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1
Low Resolution Digital Pre-Compensation Enabled
by Digital Resolution Enhancer
Yaron Yoffe, Ginni Khanna, Eyal Wohlgemuth, Erik de Man, Bernhard Spinnler
Norbert Hanik, Antonio Napoli, Dan Sadot
Abstract—Digital pre-compensation (DPC) is an indispensable
block of state-of-the-art optical transceivers, and a key enabler
for high order modulation formats (HOMFs) transmission. A
crucial component, which enables the transmission of the pre-
compensated HOMFs, is the digital-to-analog-converter (DAC).
However, as data and symbol-rates grow, the implementation of
such devices becomes highly challenging in terms of performance,
power consumption and costs.
In this work, a digital-resolution-enhancer (DRE) algorithm is
discussed, conjoined with high-end DPC methods. Simulation
results demonstrate that the DRE reduces the effect of DAC
quantization noise power by more than 8 dB for the considered
cases of 400G with 64QAM. The proposed scheme is experimen-
tally verified by transmitting a 4-bit DP-64QAM 400Gbit/s signal
in a WDM scenario over 95 km of single mode fiber.
I. INTRODUCTION
To enable high-spectral efficient capacity links it is essential
to transmit high-order modulation formats (HOMF), such as
64 quadrature amplitude modulation (QAM), 128QAM [1]
and beyond [2]. However, as the spectral efficiency increases,
achieving the required bit-error-rate (BER) performance be-
comes highly challenging. Consequently, the transmission
results being more susceptible to linear and nonlinear im-
pairments, induced also by the electronic and opto-electronic
devices constituting the transponder. Particularly, performance
is limited by the impairments of the transmitter components
such as digital-to-analog converters (DACs), driver amplifiers
(DAs) and dual-polarization Mach-Zehnder-modulators (DP-
MZMs).
Digital pre-compensation (DPC), complementary to post
equalization techniques at the receiver, has played a funda-
mental role in enabling data rates beyond >200G transmis-
sion [3], [4]. Incorporating digital signal processing (DSP) at
the transmitter enables to mitigate the bandwidth limitations
of the transceiver components, and the inherent nonlinearity of
optical modulators. Accordingly, extended transmission rates
This work was partially funded by the Israel ministry of industry and
commerce, project grant no. 57894 (Peta-Cloud) and by the German ”Bun-
desministerium f¨
ur Bildung und Forschung” under contract no. 16KIS0487K
(Celtic project SENDATE-FICUS). The authors alone are responsible for the
content.
Yaron Yoffe, Eyal Wohlgemuth and Dan Sadot are with Ben-Gurion
University, Israel. yaronyof@ee.bgu.ac.il
Ginni Khanna and Norbert Hanik are with Technical University Munich,
ginni.khanna@tum.de
Erik de Man, Bernhard Spinnler, Antonio Napoli are with Infinera,
ANapoli@infinera.com
Manuscript received xxx 19, zzz; revised January 11, yyy.
and longer distances can be achieved. Nonlinear digital pre-
distortion (DPD) has also proved to be effective in increasing
the output power of MZM based transmitters [5], [6], [7].
In order to employ effective DPC, high resolution digital-
to-analog converters (DACs), which enable to convert digitally
pre-compensated signals into complex analog waveforms, are
critical. However, as transmission rates increases, the com-
plexity of DACs forms a major technological limitation [8].
As a result, implementing such devices, that can support both
the high symbol-rate and the high-resolution requirements
of the pre-compensated HOMFs, significantly increases the
power consumption and costs of the entire system. This is
considered specifically challenging in metro and data-centers
interconnections (DCI) links due to severe power consumption
and cost requirements. For example, it has been estimated that
the power consumption of pair DACs / ADCs can count for
up 40% of the total power consumed by the DSP blocks in
metro scenario [9].
In [1], the authors have demonstrated a single-carrier
400 Gb/s DP-64QAM transmission over 80 km metro legacy
links, achieved by exploiting the entire set of available physical
number of bits (PNOB). In this contribution, we discuss an
advanced DSP technique [10], [11], [12] that enables to reduce
the impact of low resolution DACs on the signal quality. We
demonstrate for a DP-64QAM 400 Gb/s signal that the PNOB
of the DACs can be decreased from 8 to 4 bits, while maintain-
ing comparable performance. We experimentally validated the
proposed method, showing significant gains in back-to-back
(BTB) performance. We further demonstrate a DP-64QAM
wavelength division multiplexed (WDM) transmission exper-
iment with 17 channels over 95 km of standard single mode
fiber (SSMF) using 4 PNOB DACs. In addition, nonlinear
DPD transmission with 4 PNOB is verified with the proposed
solution, to allow higher transmit optical output power. The
reduction in PNOB can be used to significantly reduce the
complexity and power consumption of the transmitter, thus
providing highly attractive solutions for DCI links.
This manuscript is an extension of [13], which was pre-
sented at the European Conference on Optical Communica-
tions (ECOC) 2018 in Rome, Italy. In Sec. II we describe the
adaptive DPC used in this work; while Sec. III introduces the
digital resolution enhancer (DRE) block. Both sections deal
with the mathematical background of the two methods and
were not contained in [13]. New simulation results, providing
insights of the working method of the DRE are reported in Sec.
IV. Finally, in Sec. V we experimentally validated the proposed
technique (as also shown in [13]) and we extend it to the case
2
of nonlinear DPD (which is an additional contribution to our
work in [13]). A conclusion of the article is presented in Sec.
VI.
II. DIGITAL PRE- COMPENSATION
The performance of present and next generation high-
speed communication systems is severely limited by various
linear and nonlinear effects exhibited by the DAC, DA and
DP-MZM. Linear effects such as bandwidth limitation and
transmitter I/Q skew limit the transmission of high symbol-
rate and HOMF [14]. Additionally, the nonlinear effects of
the DA and DP-MZM hamper the system performance [5],
[15] when the transponder is driven by higher powers. For the
above reasons, DPC has become an indispensable part of the
transmitter DSP over the recent years. DPC is made up of two
operations
•Linear digital pre-compensation (L-DPC)
–Digital pre-emphasis (DPE) which overcomes band-
width limitation
–Transmitter I/Q skew compensation
•Digital pre-distortion (DPD) which overcomes the non-
linear effects of the components
In this article, DPC was implemented as described in [16].
Each tributary of the transmitter is modelled using the follow-
ing memory polynomial model
zi(n) =
P
X
p=1
(Mp+1)/2
X
m=−(Mp−1)/2
hi,m,pxp
i(n−m),(1)
In particular, the following model was used in the experi-
ments to train the DPC block
zi(n) =
15
X
m=−15
hi,m,1·xi(n−m)+
(L+1)/2
X
l=−(L−1)/2
hi,l,3x3
i(n−l) + hi,l,5·x5
i(n−l)
(2)
where xi(n)and zi(n)are the input and output samples
and hi,m,p is the coefficient of the corresponding memory
tap mand nonlinear order p. Note that the filter length Mp
depends on the nonlinearity index p. A note to the readers
here: These notation with signal xi(n)and zi(n)are explicit
for the DPC block, in continuation with our work from [15]
and is independent of the notations used in Fig. 1.
In the first experiment (see Sec. V-B and V-C), only linear
effects at the transmitter were considered and the DA and
DP-MZM were operated in the linear regime. To overcome
the bandwidth limitation and correct the transmitter I/Q skew,
only the linear part of Eq. 2 was used with P=1 and Mp=15.
In a second experiment (see Sec. V-D), the optical transmit-
ter was driven at higher DA gains to enable a higher transmitter
output power. This makes that the transmitter operates in
nonlinear regime. In order to compensate for the induced
nonlinear effects at the transmitter, DPD was implemented
according to [15]. In this case, Mp= 15 was used. For the
nonlinear terms, three configurations with order P= 3, 5 with
L= 1, signifying memoryless nonlinearity and L= 3 and L
= 5, representing nonlinearity with memory, were used.
III. DIG ITAL RESOLUTION ENHANCER
Applying DPC is essential for HOMFs transmission in the
presence of non-ideal opto-electronics and electronic devices.
In order to ensure that the quality of the digital signal is
preserved, the resolution of the DACs should be sufficiently
high, such that the quantization distortions would be negli-
gible compared to other systems’ distortions. Unfortunately,
commercially available components are either limited by their
resolutions, or require substantially increase in the power
consumption, cost and die area of the system. This is especially
challenging in systems that incorporate DPC, due to high
dynamic range requirements, which directly degrades the
signal-to-quantization-noise (SQNR) performance.
The analysis of quantization distortion has been extensively
discussed in the literature [17], [18], [19], mostly dedicated
to round-off (RO) quantizers. Commonly, the quantization is
obtained by assigning each digital sample to its nearest analog
value. This was proven to be optimal in cases where no
prior knowledge is known of the signal. In addition, under
certain conditions [18], the quantization distortion can be
modeled as, additive white noise, namely quantization noise.
The noise power, in this case, can be evaluated using the
well known ∆2
12 formula [20]. However, one major drawback
of this strategy is that it disregards completely the fact that
quantization is a deterministic nonlinear function. As the effect
of the quantization can be directly calculated, its impact can
be analytically derived and minimized.
In this section, a DRE algorithm is discussed and analyzed.
The DRE utilizes a dynamic-quantization (DQ) approach to
mitigate the quantization distortion effect on the transmission
performance. As opposed to conventional RO quantizers,
which generate white un-correlated noises, the DRE optimizes
the quantization function based on the transmitted signal
samples, which are known at the transmitter and are based
on prior knowledge of the channel response. This results
in quantization error sequences that are optimally matched
to the desired transmission, and can exceed the ∆2
12 barrier.
Consequently, the algorithm can be leveraged to either reduce
the PNOB, or to extend the capabilities of the DPC.
A. System Model and Notations
The block diagram of the system model is depicted in Fig. 1.
The transmitter DSP consists of a root raised cosine (RRC)
pulse shaping filter Hps (f), followed by DPC, as described
in section II. Denote the symbol sequence as s(n), the pulsed
shaped signal can be written as z(n) = s(n)∗hps(n), where
hps(n)is the RRC filter and ”∗” is the convolution operator.
The digitally pre-compensated signal is denoted x(n). The
DRE block performs the quantization operation, i.e., it gener-
3
RRC DPC
z(n)
DRE
x(n)
DAC
xq(n)
Channel MF
s(n)yq(n)
Fig. 1: System model block diagram. RRC filter is applied on the symbol sequence s(n), generating the pulse-shaped signal z(n). Follows,
the signal is digitally pre-compensated, and the DPC signal x(n)is quantized using the DRE algorithm. The quantized signal xq(n)is
loaded into the DAC and transmitted over the channel. At the receiver side, MF is assumed. The transmitted symbols are estimated based
on the received signal yq(n).
ates the quantized signal xq(n). For each digital sample, the
quantization error can be directly calculated as
q(n) = xq(n)−x(n).(3)
The quantized signal is then converted into analog waveform
by the DAC, and transmitted over the channel. At the receiver
side, MF is assumed. The received samples after the MF with
and without DAC quantization are denoted y(n)and yq(n)
respectively. The quantization error at this stage reads as
qeff(n) = yq(n)−y(n),(4)
where qeff(n), the effective quantization error, reflects the DAC
quantization distortion at the receiver.
The purpose of the DRE module is to optimize the quanti-
zation mapping function to achieve optimal BER performance.
As a figure of merit, the MF-mean-squared-quantization-error
(MF-MSQE) criterion is suggested, which assesses the DAC
quantization contribution to the receiver mean-squared-error
(MSE)
MF-MSQE =Eh
qeff(n)
2i.(5)
In systems that employ DPC, the response of the channel is
usually known at the transmitter, as it is used to optimize the
DPC coefficients. The channel response can be obtained either
as explained in Section II or with a pre-calibration routine [21],
[22]. This can be utilized to calculate the effective quantization
error sequence, and the resulting MF-MSQE. For instance, in
the case of linear response channel, the received quantized
signal can be written as
yq(n) =
L−1
X
l=0
h(l)xq(n−l).(6)
where h(l)is the combined impulse response of the channel
and the MF. Lis the number of taps. Consequently, the
effective quantization error is given by
qeff(n) = yq(n)−y(n) =
L−1
X
l=0
h(l)q(n−l).(7)
The latter equation suggests that the conventional RO quan-
tization is not optimal in this case. Rather, the quantized
values, xq(n), should be chosen such that the resulting er-
ror sequence, q(n), convoluted with the combined impulse
response of the channel and the MF, would lead to minimal
MSE values. In other words, quantization decisions (mapping
from digital sample into analog values) should not be viewed
independently, as their actual effect on the MF-QMSE is also
affected by previous decisions, and each decision affects both
current and future qeff(n)values.
B. Dynamic Quantization
In order to find the optimal mapping function, a DQ
approach is suggested. The term DQ is used here since the
quantization problem, defined within the previous subsection,
has dynamic properties, and can be formulated within the more
general framework of dynamic programming problems [23].
The dynamics of the problem is described as follows.
For each quantization decision, an instantaneous cost can be
directly calculated as
J(n) =
qeff(n)
2.(8)
The instantaneous cost is determined by the current decision,
i.e., the choice of q(n), and by the last L−1quantization
values, which can be regarded as the state of the system. The
performance of the quantizer is evaluated by measuring the
averaged cost function as follows
J(N)
avg =1
N
N−1
X
n=0
J(n),(9)
where Nis the length of the transmitted sequence. The relation
between the averaged cost, and the expression derived in Eq. 5,
is given by
lim
N−>∞
J(N)
avg =MF-MSQE.(10)
The purpose of DQ is to balance the trade-off between
the instantaneous costs of each decision, and its impact on
future values, acknowledging that greedy decisions may be
destructive for the MF-MSQE. This can be obtained by
carefully manipulating quantization errors. The standard RO
error is replaced by the following signal
q(n) = qro(n) + u(n)·∆,(11)
which is a sum of the round-off error qro(n), and a control
parameter u(n). The control signal is the subject of the
optimization. ∆describes the quantizer step size, i.e. analog
distance between two neighbouring output levels. Note that
qro(n)is not a parameter of choice, rather it is derived from
the received samples. To ensure finite and discrete outputs,
u(n)must satisfy
u(n)∈Zand
cmin ≤qro(n) + u(n)·∆≤cmax ,
(12)
where cmin and cmax are the quantizer minimal and maxi-
mal values, respectively. Referring to the DQ problem, we
would like to find the optimal control sequence uopt =
uopt(0), uopt (1), ..., uopt(N−1)for arbitrary sequence
4
length N, such that the cost function described in Eq. 10 is
minimized. The DQ problem is illustrated in Fig. 2.
Qro (·)h(n)
DQ control
sequence
-+
×
x(n)xro(n)qr o(n)
u(n)
qdq(n)qef f (n)
∆
Fig. 2: The DQ problem: find optimal control sequence uopt such
that E|qeff(n)|2is minimized; Qro (·)is the round-off operator to
the nearest quantization level.
Generally, finding the optimal control sequence requires
exhaustive search over all possible control values u(n), which
grows exponentially with the number of samples. For example,
for a quantizer that has only 4 bits resolution (i.e., 16 levels),
and sequence length of Nsamples, there would be 16Ndiffer-
ent quantization combinations. Computing the averaged cost
for each combination is impractical even for short sequences.
C. Digital Resolution Enhancer
The DRE solves the DQ problem efficiently by implement-
ing a block-wise low-complexity Viterbi algorithm [23]. The
Viterbi logic is used here for efficient search over the different
possible combinations, thus reducing the computational com-
plexity and hardware resources requirements.
The DRE consists of three main building blocks, as shown
in Fig. 3. At the first step, soft quantization (SQ) is applied
on the digital input. The soft quantizer generates several
quantization possibilities, according to Eq. 11-12. To maintain
reasonable complexity, the number of SQ possibilities is
limited by constraining u(n)to a smaller subset than the one
described in Eq. 12. In fact, selecting a limited number of
options, such as u(n)∈ {−1,0,1}, results in a significant
improvement, as it will be demonstrated in the following
sections. In the case of three SQ options, the output of the
SQ block can be written as
xsq (n) =
x(n) + qro(n)−∆
x(n) + qro(n)
x(n) + qro(n)+∆
,(13)
and the resulting SQ error vector is
qsq (n) =
qro(n)−∆
qro(n)
qro(n)+∆
.(14)
As second step, path metric block computes the instanta-
neous costs J(n)for each possible SQ error value according
to Eq. 8, and the averaged cost for each of the surviving
Viterbi paths. At the third step, the hard-quantization (HQ)
block eliminates converging paths, such that the number of
paths at the beginning of each stage remains constant. At the
end of the sequence (n=N), the HQ block decides on the
optimal path, which has the lowest averaged error, and the
associated sequence is being fed to the DAC.
For example, let us assume channel length of L= 3 taps.
At each stage, the number of surviving paths is 32= 9. Due
to the SQ branching procedure, the number of paths grows
to 33= 27, and for each path, the averaged squared error is
computed. The HQ block reduces the number of paths again
to 9, according to the Viterbi algorithm.
Soft
Quantization
(SQ)
Hard
Quantization
(HQ)
Path Metric
x(n)xsq (n)xq(n)
Surviving paths
PN−1
n=0 |qeff (n)|2
Fig. 3: DRE block diagram. Each digital sample x(n)is soft-
quantized by the SQ block, which transforms digital samples into
a vector of possible quantized values xsq(n). Path metric block
computes the resultant error for each possible SQ and for the entire
sequence. HQ block transforms selects optimal paths in the trellis
diagram.
The complexity of the algorithm can be estimated similarly
to other method that are based on Viterbi algorithm such as
maximum-likelihood-sequence-estimation (MLSE) [24], [25],
[26]. The required number of calculation is approximated
as ML·N, where Mis the number of SQ possibilities
(M= 3 was considered in this work) and Nis the length
of the sequence. Note that the complexity can be significantly
reduced by using channel-shortening filters, that reduces the
number of channel taps [25], [27], or by reducing the number
of states [28]. This is demonstrated in the following section. In
addition the algorithm can be applied on truncated sequences
for reduced latency, where using sequences lengths of at least
5·Lis expected to yield near-optimal performance [24].
IV. NUMERICAL SIMULATIONS
The simulation setup considered in this section is as de-
scribed in section III-A, and as shown in Fig. 1. The simulation
was designed to emulate 400G transmission systems. DP-
64QAM signals were generated at symbol-rate of 44 GBaud,
which resulted in un-coded bit-rate of 528 Gb/s. Forward-
error-correction (FEC) as in [1] was employed to achieve error-
free bit rate of ∼400 Gb/s, for pre-FEC BER values better than
3.4×10−2. The transmitter DSP implemented a RRC filter,
with roll-off factor coefficient of 0.2. L-DPC was employed
to equalize the channel. The channel frequency response
was based on real measurements of a system that included
commercially available DACs, drivers, MZMs, coherent front-
end and ADCs. The frequency response is depicted in Fig. 4.
After the DPD block, the signal was quantized using the DRE
algorithm and transmitted over the channel. At the receiver
side, additive-white-Gaussian-noise (AWGN) was assumed.
The post-processing included MF, linear equalizer (LE) for
5
0 5 10 15 20 25 30 35 40
−70
−60
−50
−40
−30
−20
−10
0
Frequency [GHz]
Normalized response [dB]
Fig. 4: Frequency response of the channel.
residual inter-symbol-interference (ISI) and a decision device
(slicer).
A. Spectral Response of the DRE Quantization Noise
In Fig. 5, the potential gain of the DRE is illustrated.
Fig. 5(a) shows the power-spectral-densities (PSDs) of the
pulse shaped signal, the pre-distorted signal and the quanti-
zation noises with and without DRE of a 4 PNOB quantizer
before the channel. The spectral image after the channel and
MF is shown in Fig. 5(b).
Fig. 5(a) clearly shows that the DRE shapes the quantization
noise inversely to the channel response, as opposed to the
conventional quantizer, which results in white-spectrum noise.
Although the overall power of the noise was larger with the
DRE, the noise spectrum was centered out of band, at the
benefit of lower in-band frequencies.
The resulting difference in the effective quantization noises,
qeff(n), with and without DRE, is visualized in Fig. 5(b). The
PSD of the quantization noise with the DRE is shown to be
much smaller, i.e., it achieves a better MF-MSQE value, as
expected. The proposed solution can be compared with addi-
tional methods that leverage oversampling to improve the ef-
fective resolution such as differential-pulse-coded-modulation
(DPCM) and noise-feedback-coding [29]. However, the noise
shaping that is presented here is merely a consequence of the
DRE optimization, and not the objective. The DRE quanti-
zation directly minimizes the MF-MSQE using the Viterbi
algorithm, therefore it is optimal.
B. Performance Analysis of the DRE
The performance of the DRE is evaluated by comparing the
MF-MSE and BER results with conventional RO quantizers.
It is assumed here that the DAC is operating at 88 Gsamp/sec,
i.e., 2 samples per symbol (SPS). Channel shortening filter was
applied on the sampled channel-impulse-response (CIR), thus,
only L=3 taps are required for the DRE. This will be further
discussed in the next subsection. Additionally, the number
of soft-quantization possibilities was also limited to three
by choosing u(n)∈ {−1,0,1}to reduce the computational
complexity.
−40 −30 −20 −10 0 10 20 30 40
−50
−40
−30
−20
−10
0
10
20
Frequency [GHz]
PSD [dB/Hz]
Pulse-shaped signal
Normalized DPD signal
Q noise w/o DRE
Q noise w DRE
(a) Spectral image, before the channel, of: the pulsed-shaped
signal prior to pre-compensation, z(n), signal after linear pre-
compensation, x(n), RO quantization noise, qro(n)without (w/o)
DRE, and quantization noise with (w) DRE, q(n).
−40 −30 −20 −10 0 10 20 30 40
−60
−50
−40
−30
−20
−10
0
10
Frequency [GHz]
PSD [dB/Hz]
Received signal
qeff w/o DRE
qeff w DRE
(b) Spectral image, after the channel, of: the received signal, y(n),
effective quantization noises qeff(n)without (w/o) DRE and with (w)
DRE
Fig. 5: Spectral images before (a) and after (b) the channel
and MF.
The improvement in the MF-MSE, achieved by applying
the DRE, is demonstrated in Fig. 6. The figure shows the MF-
MSE values for the cases without DAC quantization (infinite
precision), 4 bits quantization without and with DRE and 5
bits quantization without and with DRE. The x-axis in the
figure describes the signal-to-noise (SNR) between the non-
quantized signal and the channel AWGN. For the 4 bits case, it
is shown that standard RO quantizer is limited to only 17.5 dB,
which is below the required pre-FEC value. On the other hand,
the 4 bits DRE quantized signal achieves MF-MSE value of
26.1 dB, and can support the 3.4×10−2FEC requirement,
with <1 dB penalty compared to the ideal scenario without
DAC quantization. The 4 bits quantizer with DRE can also
support FECs that require smaller BER values. For example
BER of 1×10−3can also be achieved with the 4 bits quantizer.
As for the 5 bits case, similar gain is reported. The 5 bits
6
RO quantizer is shown to achieve MF-MSE value of 24 dB,
whereas the DRE quantizer reaches 32.6 dB. In both cases, 4
and 5 PNOB, the DRE gain is 8.6 dB. It is also shown that the
4 PNOB DRE outperforms the 5 PNOB RO quantizer. BER
results are depicted in Fig. 7. Similarly to the MF-MSE results,
it is demonstrated that the 4 bits DRE quantizer can easily
achieve the required pre-FEC value of 3.4×10−2, and thus
meets the 400G transmission requirement. The SNR penalty is
∼1dB at the FEC threshold. This is opposed to the standard
4 bits RO quantizer which has BER floor of 1×10−1. A
significant improvement is also shown for the 5 bits case.
The results are compared with the MF bound [24], indicating
that the DPC has negligible loss compared to the optimal
performance.
The results in Figs. 6 and 7 are only provided for 4-5 PNOB,
as it is assumed that at lower resolutions the quantization
noise will dominate over other systems’ noise mechanisms.
In the cases of higher DAC resolutions, e.g. 6-8 bits, the
DRE is still expected to contribute to SNR gain via the noise
shaping, whereas the quantitative gain values will depend on
the relative contribution of the quantization noise vs other
systems’ distortions. Achievable MF-MSQE values with and
without the DRE for 4-8 bits DACs are shown in Table I.
10 15 20 25 30 35 40
10
15
20
25
30
35
40
45
FEC limit 3.4e-2
FEC limit 1e-3
SNR [dB]
MF-MSE [dB]
Infinite precision
4b w/o DRE
4b w DRE
5b w/o DRE
5b w DRE
Fig. 6: MF-MSE results for 4 and 5 bits quantization with (w)
and without (w/o) DRE. Infinite precision curve represents the
ideal case without DAC quantization.
TABLE I: SNR results versus number of bits
Number of bits MF-MSQE
w/o DRE [dB]
MF-MSQE
with DRE [dB]
DRE gain [dB]
4 17.5 26.1 8.6
5 24 32.6 8.6
630.3 38.9 8.6
7 36.3 44.8 8.5
8 41.8 49.9 8.1
C. Sample-per-Symbol (SPS) Requirement
As shown in Fig. 5, the DRE effectively manipulates the
spectral response of the quantization noise. Therefore, one
5 10 15 20 25
10−4
10−3
10−2
10−1
FEC limit 3.4e-2
FEC limit 1e-3
SNR per bit [dB]
BER
MF bound
Infinite precision
4b w/o DRE
4b w DRE
5b w/o DRE
5b w DRE
Fig. 7: BER vs SNR curves for 4 and 5 bits quantization with
(w) and without (w/o) DRE. Infinite precision curve represents
the ideal case without DAC quantization. MF bound is the
optimal results for AWGN channel without ISI.
crucial parameter in this method is the number of SPS. In case
of large SPS, the noise shaping can become more efficient and
better SNR gain can be expected. The relation between the SPS
and the MF-MSQE for the simulation channel is evaluated
using Monte-Carlo simulations, and provided in Fig. 8. In
these simulations, the symbol-rate was kept fixed at 44 GBaud,
and the DAC rate was changed according to the SPS. The DRE
algorithm is shown to be more sensitive to SPS than the RO
quantizers. For instance, with 1.7 SPS the SNR gain is 6.5 dB,
compared to 8.6 dB with 2 SPS. 1.4 SPS provides SNR gain
of only 3.5 dB in this case.
However, it is worth noting that the DRE gain also depends
on the channel bandwidth compared to the sampling rate.
The lower the bandwidth, the more shaping gain can be
achieved. For example, in Fig. 9, DRE gain is plotted for
varying symbol-rates, for the same simulation channel (fixed
analog bandwidth), and at constant SPS of 1.4. DRE gain is
calculated for 4 bits, by comparing the MF-MSQE for the
cases with and without the DRE. The performance is shown
to improve from 3.5 dB to 6 dB as the symbol-rate increases
from 44 GBaud to 64 GBaud, as there is more out-of-band
frequencies for more aggressive noise shaping. However, when
the symbol rate further increases, the MF-MSE degrades due
to the bandwidth limitation of the channel of Fig. 4, and the
resulting excessive inter-symbol interference (ISI), thus the
relative improvement is reduced. In [11], where the channel
bandwidth was much narrower compared to the considered
setup in this work, ∼6 dB gain with 1.28 SPS is reported.
D. Optimizing the Number of Taps
In practice, accurate modeling of the channel impulse
response from Eq. 6 may require large number of taps. To
reduce the computational complexity, the use of channel-
shortening (CS) filter [25], [27] is suggested. It is assumed
that the channel phase response has less impact on the DRE
7
1.41.51.61.71.81.92
18
21
24
27
30
33
SPS
MF-MSQE [dB]
RO B=4
DRE B=4
RO B=5
DRE B=5
Fig. 8: MF-MSQE results vs SPS for symbol-rate of
44 GBaud.
44 48 52 56 60 64 68 72 76 80
3
4
5
6
7
Symbol rate [Gbaud]
DRE gain [dB]
4b DRE gain
Fig. 9: DRE gain vs symbol-rate at 1.4 SPS.
performance compared to the channel magnitude response.
Therefore, the original impulse response of the channel can
be replaced by an equivalent filter that has similar magnitude
response and minimal phase. Thus, the number of significant
taps is reduced. In Table II, the MF-MSQE and gain is
provided for different number of taps, indicating that most
of the DRE effectiveness is obtained by using only 3 taps.
TABLE II: SNR results versus number of taps
Channel taps (L) MF-MSQE [dB] DRE gain [dB]
2 22.4 4.8
3 26.1 8.6
4 26.6 9.1
5 26.7 9.2
V. EXPERIMENTAL SET UP A ND RE SU LTS
We conducted experiments with DRE in the following two
scenarios:
•DRE with L-DPC overcoming only bandwidth and skew
limitations
•DRE with DPD overcoming also nonlinear effects of the
components
A. Experimental Setup
The WDM experimental setup is shown in Fig. 10 also
as reported in [13]. The same setup, without WDM loading,
was also used for optical BTB (OBTB) measurements. Both
transmitters consisted of 4 channel DACs, DAs and DP-MZM.
DP-64QAM 44 GBaud signals with roll-off coefficient 0.2
were generated in DSP and pre-compensated as described
in Section II. The digital samples were then quantized us-
ing the DRE algorithm, and using standard RO quantizer
for comparisons. The DACs operated at a sampling rate of
88 GSamples/s (2 SPS), with a PNOB of 8 and ENOB of
6. The analog bandwidth of the DAC is ∼16 GHz. The
quantization was implemented for PNOB of 8, 5 and 4 bits
(with and without DRE). 4 and 5 PNOB quantizers were
obtained by choosing smaller number of levels out of the 8
PNOB DACs. Digital samples after suitable DPC and DRE
with different quantization levels were then loaded into the
DACs. The neighboring channels were decorrelated using a
wavelength selective switch (WSS), achieved by delaying each
consecutive channel by fibers of lengths ranging from 1 m
to 8 m, then multiplexed with the channel under test (CUT)
in the WSS and launched into the link. The link consisted
of 95 km of SSMF (1 span) with 0.20 dB/km attenuation
and 16.9 ps/(nm·km) dispersion. EDFAs with noise figure
of 6 dB were used to amplify the signals after the span.
At the receiver, optical signals were converted into electrical
domain with a coherent front-end; an ADC with 18 GHz 3dB-
bandwidth was used to capture a shot of 5×105samples per
tributary. The frequency response of the BTB channel is shown
in Fig. 4. The receiver DSP included resampling, accumulated
dispersion compensation with a frequency domain equalizer
and correction of the carrier frequency offset. After data-aided
2×2 equalization, carrier phase estimation used distributed
pilot symbols to enable non-differential transmission. Finally,
soft demapping and decoding were performed and BER was
estimated by error counting.
B. Experimental Results: BER versus OSNR
The OBTB results are reported in Fig. 11. The figure shows
the BER results for 4,5 and 8 bits quantizer with and without
DRE. It is clearly observed that 4 bits standard RO quantizer
does not achieve the required pre-FEC value of 3.4×10−2. On
the other hand, 4 bits DRE quantized signal is shown to reach
the required value at optical-signal-to-noise-ratio (OSNR) of
30 dB. The measured OSNR penalty is only 1.5 dB compared
to 8 bits RO quantizer. The 4 bits DRE also outperforms the
5 bits RO quantizer, with 1 dB gain at the considered FEC
threshold. Additionally, it is shown that 5 bits DRE quantizer
achieves the same performance as the 8 bits RO quantizer. A
gain of more than 2 dB is demonstrated compared to the case
without DRE. It should be noted that no improvement is shown
between the 8 bits cases with the DRE and without the DRE.
8
DP-64QAM
44 GBaud
DPE, DRE
DP-64QAM
44 GBaud
DPE, DRE
4 Channel
DAC 16GHz
ENOB ~6
4 Channel
Driver
Amplifier
LASER
4 Channel
DAC 16GHz
ENOB ~6
4 Channel
Driver
Amplifier
LASER BOX
16 Channels
DP-MZM
WSS
OSA
NOISE
LOADING
COUPLER
COHERENT
RX
4 Channel
ADC 80Gs/s
ENOB ~ 6
LO
OFFLINE
RX
DSP
95km SSMF
Fig. 10: Experimental setup used for WDM transmission. Inset shows received spectrum and DP-64QAM constellation.
The larger the quantization noise, compared to other systems’
distortions, the larger is the gain from DRE. However, when
quantization does not form a limiting factor only negligible
improvement is achieved.
The BER results, provided here, support the simulation
results described in section IV. It is shown that the DRE
enables to reduce the PNOB from 8 to 4 while applying
L-DPC, thus leading to a considerable reduction in power
consumption and cost.
22 24 26 28 30 32 34 36
1×10−2
3×10−2
5×10−2
7×10−2
9×10−2
1.1×10−1
FEC limit 3.4e-2
OSNR [dB]
BER
4b w/o DRE
4b w DRE
5b w/o DRE
5b w DRE
8b w/o DRE
8b w DRE
Fig. 11: BER vs OSNR for 4,5 and 8 bits quantization with
(w) and without (w/o) DRE.
C. 64QAM WDM Transmission Setup
Based on the previous analysis and by employing the same
experimental setup, we carried out an experiment on the
95 km link (typical distance for DCI), with 17×400G 64QAM
channels, where the performance of the central channel was
evaluated. The experimental setup for WDM transmission is
shown in Fig. 10. The setup is the same as described in the
preceding subsection, with the same parameters. In all cases
only DRE quantization was considered.
In Fig. 12, BER results vs launched power are presented,
thus the optimal transmitted power can be extracted. Similarly
to Fig. 11, Fig. 12 demonstrates as well that transmission over
95 km with only 4 PNOB DACs can be obtained with a pre-
FEC threshold of 3.4×10−2. Additionally, the case of 5 PNOB
with DRE achieves almost identical results as the 8 PNOB
case.
−6−4−2 0 2 4
5×10−2
4×10−2
3×10−2
2×10−2
FEC limit 3.4e-2
Launch Power [dBm]
BER
8b w DRE
5b w DRE
4b w DRE
Fig. 12: BER vs launch power for 4,5 and 8 bits quantization
with (w) DRE.
D. Digital pre-distortion with DRE
The proposed DRE was also verified with nonlinear DPD.
In these experiments, the DAs gain was increased in order
to increase the output power of the MZMs, whereas the
nonlinearity of the modulators was compensated by means
of Volterra based DPD, as described in section II. Using the
non-linear DPD, approximately 3dB gain is achieved in the
MZMs output power [5]. In this setup, 32 GBaud 64QAM
9
signals were transmitted, and FEC threshold of 4.2×10−2
was considered. The required OSNR (ROSNR) to reach the
FEC threshold was measured for 4,5 and 8 bits quantization,
with and without DRE.
ROSNR results are presented in Fig. 13, for nonlinear orders
of P= 1,P= 3 and P= 5. For nonlinear order of P= 1,
the 4 bits DRE quantization showed improvement of 6 dB
in the ROSNR, compared the case without DRE. Smaller
improvement of 0.5 dB was shown for the 5 bits quantization.
For nonlinear order of P= 3, the DRE gain was 4.9 dB at the
case of 4 bits and 0.6 dB for 5 bits. Nonlinear order of P= 5
demonstrated improvement of 5.2 dB for 4 bits, and 0.7 dB for
5 bits. 8 PNOB cases yielded the best (lowest) ROSNR results
of 24 dB, which is only 0.1 dB below the results measured
for 4 PNOB with our proposed DRE.
45678
22
24
26
28
30
32
Number of bits
ROSNR @FEC threshold 4.2×10−2
NL order 1, w/o DRE
NL order 1, w DRE
NL order 3, w/o DRE
NL order 3, w DRE
NL order 5, w/o DRE
NL order 5, w DRE
Fig. 13: ROSNR vs number of DAC bits with (w) and without
(w/o) DRE.
VI. CONCLUSIONS AND SUMMARY
The performance of low-resolution DPC, aided by DRE
algorithm is verified in simulation and experimental results.
It is shown, both numerically and experimentally, that the
DRE can increase the effective resolution of the DAC by
more than 8 dB. We utilized the DRE to generate 400G
64QAM signals using only 4 PNOB. A significant improve-
ment is demonstrated in OBTB experiments. Additionally, the
experimental results correspond to the theoretical analysis. The
proposed method has also been verified by transmitting 400G
signals over 95 km of SSMF, which is a typical distance for
DCI. Nonlinear 4 PNOB DPD with DRE was also verified,
with over 5 dB gain. This achievement paves the way to the
utilization of DPC, based on low-resolution DACs, which can
dramatically reduce the cost and power consumption of the
transmitter.
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