transmission
experiments, including the first over-2-Tbps/λ digital coherent
transmission [23].
III. O
PERATION PRINCIPLE OF ELECTRONIC
IFI-MUX
In contrast to BB-MUX, IFI-MUX extends the signal
bandwidth beyond f
cutoff
by utilizing IF images generated in the
MUX systems. Thus, IFI-MUX is effective also for DACs
having f
cutoff
smaller than f
s
/2. In this section, we first describe
the operation principles of several different electronic IFI-MUX
systems in an intuitive manner by using visual representations
of spectra. After that, we provide a general analytical model that
comprehensively captures the principles of various IFI-MUX
systems and offers a design method for digital pre-processors
Fig. 2. Configuration and operation principle of a BB-MUX system.
Fig. 3. Configuration and operation principle of a mixer-based dual-DAC IFI-
MUX system with an analog HPF.
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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4
based on a frequency-domain perspective. We will not
elaborate here on the time-domain description of such a model,
but ones are given in [24], [25]. Hereinafter, unless otherwise
specified, we will assume the use of DACs with a f
cutoff
smaller
than f
s
/2 and with negligible aliases. The analog frequency
responses of the DACs up to f
cutoff
will be assumed to be pre-
compensated in the DSP.
A. Mixer-based IFI-MUX
Fig. 3 shows the configuration and operation principle of a
basic mixer-based IFI-MUX [12]. After its ADC-side
counterpart, this type of mixer-based concept is often referred
to as digital bandwidth interleaving (DBI) [8]. In the DSP, a
virtual target signal with a bandwidth up to 2B is generated and
spectrally sliced. The lower-frequency (LF, red) component and
the down-converted higher-frequency (HF, blue) component
are sent to the two DACs, respectively. In the analog domain,
the output from the DAC handling the HF component is up-
converted to the IF clock frequency of f
clk
=B with a mixer and
its LSB is filtered out by an analog high-pass filter (HPF).
Finally, the components are combined together to generate the
physical target signal. Thus, arbitrary signals with bandwidths
up to nearly twice that of each DAC can be generated. The HPF
and the combiner can be replaced by a diplexer.
Fig. 4 shows a triple-DAC system based on a similar
principle [26], [27]. Here, f
clk
=2B is used to up-convert the
outputs from two out of the three DACs. The DAC in the middle
handles the middle-frequency (MF, green) component, and the
upper sideband (USB) of the up-converted MF signal is cut off
by an analog low-pass filter (LPF). Therefore, in the digital
domain, a flipped copy of the MF component of the virtual
target signal is sent to that DAC. The other two DACs handle
the LF and HF components. The physical target signal is
obtained by combining the three components. The LPF, the
HPF and the combiner can be replaced by a triplexer.
In practice, analog filters have finite sharpness and extinction
ratio, and the IF clocks may leak from the mixers. Distortions
due to these imperfections can be suppressed by slightly
shifting the IF clock frequencies, setting guard bands around
those frequencies, and applying digital pre-compensation [26],
[27].
As shown in Fig. 5, it is also possible to omit the analog
filters, which are generally larger than the other components,
are not tunable, and require a guard band to avoid distortion. By
digitally adding a phase-inversed copy of the LSB of the HF
component to the LF component before it is sent to the DAC,
we can cancel out the LSB of the HF component in the analog
domain [28], [29].
B. IFI-MUX with an RF IQ modulator (RF-IQM)
Fig. 6 shows the configuration and operation principle of
another analog-filter-less IFI-MUX system based on an RF IQ
modulator (RF-IQM) [30]. Here, the target signal, which
actually is a baseband signal with a bandwidth up to 2B, is
interpreted as an IF signal at around a carrier frequency of B. In
the DSP, the I and Q components of the IF signal are extracted
as the sub-signals to be sent to the DACs. This can be done, for
example, by multiplying the virtual target signal by cos(2πBt)
and −sin(2πBt), respectively, before applying digital LPFs with
a cutoff frequency of B. In the analog domain, the sub-signals
corresponding to the I and Q components are up-converted to
the IF frequency of f
clk
=B with a phase difference of π/2
between them. Finally, they are combined together to generate
the physical target signal.
The schematic spectra in Fig. 6 are explained as follows. The
analytic signal corresponding to the IF signal can be represented
as x(t)e
j2Bπt
={x
I
(t)+jx
Q
(t)}e
j2Bπt
, where x
I
(t) and x
Q
(t) are the
real-valued I and Q sub-signals. Since x
I
(t)={x(t)+x
*
(t)}/2 and
x
Q
(t)=−j{x(t)−x
*
(t)}/2, the spectra of the two sub-signals are
X
I
(f)={X(f)+X
*
(−f)}/2 and X
Q
(f)= −j{X(f) −X
*
(−f)}/2. Here, X(f)
corresponds to a spectrum obtained by shifting the positive-
frequency part of the target signal spectrum by −B. Therefore,
the two sub-signals contain the HF (blue) component with
relative phases of 0 and −π/2, respectively. Meanwhile, as
X
*
(−f) is obtained by flipping X(f) around DC, the two sub-
signals also contain the flipped copy of the LF (red) component
with relative phases of 0 and +π/2, respectively. After being up-
converted with the orthogonal-phase IF clocks in the analog
Fig. 4. Configuration and operation principle of a mixer-based triple-DAC IFI-
MUX system with analog LPF and HPF.
Fig. 5. Configuration and operation principle of an analog-filter-less mixer-
based IFI-MUX system.
Fig. 6. Configuration and operation principle of an RF-IQM as an IFI-
MUX
system.
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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5
domain, all unnecessary components cancel each other out in
the combiner, leaving only the target signal.
C. IFI-MUX with an analog multiplexer (AMUX)
An AMUX is a linear selector that makes the two input
signals pass through alternately at the clock frequency, f
clk
, as
shown in Fig. 7(a) [13], [14], [20], [35]. This function can be
represented by the equivalent model shown in Fig 7(b), where
the input signals are multiplied by pulse trains having levels of
zero and one alternately at f
clk
before they are combined. In the
frequency domain, this corresponds to generating images
around f
clk
and superposing those images with the original
baseband signals, where the relative phases of the images with
respect to the baseband signals differ by π for the two inputs.
The relative amplitude of the images compared with that of the
baseband signals, r, depends on the AMUX’s response speed at
f
clk
. The typical range of r is approximately 0.5 to 0.6 in practice.
Fig. 8 shows the configurations and operation principles of
two different IFI-MUX systems using AMUXs clocked at 2B
and B, respectively [35]. As well as being analog-filter-less,
each configuration is totally symmetric with respect to the two
DACs, which are simply connected to the AMUX. In the DSP,
we use a digital spectral weaver (DSW), which generates the
sub-signals by combining LF and HF components of the virtual
target signal and their flipped copies so that it functions as an
inverse system of the analog part of the IFI-MUX system. The
spectra in Fig. 8 intuitively represent the operation principles,
where the physical target signals are synthesized by
superposing the sub-signals with a bandwidth of B and their
images generated around f
clk
in the AMUX. Similar to the
principles shown in Figs. 4 and 5, all unnecessary components
cancel each other out when all the baseband components and
images of the sub-signals are combined, leaving only the target
signal in the frequency region up to 2B.
In the system with f
clk
=2B shown in Fig. 8(a) [13], [14], the
DSW adds flipped copies of the HF components to the LF
components with complementary phases to generate two sub-
signals. The amplitude ratio of the LF and HF components is
set to 1:1/r to smoothly concatenate the baseband components
and images in the analog domain. Setting this ratio to 1:1 is also
acceptable if an amplitude step at around f=B is allowed; in this
case, the DSW corresponds to a simple time-domain
demultiplexer converting the sampling rate from 4B to 2B. The
output from the AMUX includes a residual image in f>2B,
which is naturally suppressed due to the roll-off of the
frequency responses of the AMUX itself and the optical
modulator in most cases.
The other system with f
clk
=B shown in Fig. 8(b) relaxes the
requirement for the clock speed by half in addition to
suppressing the residual image [33], [34]. The DSW for this
configuration can be derived analytically as discussed later.
D. IFI-MUX with an AMUX and a mixer in combination
Fig. 9 shows a triple-DAC IFI-MUX system using an AMUX
Fig. 7. (a) Functional diagram and (b) equivalent model of an AMUX.
Fig. 8. Configuration and operation principle of IFI-MUX systems using AMUXs with clock frequencies of (a) 2B and (b) B.
Fig. 9. Configuration and operation principle of a triple-DAC IFI-
MUX system
with an AMUX and a mixer.
This article has been accepted for publication in IEEE/OSA Journal of Lightwave Technology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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6
and a mixer [36]. This is also an analog-filter-less system,
where the outputs from the top and middle DACs are sent to the
AMUX clocked at 2B, while that from the bottom DAC is up-
converted by the mixer driven also at 2B before they are
combined. The attenuation with a factor of r after the mixer
reflects the specific configuration used in [34] and is not
essential. The DSW is designed so that a physical target signal
with a bandwidth up to 3B is generated through spectral
superposition in the analog domain. Among the various
possible configurations of analog-filter-less triple-DAC IFI-
MUX, this particular one has an advantage of being compatible
with a time-interleaved digital nonlinear compensation [36].
The operation principle of this system is rather complicated
to merit a visual spectral representation. The analytical model
presented in the next sub-section provides a more thorough
explanation.
E. General model for IFI-MUX systems
As described so far, the concept behind IFI-MUX goes
beyond just frequency-division multiplexing (FDM), and is
based on an combination of digital pre-processing and analog
superposition of IF images and baseband signals. This
perspective leads to the general model shown in Fig. 10, which
provides a basis for understanding the principles of the IFI-
MUX systems and for designing digital pre-processors for them.
As shown in Fig. 10(a), the system consists of a DSP with a
DSW, N DACs, and a MUX subsystem in the analog domain
driven with clocks at frequencies of B, 2B, ..., (N−1)B. In
referring to this model, we will use the term DSW to describe
all types of digital pre-processor for IFI-MUX systems,
including those we previously called a slicer or I/Q separator.
In the DSP, the virtual target signal, U, which is an arbitrary
signal with a bandwidth up to NB, is separated into N spectral
slices, U
1
, U
2
, ..., U
N
, each with a bandwidth of B. The DSW
converts those slices into the sub-signals, V
1
, V
2
, ..., V
N
, each
with a bandwidth of B, where V
k
is converted to an analog signal
by the k-th DAC and sent to the MUX subsystem. In the figure,
for simplicity, the DACs are assumed to have B≤f
cutoff
<f
s
/2 and
thus generates no aliases; for DACs with ,f
cutoff
≥f
s
/2, we should
set B=f
s
/2 and take the alias into account as (
) in the second
Nyquist zone (f
s
/2≤f<f
s
). Finally, the physical target signal,
which is also denoted as U, is generated as the output from the
MUX subsystem. In other words, the DSW is designed such
that the final physical output signal matches the signal
represented by the digital input, under the given hardware
configuration. For simplicity, we will ignore the out-of-band
residual images that may appear in the frequency range of f>NB
in the final output. We define U(f), U
k
(f), and V
k
(f) as spectra of
analytic signals that have no negative-frequency components,
and define all U
k
(f) so that they correspond to the slices that are
down-converted to the DC. Therefore, *+*
,
%. For simplicity, the arguments of the spectral
functions will be omitted from the figures and symbols in the
text unless the frequency dependence has to be emphasized.
Fig 10(b) schematically represents the spectral superposition
that takes place in the MUX subsystem. For each V
k
, the images
around all clock frequencies are taken into consideration, while
some of them may be absent in individual cases. Each image
consists of (
as the USB and its flipped copy (
) as the LSB.
Each U
k
in the analog (physical) domain is obtained as a
superposition of the USB of the images around (k−1)B and the
LSB of those around kB. Although they are not illustrated in the
figure, the amplitudes and phases of those images vary from one
another depending on the configuration of the MUX subsystem.
As such, the analog part of the system can be interpreted as a
2N×N multi-input multi-output (MIMO) system with V
1
, V
2
, ...,
V
N
, and their flipped copies (
- , (
- , ... (
,
) as inputs and U
1
,
U
2
, ..., U
N
as outputs, as shown in Fig. 10(c). Here, the channel
matrix, H, corresponds to the response of the MUX subsystem.
The MIMO system is represented as
./01
1
-23
where .*
*
4 *
,
5
1(
(
4 (
,
5
1
-(
-(
-4 (
,
)
5
6
and H is an N×2N matrix. In H, each element, H
kl
, in the left
half (l≤N) represents the amplitude and phase of the USB of the
image of the l-th DAC’s output at around the frequency of
(k−1)B, and that in the right half (l≥N) represents those for the
LSB around kB. The DSW is designed on the basis of H so that
it generates sub-signals V
1
, V
2
, ..., V
N
that satisfy (3) from
Fig. 10. General model for IFI-
MUX systems. (a) Configuration. (b) Spectral
superposition of the baseband signals and images. (c) Interpretation of the
analog part of the model as a MIMO system. (d) Interpretation of the DSW as
an inverse MIMO system.
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7
information of the target signal U. This operation corresponds
to the inverse of (3), but since
H
is not a square matrix, its
inverse does not exist. Meanwhile, from the examples discussed
in the previous sub-sections, it can be inferred that not only U
1
,
U
2
, ..., U
N
but also their flipped copies
*
)
,
*
)
, ...
*
,
)
are
required to generate V
1
, V
2
, ..., V
N
, as shown in Fig. 10(d). Here,
we first flip (3) as
.
-/
-01
-
12/
7
)/
8
)01
-
129
where
H
L
and
H
R
are N×N matrices corresponding to the left
and right half of
H
, respectively. By permuting the upper and
lower halves of the
V
vector and accordingly the left and right
halves of the
H
matrix, (5) can be rewritten as
.
-/
8
)/
7
)01
1
-2:
Then, (3) and (6) can be combined as
0.
.
-2/
;
01
1
-2<
where
/
;
0/
7
/
8
/
8
)/
7
)2=
If
H
sq
is not regular at any frequency in the range from 0 to B,
the MUX subsystem cannot be used for IFI-MUX. Otherwise,
01
1
-2/
;
0.
.
-2>
The desired operation of the DSW is expressed by an N×2N
matrix,
G
, corresponding to the top half of
/
;
:
1?0.
.
-2%@
where
?
;
/
;
0?
7
?
8
?
8
)?
7
)2
??
7
?
8
%%
Here,
G
L
and
G
R
are N×N matrices corresponding to the upper-
left and upper-right quarter of
G
sq
. Thus, the desired DSW is
interpreted as a digital processor that separates the virtual target
signal U into slices U
1
, U
2
, ..., U
N
, generates their flipped copies
*
)
,
*
)
, ...
*
,
)
, and executes an 2N×N MIMO calculation
represented by (10) to generate sub-signals V
1
, V
2
, ..., V
N
. As
such, the analytical model enables systematic design of DSWs
for IFI-MUX systems of arbitrary complexity.
Table I summarizes the nominal
H
matrices for the
configurations described in the previous sub-sections and the
G
matrices derived from those
H
matrices through the use of (8)
and (11). These represent ideal cases where all components
have perfectly flat frequency responses with no loss. Non-
essential scaling factors are omitted. For the DBI systems
shown in Figs. 3 and 4,
H
and
G
represent simple 1:1
relationships between the slices and the sub-signals. For the
filter-less mixer-based system shown in Fig. 5, H
14
=1
corresponds to the un-filtered LSB of the mixer’s output, and
G
14
=−1 cancels that residual LSB. For the RF-IQM shown in
Fig. 6, H
21
=H
13
=1 and H
22
=H
14
=j correspond to the image
generation in the I and Q mixers, respectively, and the derived
G
corresponds to the operation of the I/Q separator. For the
AMUX-based system shown in Figs. 7 and 8, H
11
= H
12
=1
correspond to the baseband components of the sub-signals from
the two DACs, while H
21
= H
13
=r and H
22
= H
14
=−r correspond
to the images of them, respectively, all included in the AMUX’s
output. The derived
G
agrees with the DSW illustrated in Fig.
8. For the hybrid triple-DAC system shown in Fig. 9, H
11
=
H
12
=1 correspond to the baseband components of the signals
from the top and middle DACs connected to the AMUX, H
31
=
H
24
=r and H
32
= H
25
=−r correspond to their images, while
H
33
=H
26
=2jr corresponds to the signals from the bottom DAC
up-converted by the mixer. The derived
G
corresponds to the
DSW illustrated in Fig. 9.
In practice, each element of
H
has a frequency dependence
due to the responses of the components, including the DACs,
mixers, filters, combiners, AMUXs, and connecting cables.
Imbalances between the components are also reflected in those
elements. Furthermore, some elements corresponding to the
zero elements in the nominal
H
can be non-zero in practice
because of higher-order spurious images or residual baseband
components. The actual
H
(f) including such frequency
dependences, imbalances, and linear imperfections is typically
measured by using some test signals before defining the DSW.
By deriving
G
(f) from
H
(f), we can make the DSW function
also as a compensator for the frequency dependence and
imperfections. In the DSP, the digital MIMO filter
corresponding to
G
(f) is implemented as a set of finite-impulse-
response FIR filters. Given that each FIR filter has a length of
L, we can obtain the coefficients for each FIR filter by solving
(8) and (11) for L distinct frequency points. This zero-forcing
approach is not the sole option. For example, the filter
coefficients can be optimized on the basis of the minimum
mean-squared error criterion, as is generally done in MIMO
systems. Once determined, the DSW does not require fast
adaptive updates unless the MUX subsystem includes sensitive
TABLE I
N
OMINAL
H
AND
G
FOR IDEAL
IFI-MUX
SYSTEMS
Fig.
# H G
3
A
%
@
@
@
@
%
@
@
B
A
%
@
@
@
@
%
@
@
B
4
C
%
@
@
@
@
@
@
@
@
@
%
@
@
@
%
@
@
@
D
C
%
@
@
@
@
@
@
@
@
@
%
@
@
@
%
@
@
@
D
5
A
%
@
@
%
@
%
@
@
B
A
%
@
@
%
@
%
@
@
B
6
0
@
@
%
E
%
E
@
@
2
0
@
%
%
@
@
E
E
@
2
7, 8
A
%
%
F
F
F
F
@
@
B
G
%
%
F
@
%
%
%
F
@
%
H
9
C
%
%
@
@
@
@
@ @ @ F F 'EF
F F 'EF @ @ @D
I
J
J
K
%
@
%
'
F
@
%
'
F
@
% @ %
'F @ %
'F @
@
@
E
'
F
@
E
'
F
@
L
M
M
N
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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8
components such as optical fiber. Infrequent updates may be
required to compensate for long-term variations.
IV. O
PERATION PRINCIPLE OF OPTICAL
IFI-MUX
The operation principle of the optical IFI-MUX is essentially
the same as that for the electronic one; it extends the signal
bandwidth beyond the f
cutoff
of the DACs by utilizing optically
generated images. This means that the model discussed in the
last section also applies to the optical IFI-MUX systems.
Compared with an electronic IFI-MUX, the optical approach
provides higher bandwidth scalability because the final output
signal bandwidth is not restricted by the electronics. However,
this advantage comes at the cost of greater hardware complexity.
The OAWG is a type of IFI-MUX based on FDM, but many
other types of optical IFI-MUX are possible, as inferred by
analogy with the electronic IFI-MUX. In the optical IFI-MUX
systems for digital coherent transmission, an optical IQM is
used as a unit building block. The optical IQM itself is also a
dual-DAC IFI-MUX system, but this perspective does not seem
to be commonly held. In this section, we first briefly describe
this point before discussing the OAWG based on the analytical
model. After that, we present some approaches to building
alternative optical IFI-MUX systems with reduced hardware
complexity. For simplicity, we will show single-polarization
configurations, but their extension to dual-polarization
configurations is straightforward.
A. Optical IQM as a dual-DAC IFI system
As described in Section III-B, an RF-IQM is considered to
be a type of a dual-DAC IFI-MUX system. An optical IQM can
interpreted in the same way, as shown in Fig 11. Compared with
the RF-IQM shown in Fig. 6, the clock, mixers, and electronic
combiner have been replaced by an LD, Mach-Zehnder
modulators (MZMs), and an optical coupler, respectively. The
π/2 phase shifter is implemented in the optical domain. The
carrier frequency, f
LD
, corresponds to the IF frequency.
Consequently, the unit bandwidth of the optical bandwidth
extension is not that of the optical IQM, 2B, as commonly
believed, but rather half of it, B.
B. FDM-based OAWG system
Fig. 12 shows the configuration and operation principle of an
FDM-based OAWG system, where M optical IQMs and 2M
DACs (two for each IQM) are used [17], [37], [38]. In the DSP,
the target complex signal with a total bandwidth of 2MB is
virtually generated and separated into M slices, each with a
bandwidth of 2B. Each slice is sent to an optical IQM via a
digital I/Q separator and a pair of DACs. In the optical domain,
continuous-wave (CW) light from a laser diode (LD) is
converted into an optical comb with a free spectral range (FSR)
of 2B by using a comb generator, which is typically an electro-
optic modulator driven at a clock frequency of 2B. The comb
lines are separated by an optical demultiplexing filter and sent
to different IQMs, where the slices are up-converted to the
optical frequencies of the respective comb lines. The up-
converted slices are finally combined in a multiplexing filter to
generate the physical target signal. As such, arbitrary signals
with bandwidths up to M times that of each IQM’s capability
can be obtained.
C. Filter-less optical IFI-MUX systems
The FDM-based OAWG has been considered to be the most
intuitive and natural approach to optically extending transmitter
bandwidth. However, it has some room for improvement. From
an implementational point of view, the optical filter used to
separate the comb lines is the most challenging part. Typical
filters for wavelength division multiplexing (WDM), such as
arrayed waveguide gratings, can be used, but such filters tend
to be large as a component in the transmitter. Furthermore,
those filters are essentially “colored,” i.e., sensitive to the
absolute frequency of the input CW light; this characteristic is
undesirable for a transmitter. In analogy with the electronic IFI-
Fig. 12. Configuration and operation principle of an FDM-based OAWG system with M optical IQMs.
Fig. 11. Operation principle of the optical IQM as a dual-DAC IFI-
MUX
system.
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
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9
MUX, the filter can be omitted by allowing spectral overlaps
and applying a DSW. Another issue regards the clock frequency.
As mentioned in Section IV-A, the unit bandwidth can be B
rather than 2B, and thus the FSR of the comb can also be B. This
relaxes the requirement for the clock source and its associated
components.
One way of implementing such a system is to transplant the
principle of an electronic filter-less IFI-MUX directly into the
optical domain. For example, an optical selector switch based
on a high-speed MZM provides the same functionality as an
electronic AMUX [39], [40], [41]. Furthermore, as a method
unique to the optical domain, the configuration shown in Fig.
13 is also possible [42], [43]. An integrated modulator with a
differential phase modulator (DPM) followed by two optical
IQMs is used with four DACs and a DSW. The DPM is driven
at f
clk
=B and it splits the input CW light from the LD and
modulates their phases in a push-pull manner, generating B-
spaced optical subcarriers (or comb lines) with relative phases
as illustrated in the figure. The relative amplitudes and phases
of the subcarriers are determined by the modulation depth α
(swing voltage divided by the half-wave voltage), and the
nominal
H
=(
H
L
H
R
) for this system is represented as [43]
/
7
I
K
O
PEO
PO
PEO
P
O
PEO
PO
PEO
P
O
Q
PEO
Q
PO
Q
PEO
Q
P
O
PEO
PO
PEO
P
L
N
/
8
I
K
O
PEO
PO
PEO
P
O
Q
PEO
Q
PO
Q
PEO
Q
P
O
PEO
PO
PEO
P
O
PEO
PO
PEO
P
L
N
%'
where J
n
denotes an n-th order Bessel function of the first kind.
H
sq
derived using (8) is regular for at least 0<α<1.2π, which
covers realistic driving conditions. Thus, the DSW can be
designed on the basis of (10). In practice, the frequency
responses of the DACs, DPM, IQMs, driver amplifiers (not
shown in the figure), and associated passive components are all
incorporated in
H
(f), enabling the DSW to compensate for all
frequency dependences and imbalances. As such, optical IFI-
MUX systems can also be implemented without using any
optical filters and with a clock frequency of B rather than 2B,
making the system compact and colorless, and relaxing the
requirements for the clock system.
The idea of omitting the optical filter from the OAWM
system and allowing spectral overlaps that are digitally
resolvable has recently been demonstrated for the receiver side
[44], [45], [46], [47].
D. Optical time-division multiplexing (OTDM) as IFI-MUX
The IFI-MUX systems based on the AMUX [13], [14], [33],
[34], [35] and the optical selector [40], [41] can also be regarded
as TDM systems. This implies the IFI-MUX concept includes
TDM, whether electronic or optical. Indeed, considering that
the pulse train for each TDM tributary is a type of frequency
comb with an FSR corresponding to its repetition rate, every
TDM system can be represented by
H
in a similar way as (12),
where each element represents the amplitude and phase of each
comb line. This is a manifestation of the seamless link between
TDM and FDM [48], [49].
OTDM is a commonly used way of generating optical signals
with symbol rates (and thus bandwidth) beyond the capabilities
of electronics [50], [51]. While it has not been widely explored,
the application of the concept of IFI-MUX to OTDM systems
not only provides an alternative interpretation of their operation
principle, but possibly offers some benefits, such as the ability
to generate arbitrary target signals and to compensate for linear
imperfections in the analog system. In practice, however, most
of the experimental setups for OTDM are incompatible with the
IFI-MUX concept because the signal generation is emulated by
combining delayed copies of the tributaries in the optical
domain. Nevertheless, for OTDM systems with relatively small
numbers of tributaries, full implementation of modulators for
all tributaries is possible, thereby enabling the application of the
IFI-MUX concept. In particular, an OTDM transmitter using
carrier-suppressed-return-to-zero (CSRZ) pulses for two TDM
tributaries was demonstrated with a digital calibrator based on
the DSW, which significantly improved the signal quality and
tolerance to spurious frequency components included in the
pulses [52], [53].
V. R
EVIEW OF EXPERIMENTAL RESULTS
Over the past decade, a number of high-speed transmission
experiments utilizing bandwidth extension techniques have
been reported. In this section, we first review the electronic
components for IFI-MUX, such as the AMUX. Then, we
review the state of the art of IMDD and digital coherent
transmission experiments utilizing bandwidth extension
techniques. Note that the bit rates cited below are net bit rates
excluding overheads for forward-error-correction (FEC) codes.
A. Electronic components for bandwidth extension
DACs for optical transmission systems are basically
Fig. 13. Configuration and operation principle of a filter-less colorless optical IFI-MUX system.
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10
fabricated as parts of the DSPs on a CMOS platform. On the
other hand, as discussed in the Introduction, the electronic
MUX components are supposed to be implemented in the FE
module. The requirements for those MUX components include
large bandwidth, high break-down voltage, and low loss, while
their circuit complexities are moderate. Compound platforms,
such as silicon germanium (SiGe) bipolar CMOS (BiCMOS) or
indium phosphide (InP) heterojunction bipolar transistor (HBT),
are suitable for such circuits.
Indeed, extensive research on AMUX aimed at optical
transmitters has been conducted using InP HBT [31], [32], [54],
[55], [56], [57], [58], and SiGe BiCMOS [59], [60], [61], [62],
[63] technologies. Table II summarizes the key characteristics
of those AMUXs including the peak cutoff and maximum
oscillation frequencies (f
T
and f
max
) of the transistor, analog 3-
dB bandwidths for the signal paths, and power consumption.
Bandwidths exceeding 100 GHz have been demonstrated [56],
[58], [62]; such results are promising for >200-GBaud
applications.
Meanwhile, other components, e.g., combiners and mixers,
have been developed mainly for wireless and measurement
systems and are widely available as off-the-shelf products.
Recently, researches on those components with extremely large
bandwidths (around 200 GHz) have also been reported [64],
[65].
B. IMDD transmission using bandwidth extension techniques
Despite that IMDD adopted DSP later than digital coherent
systems did, the field has recently seen active research on DSP-
based technologies because of the strong demand for higher
data rates [66]. Meanwhile, optical IM components such as
directly and externally modulated lasers (DMLs and EMLs)
with large electro-optic (EO) bandwidths have been actively
developed [67], [68], [69], [70], [71], [72], [73], leaving the
DACs’ bandwidths behind. MZMs are also evolving toward
larger bandwidths and smaller footprints [74], [75], [76].
Electronic IFI-MUX is a promising way to bridge the
bandwidth gap between those components and DACs.
The first experimental demonstration of electronic IFI-MUX
[13], [14] used two 60-GS/s CMOS DACs, an InP HBT AMUX,
and an O-band EML to generate an 80-GBaud four-level pulsed
amplitude modulation (PAM4) signal. The sub-signal
bandwidth of the DACs was around 20 GHz, while the
bandwidths of the AMUX and EML were around 40 GHz and
>50 GHz, respectively. Shortly thereafter, a 100-GHz-
bandwidth mixer-based IFI-MUX (DBI) system was
demonstrated, in which three CMOS DACs were used to
generate PAM signals with symbol rates up to 190 GBaud [25],
[26]. Subsequently, CMOS-DAC-based 200, 250, and 333-
Gbps/λ IMDD transmissions were also achieved using AMUX-
based IFI-MUX transmitters with an EML [77], [33], [34] and
an InP MZM [78], [79]. In these experiments, discrete
multitone (DMT) modulation was employed. Meanwhile,
entropy loading (EL) has emerged as a more powerful
multicarrier approach to reach the channel capacity [80], [81].
By employing EL in a three-CMOS-DACs mixer-based IFI-
MUX system with a thin-film lithium niobate (TFLN) MZM,
even higher IMDD bit rates of 460.9 and 538.8 Gbps/λ were
achieved [82], [83]. Transmissions at >300 Gbps/λ with DMLs
were also demonstrated using EL and IFI-MUX with two
CMOS DACs [84], [85], [86]. However, such multicarrier
formats may not be ideal for IMDD systems with stringent cost
requirements. Regarding single-carrier PAM formats, 400
Gbps/λ and higher rates have been achieved with CMOS-DAC-
based IFI-MUX transmitters employing probabilistic shaping
(PS) [87], [83], [88], [36]. Recently, numerous laboratory
experiments have used SiGe DACs with f
cutoff
>f
s
/2. IMDD
transmissions using SiGe DACs and SiGe AMUXs have been
demonstrated with data rates up to 467.1 Gbps/λ [89], [90]. BB-
MUX systems with SiGe DACs available as benchtop AWGs
[21], [22] have also been widely used in high-speed IMDD
experiments [91], [92], [93], [94], [95], [96].
Fig. 14 provides an overview of the reported IMDD
transmission experiments at per-wavelength data rates of 350
Gbps/λ or higher. The data rates of single-carrier transmissions
TABLE II
K
EY CHARACTERISTICS OF
AMUX
S DESIGNED FOR OPTICAL
TRANSMITTERS
Ref. Technology f
T
/f
max
,
GHz
3-dB BW,
GHz
Power
cons., W
Notes
[31] (’11)
InP HBT n/a >40 n/a
[54] (’16)
500-nm
InP HBT 290/320
>50* 0.5
[55] (’17)
500-nm
InP HBT 290/320
63* 0.84
[56] (’18)
250-nm
InP HBT 460/480
>110 0.9
[57] (’20)
700-nm
InP HBT 340/410
n/a n/a
[58] (’22)
500-nm
InP HBT 360/450
108 1.3 High gain:
25.7 dB
[59] (’17)
130-nm
SiGe BiCMOS
300/500
>67 1.06
[60] (’20)
55-nm
SiGe BiCMOS
320/370
>53* 0.7 4:1 MUX
[61] (’20)
55-nm
SiGe BiCMOS
320/370
n/a 2.17
[62] (’21)
130-nm
SiGe BiCMOS
470/610
>110 1.07-1.22
[63] (’22)
130-nm
SiGe BiCMOS
300/500
29* 1.06 6-dB BW:
61 GHz
*Measured as connectorized modules (otherwise measured on-chip)
Fig. 14. Overview of high-speed IMDD transmission experiments.
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11
(solid-edge symbols) are plotted against the symbol rate, while
those of the multicarrier transmissions (dotted-edge symbols)
are plotted against the effective symbol rate defined as twice the
baseband signal bandwidth including guard-bands. Purple and
orange symbols represent systems based on CMOS and SiGe
DACs, respectively, while the asterisks, circles, and triangles
denotes those using one, two, and three DACs, respectively.
The open symbols represents IFI-MUX, while the circles with
crosses represents BB-MUX. The dashed lines denote intra-
channel spectral efficiency, which is defined as the bit rate
divided by the symbol rate. In most of the experiments with bit
rates higher than 400 Gbps/λ, the spectral efficiencies are
roughly around 2.5 bps/Hz. None of these results should be
compared directly because their other experimental conditions,
such as the wavelength band, transmission distance, and
assumed FEC code, are inconsistent. Nevertheless, this figure
shows that MUX techniques are promising approaches for
achieving IMDD systems operating at data rates of 400 Gbps/λ
or higher at high symbol rates.
C. Digital coherent transmission using bandwidth extension
techniques
In the field of digital coherent transmission, the analog
bandwidth enhancement of the DACs has also lagged behind
those of the modulators. This has motivated research on
electronic bandwidth extension techniques. In the first digital
coherent transmission experiment employing electronic IFI-
MUX, CMOS DACs operating at 64 GS/s and InP HBT
AMUXs were used to generate a 96-GBaud quadrature phase-
shift keying (QPSK) signal that was transmitted over a distance
of 12,120 km [98]. Since then, the AMUX-based IFI-MUX has
been used in several high-symbol-rate digital coherent
transmission experiments with CMOS DACs having moderate
analog bandwidths [99], [100], [101], [102], [103], [104], [105].
In addition, an integrated optical frontend module containing
InP HBT AMUXs and an InP optical IQM in a single package
has also been demonstrated for the implementation as shown in
Fig. 1(b), proving the high affinity of the AMUX for integration
[106], [107], [108]. Mixer-based electronic IFI-MUX (DBI)
using three CMOS DACs in each signaling dimension has also
been applied to coherent transmitters, achieving bit rates of up
to 1.58 Tbps/λ [109], [110]. Another approach is based on RF-
IQMs; it has been used in several high-symbol-rate
transmission experiments with CMOS DACs [30], [111], [112],
[113], [114], [115], [116], [117], [118]. Of course, CMOS
DACs themselves have also been evolving; Up to 1.3 Tbps/λ
has been reported with transmitters using one CMOS DAC for
each dimension [119], [120], [121], [122], while the latest
commercial DSPs seem to exhibit even higher capabilities.
Meanwhile, as SiGe DACs with f
cutoff
>f
s
/2 have become major
options for laboratory experiments, digital coherent
transmission using such DACs have been increasingly reported.
Using one SiGe DAC at 1 sps in each signaling dimension,
digital coherent transmissions at data rates of up to 1.96 Tbps/λ
have been reported [123], [124], [125], [126], [127], [128]. BB-
MUX systems with SiGe DACs have enhanced the bit rates up
to 2.11 Tbps/λ [22], [23], [129], [130], [131], [132]. By
combining a BB-MUX system with SiGe DACs and the mixer-
based electronic IFI-MUX (DBI) systems, an even higher bit
rate of 2.42 Tbps/λ has been reported [133].
Digital coherent transmitters using optical IFI-MUX have
been extensively studied since the first experimental
demonstration of the OAWG [17]. Single-carrier optical signals
with bit rates up to 1 Tbps/λ have been demonstrated with the
FDM-based OAWGs having fiber-connected parallel optical
IQMs and CMOS DACs [134], [135], [136]. Recently, a
feedback optical-phase stabilizer to compensate for the optical
phase fluctuation in the fiber connecting the IQMs has been
demonstrated [137]. An OAWG with this stabilizer generated
signals at symbol rates up to 320 GBaud [138], [139].
Meanwhile, optical-filter-less IFI-MUX systems have achieved
bit rates up to 1.6 Tbps/λ with CMOS DACs [40], [41], [42],
[43]. Recently, a >2.5-Tbps/λ transmission has been
demonstrated by combining the SiGe DACs with f
cutoff
>f
s
/2 and
a CSRZ-OTDM transmitter calibrated by a DSW [52], [53].
The combination of electronic and optical IFI-MUX is also
promising for bridging the bandwidth gap between CMOS
DACs and optical modulators as well as synthesizing optical
signals with bandwidths even larger than that of the modulators.
We recently achieved a transmission at 2.3 Tbps/λ by using RF-
IQMs and a CSRZ-OTDM modulator in combination with a
16×8 DSW and CMOS DACs [140].
Fig. 15 provides an overview of digital coherent transmission
experiments at per-wavelength data rates of 1.2 Tbps/λ or
higher. The notation in Fig. 15 follows that of Fig. 14, except
as follows: the numbers of DACs are those used in each
dimension, and the diamonds denotes four DACs in each
dimension. The open and filled symbols denotes electronic and
optical IFI-MUX, respectively. Again, direct comparison
between the results should not be made due to the inconsistent
conditions. For most of the results with bit rates higher than 1.6
Tbps/λ, the spectral efficiencies are roughly between 10 and 14
bps/Hz. Bit rates exceeding 2 Tbps//λ have only been achieved
with MUX techniques, making apparent their high scalability.
Fig. 15. Overview of high-speed digital coherent transmission experiments.
This article has been accepted for publication in IEEE/OSA Journal of Lightwave Technology. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
12
VI. C
ONCLUSION
The analytical model described in this paper provides a basis
for designing transmitter systems that utilize analog electronic
and optical MUX techniques based on multiple DACs in each
signaling dimension. For such techniques to be practical,
various implementation challenges need to be addressed,
including integrating multiplied numbers of DACs in the DSP,
implementing high-speed clock systems for the MUX
components, and so on. Moreover, as the analog bandwidths of
DACs are continuing to expand, to what extent serial speed-up
should be pursued and at what point parallelization should be
relied upon remain open questions. Regarding the optical IFI-
MUX, there is room for debate on its advantages and
disadvantages compared to conventional multicarrier
transmission with non-phase-synchronized optical subcarriers.
The benefits of the optical IFI-MUX include elimination of
guard bands between the subchannels and capability of digital
nonlinear compensation over the whole spectral band, while its
drawbacks include the need for synchronization of larger
number of DACs. Nevertheless, MUX techniques hold great
promise as viable solutions for realizing multi-Tbps/λ
transmitters in the future.
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content may change prior to final publication. Citation information: DOI 10.1109/JLT.2024.3484571
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
