1. Advanced Optical Communications
Report of the virtual laboratory sessions
2015/16
Student:
Pietro Santoro (218531)
Teacher:
Vittorio Curri
POLITECNICO DI TORINO
Master Degree in Telecommunication Engineering

3. Pietro Santoro
Table of Contents
INTRODUCTION: ............................................................................................................................................................................1
HOMEWORK 1: MULTI-SPAN TRANSMISSION LINKS ................................................................................................... 2
1.1 Multi-span transmission link in linear regime 2
1.2 Multi-span transmission link in “saturated” regime 5
1.3 Resilience properties of a multi-span transmission link in “saturated” regime 10
1.3.1 Lower transmitting power 10
1.3.2 Failure of the 6th
amplifier 11
1.3.3 Failure of the 12th
amplifier 14
HOMEWORK 2: OPTICAL LINK ANALYSIS BY USING OPTSIMTM ........................................................................... 16
2.1 Optical link with noisy channel 16
2.1.1 Optical link with noisy channel: qualitative analysis 18
2.1.1.1 IMDD-NRZ 18
2.1.1.2 IMDD-RZ 20
2.1.1.3 DPSK 21
2.1.1.4 PSBT 23
2.1.2 Optical link with noisy channel: quantitative analysis 25
2.2 Optical link with noisy and dispersive channel 27
2.2.1 Optical link with noisy and dispersive channel: quantitative analysis 28
2.2.1.1 BER curves and Q-factor vs Dacc curve 29
2.2.1.2 BER curves and Q-factor vs Dacc curve: focus on the PSBT 30
2.2.2 Optical link with noisy and dispersive channel: quantitative analysis 32

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Introduction
The following report contains the results that have been obtained during the hours dedicated to the virtual
laboratory sessions of Advanced Optical Communication: a course of the Master degree in
Telecommunication engineering that has been held from Prof. Vittorio Curri. The structure of the chapters
has been organized along the lines of the homeworks that have been assigned.
The computations and the plots has been realized with MATLAB
®
and OptSimTM
.

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1 – Multi-span transmission links
The first part of report contains the results obtained from the solution of the Homework 1 that has been
assigned during the course of Advanced Optical Communications. The focus of the chapter is on the study
of a multi-span optical communication system with the aim of better understanding the role of the
parameters and the most important tradeoffs. In the following we will consider the overall transmission
system working with EDFAs both in linear and “saturated” regime:
 Linear regime: in this case the EDFAs are considered working with constant gain 𝐺 and
transparency conditions (𝐺 = 𝐴−1
).
 “Saturated” regime: in this more realistic model, the EDFAs are considered working with a
nonlinear behavior. As for every amplifier we will consider a saturation power P𝑠 and a gain 𝐺 that
depends both on the length of the span and on the input power. This model will give us the
opportunity of studying in details some important transient phases of the system like the initial
power injection and the case of the fault of one EDFA in the chain.
1.1– Multi-span transmission link in linear regime
The system we want to analyze is depicted in figure 1.1. It is a simplified scheme of a WDM system with
𝑁𝑐ℎ = 100 different wavelengths (or channels). For each WDM channel we have a set of elements that
are repeated periodically for each span: span length and EDFA are identical (in terms of gain and introduced
ASE noise). The most important assumption we have done in this part of the analysis is that the amplifiers
are considered in “transparency condition”: each EDFA compensates for the degradation of the signal in
the previous span: 𝐺𝐴−1
= 1). The main parameters of the system are listed below:
 𝑅 𝑠 = 32 [Gbaud/s] - Baud rate
 𝑓0 = 193 [THz] - working frequency of the system - C band
 𝐵𝑎𝑚𝑝 = 5 [THz] - bandwidth of the EDFA
 𝑁𝑐ℎ = 100 Number of WDM channels
 𝛼 𝑑𝐵 = 0.22 [dB/km] - fiber attenuation
 𝐴 𝑑𝐵 = 3 [dB] - Attenuation due to connectors, bending etc.
 𝐹𝑑𝐵 = 4.5 [dB] - Noise figure
 𝑃𝑇𝑋,𝑐ℎ,𝑑𝐵𝑚 = −3 [dBm] - transmitted power per each WDM channel
The requirements of the systems are expressed in terms BER, length and OSNR:

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 𝐵𝐸𝑅 𝑇𝐴𝑅𝐺𝐸𝑇 = 10−3
 𝐿 𝑚𝑎𝑥 = 3000 [km]
 𝑀𝑎𝑟𝑔𝑖𝑛 𝑑𝐵 = 2 [dB]
 𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇,𝑑𝐵 = 13 + 𝑀𝑎𝑟𝑔𝑖𝑛 𝑑𝐵 [dB]
The “margin” is useful because we want the system must guarantee the minimum requirements also in
case of unexpected impairments (splices, bending and additional connectors).
Figure 1.1 - Simplified scheme of a WDM multi-span optical link
The first goal of the analysis is to find the minimum number of spans 𝑀 such that the 𝑂𝑆𝑁𝑅 at the receiver
(𝑂𝑆𝑁𝑅 𝑅𝑋) is larger or equal than the 𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇 . The computation has been done thanks to the
implementation of a loop that investigates whether the system satisfy the following inequality by varying
𝑀:
𝑂𝑆𝑁𝑅 𝑅𝑋 =
𝑃𝑐ℎ
𝑀(𝐺 − 1)ℎ𝑓0 𝑅𝑠 𝐹
≥ 𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇 + 𝑀𝑎𝑟𝑔𝑖𝑛
for i=1:length(M)
if (OSNR_dB(i) >= OSNR_target_dB)
OSNR_best = OSNR_dB(i);
M_best = M(i);
L_span_best = L_span(i);

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break
end
end
Code extract 1.1 - Computation of optimum M in MATLAB
As expected from the theory, for a fixed length of the system 𝐿 𝑚𝑎𝑥 the 𝑂𝑆𝑁𝑅 is an increasing function of
𝑀: by increasing the number of span 𝑀 we are decrementing the span loss and consequently the gain 𝐺
that each EDFA has to apply to compensate from the loss in the previous span.
Figure 1.2 - OSNR in function of the number of spans M
The optima that have been found are the following:
 𝑀 𝑏𝑒𝑠𝑡 = 62
 𝐿 𝑠𝑝𝑎𝑛,𝑏𝑒𝑠𝑡 = 48.38
 𝑂𝑆𝑁𝑅 𝑅𝑋,𝑏𝑒𝑠𝑡 = 15.003 [dB]
At this point the system is studied by fixing the optimum results we have already found:
I. If I increase the number of span M the 𝑂𝑆𝑁𝑅 𝑅𝑋 in Rs goes below the minimum required value
𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇,𝑑𝐵 (figure 1.3).
II. If we consider the whole WDM system and the transmission of all the 𝑁𝑐ℎ channels is possible to
understand what is the noise contribution of each EDFA that is added in the chain because we
know that the added noise power is:
𝑃 𝑁 = (𝐺 − 1)ℎ𝑓0 𝐵𝑎𝑚𝑝 𝐹
Along the link we have a constant signal power 𝑃𝑇𝑋 = 0.0501 [𝑊] (because of the transparency
conditions) and an increasing noise power with a peak of 𝑃 𝑁 = 0.004 [𝑊] in proximity of the last
span. The noise power is strictly related to the bandwidth of the EDFA: if we use a large 𝐵𝑎𝑚𝑝 we
can extend the number of wavelengths for our WDM system but with the price of the increment of
the overall power in the link and the decrement of the 𝑂𝑆𝑁𝑅 𝑅𝑋 . The graphical representation of
what we have said before is in the figure 1.4.

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Figure 1.3 - OSNR in Rs for different M around the optimum value Mbest
Figure 1.4 - Noise, signal and total power for different M
1.2 - Multi-span transmission link in “saturated” regime
In this part of the chapter we will consider the same WDM system of the previous point (figure 1.1) but this
time EDFAs working in saturated regime. In these conditions, each EDFA has no more a constant gain
because it varies w.r.t. the power at its input:
𝐺 = 𝐺0 𝑒
−
𝑃 𝐼𝑁
𝑃𝑠
(𝐺−1)
where 𝐺0 = 27 𝑑𝐵 is the “unsaturated gain” and 𝑃𝑆 is the amplifier saturation power.
Before continuing with the analysis let us open a parenthesis to better explain what happens in our multi-
span link with this conditions. The attenuation in each span is always the same (uniform span length 𝐿 𝑠𝑝𝑎𝑛)

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but the gain of the EDFA does not exactly compensates for it in all the spans. Let us focus on this concept:
our multi-span link can be seen as the periodic repetition of fiber spans and EDFAs (figure 1.5);
Figure 1.5 – Simplified representation of a multi-span link
The output power of the ith
amplifier is reduced by a factor A and the input power of amplifier i+1 becomes:
𝑃𝑖𝑛,𝑖+1 = 𝐴 ∙ 𝑃𝑜𝑢𝑡,𝑖 or 𝑃𝑜𝑢𝑡,𝑖−1 = 𝐴−1
∙ 𝑃𝑖𝑛,𝑖
In the following figures is depicted the transient phase:
Figure 1.6 a, b and c - Evolution of the transient phase in a multi-span link in “saturated” regime
If at the transmitter it is launched a low power on the chain the first EDFA will provide higher gains instead
of compensating only the span loss; the signal power along the link in increasing span after span and the
gain decreases because it approaches saturation (intersection of the two characteristics). At this point the
system works at steady state and the total power output of the EDFAs across the link is equal to an
asymptotic, constant value called output saturation power 𝑃𝑜𝑢𝑡,∞. If we use a launching power 𝑃𝑇𝑋 <
𝑃𝑜𝑢𝑡,∞ or 𝑃𝑇𝑋 > 𝑃𝑜𝑢𝑡,∞ a transient phase occurs (it can be qualitatively observed in figure 1.7) and the
model that better fit with this scenario is the exponential gain model.
Figure 1.7 - Transient behavior of the multi-span link in “saturated” regime
This model is nearer the realistic case because it takes into account the fact that the EDFA cannot
compensate as much we want for too long span loss but can amplify with a maximum gain reached in
saturation. A more convenient way to define the saturation power is the minus 3 dB saturation power. It is
the input power 𝑃𝑖𝑛,−3𝑑𝐵 and the output power 𝑃𝑜𝑢𝑡,−3𝑑𝐵 at which the amplifier gain 𝐺 =
𝐺0
2
:

11. Pietro Santoro
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Pout,−3dB = 𝑃𝑠
ln 2
1−
2
𝐺0
P𝑖𝑛,−3dB = ln 2 ∙ 𝑃𝑠
1
1−
2
𝐺0
At this point let us come back to our analysis where we have used a model that simplify the computation:
the constant gain model. Here we are assuming that the system is already in its steady state and that we
start transmitting directly at the value 𝑃𝑜𝑢𝑡,∞ = 𝑃𝑇𝑋,𝑐ℎ ∙ 𝑁𝑐ℎ = 17 𝑑𝐵𝑚 . The goal is again to find the
minimum number of spans M such that the OSNR at the receiver (OSNRrx) is larger or equal than the
OSNRTARGET .
The OSNR at the receiver can be computed by using the following formulas:
𝑂𝑆𝑁𝑅 𝑟𝑥 =
𝑃𝑐ℎ(𝐴 𝑠 𝐺∞) 𝑀
(𝐺∞ − 1)ℎ𝑓0 𝑅𝑠 𝐹
1 − (𝐴 𝑠 𝐺∞) 𝑀
1 − 𝐴 𝑠 𝐺∞
≥ 𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇 + 𝑀𝑎𝑟𝑔𝑖𝑛
𝐺∞ =
𝑃𝑜𝑢𝑡,∞ + ℎ𝑓0 𝑅𝑠 𝐹
𝑃𝑜𝑢𝑡,∞ ∙ 𝐴 𝑠 + ℎ𝑓0 𝑅𝑠 𝐹
And 𝐴 𝑠 is the fiber attenuation.
The computation of the inequality has been done with a similar loop and the obtained optimum results are
the following:
 𝑀 𝑏𝑒𝑠𝑡 = 63
 𝐿 𝑠𝑝𝑎𝑛,𝑏𝑒𝑠𝑡 = 47.619
 𝐺∞ = 22.248 𝑑𝐵
 𝑂𝑆𝑁𝑅 𝑅𝑋,𝑏𝑒𝑠𝑡 = 15.007 [dB]
In the following plot (figure 1.7) is possible to see the graphical representation of M in function of the
OSNR. Similarly for what we have seen for figure 1.2 we are dealing with an increasing function:
Figure 1.8 - OSNR in function of the number of spans M
If we want to know what is the required 𝑃𝑜𝑢𝑡,−3𝑑𝐵 of the EDFA in order to satisfy the design constraint we
can use exploit the following formula:

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𝑃𝑜𝑢𝑡,∞ = 1.44
1
1 − 𝐴 𝑠
ln(𝐴 𝑠 𝐺0) ∙ 𝑃𝑜𝑢𝑡,−3𝑑𝐵
from which we obtain:
𝑃𝑜𝑢𝑡,−3𝑑𝐵 = 10.284 𝑑𝐵𝑚
At this point the system is studied by applying the optimum results we have already found for the number
of spans:
I. If I increase the number of span M the 𝑂𝑆𝑁𝑅 𝑅𝑋 in 𝑅 𝑠 goes below the minimum required value
𝑂𝑆𝑁𝑅 𝑇𝐴𝑅𝐺𝐸𝑇,𝑑𝐵 (figure 1.8)
Figure 1.9 - OSNR in Rs for different M around the optimum value Mbest
II. Similarly to the previous analysis we will consider the whole WDM system and the transmission of
all the Nch channels and we will confirm that is possible to understand what is the noise
contribution of each EDFA that is added in the chain:
Figure 1.10 - Noise, signal and total power for different M

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If we compare the graph with the similar one we have obtained in figure 1.4 we can notice that the
total power is constant along the link because the power at the output of the EDFA is fixed because
is the steady-state and the noise addition is compensated by the system with a reduction of the
signal power.
In the homework1 has been required to repeat the whole analysis by considering 𝐺0 = 27 𝑑𝐵 and
𝑃𝑜𝑢𝑡,−3𝑑𝐵 = 1 𝑑𝐵𝑚 and the same transmitted power level. By comparing this value with the one that has
been obtained in the “saturated” regime analysis we can notice that this time we have a 𝑃𝑜𝑢𝑡,−3𝑑𝐵 that is
10 times lower. As a consequence also 𝑃𝑜𝑢𝑡,∞ will be also lower because the relationship that bounds the
two is always the same:
𝑃𝑜𝑢𝑡,∞ = 1.44
1
1 − 𝐴 𝑠
ln(𝐴 𝑠 𝐺0) ∙ 𝑃𝑜𝑢𝑡,−3𝑑𝐵
We have a lower 𝑃𝑜𝑢𝑡,∞ and the same launching power as before. Since we are not starting from steady
state, the gain this time must be computed by using the exponential model. From the result it has been
observed that the best number of span M for which the system is able to satisfy the minimum
requirements is for 𝑀 → ∞ and we know that it is not feasible because with the increment of the number
of spans the contribution of extra loss becomes more and more prevalent: even if the span lengths are as
small as possible, the loss span and so the amplifier gain are more or less constant, little higher than the
extra loss (3dB), with the only consequence to increases the noise with the introduction of other amplifiers.

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1.3 - Resilience properties of a multi-span transmission link in “saturated”
regime
In this part of the report we will analyze some “erroneous” situation that may occurs in a real system by
taking into account the setting we have optimized in section 1.2. ( 𝑀 𝑏𝑒𝑠𝑡 = 63 and 𝐿 𝑠𝑝𝑎𝑛,𝑏𝑒𝑠𝑡 = 47.619 ).
The goal of this analysis is to establish whether the system goes out of service or not (our definition of out
of service is the one where the effective BER exceed the 𝐵𝐸𝑅 𝑇𝐴𝑅𝐺𝐸𝑇). The cases we will study are the
following:
1. Lower transmitting power because the transmitter goes out of order giving a power 10 dB lower
than the required one
2. Failure of the 6th
amplifier of the chain because it goes out of order giving a gain 10 dB lower than
the required one
3. Failure of the 12th
amplifier of the chain because it goes out of order giving a gain 10 dB lower than
the required one
Let us consider the three cases one by one.
1.3.1 - Lower transmitting power
The analysis can be done by considering the TX failure both after the system is already in steady state
(constant gain model) and when it is not (exponential gain model) but for the reason why we are launching
a power that is lower than 𝑃𝑜𝑢𝑡,∞ we will use the second model by computing the gain and the 𝑂𝑆𝑁𝑅 for
each span thanks to the implementation of the following loop:
for i=1:M_best+5
gain = @(x) ( x-G0*exp(-Pin(i)/Ps*(x-1)));
G(i)=fzero(gain,[0 1000]);
Pin(i+1)=(Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1)))*(A);
Psignal(i+1)=Psignal(i)*A*G(i);
if (i==1)
P_noise(1)=(h*f_0*B_amp*F*(G(1)-1));
P_noise_Rb(1)=(h*f_0*Rb*F*(G(1)-1));
end ;
if i>1
P_noise(i)=P_noise(i-1)*G(i)*A+(h*f_0*B_amp*F*(G(i)-1));
P_noise_Rb(i)=P_noise_Rb(i-1)*G(i)*A+(h*f_0*Rb*F*(G(i)-1));
end
P_tot(i)=Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1));
OSNR(i)=P_ch*prod(G(1:i))*A^i/P_noise_Rb(i);
end ;
load('OSNR_i_point2.mat');
OSNR_i_dB_point2=10.*log10(OSNR_i_point2);
OSNR_dB=10.*log10(OSNR);
M_t=ceil(interp1(OSNR_dB,M_i,OSNR_target_dB));
Code extract 1.2 - Computation of the gain for each span (exponential model)
In figure 1.11 has been plotted the OSNR that we have at the output of the chain when we add one by one
a span at a time:

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Figure 1.11 - OSNR in RS in function of the number of spans M
As we can see from the figure after the 53th
span the system is not more able to satisfy the minimum
requirements. Our analysis can be further validated by investigate about the power distribution (signal and
noise power) in the link (figure 1.12):
Figure 1.12 - Power distribution in Bamp in function of the number of spans M
In the first spans it is possible to observe the transient phase that occurs when it is used a launching power
𝑃𝑇𝑋 < 𝑃𝑜𝑢𝑡,∞ .
1.3.2 - Failure of the 6th amplifier of the chain
In this second case we can directly study the system by assuming starting in steady state and by using
constant gain model. At a certain point the 6th
amplifier of the chain goes out of order giving a gain 10 dB
lower than the required one. The loop in MATLAB has been properly modified in order to cope with this
condition:

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for i=1:M_best+5
gain = @(x) ( x-G0*exp(-Pin(i)/Ps*(x-1)));
G(i)=fzero(gain,[0 1000]);
Pin(i+1)=(Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1)))*(A);
Psignal(i+1)=Psignal(i)*A*G(i);
if (i==1)
P_noise(1)=(h*f_0*B_amp*F*(G(1)-1));
P_noise_Rb(1)=(h*f_0*Rb*F*(G(1)-1));
end ;
if i>1
P_noise(i)=P_noise(i-1)*G(i)*A+(h*f_0*B_amp*F*(G(i)-1));
P_noise_Rb(i)=P_noise_Rb(i-1)*G(i)*A+(h*f_0*Rb*F*(G(i)-1));
end
P_tot(i)=Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1));
if i==6
G(i)=G(i)/10;
Pin(i+1)=(Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1)))*(A);
Psignal(i+1)=Psignal(i)*A*G(i);
P_noise(i)=P_noise(i-1)*G(i)*A+(h*f_0*B_amp*F*(G(i)-1));
P_noise_Rb(i)=P_noise_Rb(i-1)*G(i)*A+(h*f_0*Rb*F*(G(i)-1));
P_tot(i)=Pin(i)*G(i)+(h*f_0*B_amp*F*(G(i)-1));
end;
OSNR(i)=P_ch*prod(G(1:i))*A^i/P_noise_Rb(i);
end ;
OSNR_dB=10.*log10(OSNR);
M_t=ceil(interp1(OSNR_dB,M_i,OSNR_target_dB))
Code extract 1.3 - Computation of the gain for each span (exponential model)
In Fig. 1.13, we can note that as the previous case, after the 53th span the OSNR goes below the threshold
leading the system under the minimum working requirements:
Figure 1.13 - OSNR in RS in function of the number of spans M

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As we expect from theory the OSNR drastically decreases after the break point and the causes of this
behavior can be simply explained by referring to the input power of the 7th
amplifier that is lower than
𝑃𝑜𝑢𝑡,∞. The system returns again in steady state between the 10th
and the 15th
span and this can be noticed
from the slope of the figure is again similar to the one without EDFA breaking and from the following figure
that shows the evolution of the gain in each amplifier:
Figure 1.14 - Evolution of the gain in the i
th
amplifier of the chain
The EDFAs that have higher gain are the one that introduce more amount of noise because of the loss in
OSNR and this can be validated by looking at the power distribution in the chain (figure 1.15):
Figure 1.15 - Power distribution in Bamp in function of the number of spans M

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1.3.3 - Failure of the 12th amplifier of the chain
In this third and last case we have repeated the same analysis we have done in the previous point and by
slightly modifying the code in MATLAB we have simulated the scenario in which the 12th
amplifier of the
chain goes out of order giving a gain 10 dB lower than the required one. In the figure 1.16 we can note that
as before, after the 53th span the OSNR goes below the threshold leading the system under the minimum
working requirements:
Figure 1.16 - OSNR in RS in function of the number of spans M
The same reasoning we have done in the previous case is valid for this case about gain and power
distribution (figure 1.17 and 1.18).
Figure 1.17 - Evolution of the gain in the i
th
amplifier of the chain

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Figure 1.18 - Power distribution in Bamp in function of the number of spans M

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Homework 2 - Optical link analysis by using
OptSimTM
In this second part of the report has been required to provide qualitative and quantitative analyses of a
standard optical link by using the software environment provided from OptSimTM
. The goal of the research
is to do a qualitative analysis on the eye diagram and on the spectrum and a quantitative one on the target
𝑂𝑆𝑁𝑅 for the target 𝐵𝐸𝑅, on the 𝐷 𝑎𝑐𝑐 and on the 𝑄 − 𝑝𝑒𝑛𝑎𝑙𝑡𝑦. Each analysis has been done for different
channels:
 noisy channel
 noisy and dispersive channel
for different modulation formats at the transmitter:
 IMDD-NRZ
 IMDD-RZ
 PSBT
 DPSK
and finally for different detector at the receiver:
 IMDD and PSBT
 DPSK
In order to completely treat all the possible cases the analysis will be initially divided into two sections by
considering first the different channels.
2.1 - Optical link with noisy channel
Figure 2.1 - Block diagram of the simulated link (from OptSim
TM
)
The block diagram that is possible to observe in figure 2.1 has been realized in OptSimTM
by following the
instruction that are listed in detail in the Homework2. The most important parameters that has bet initially
set and will be kept for all the simulations are the followings:

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 𝑓0 = 193 [THz] - working frequency of the system - C band
 𝑠𝑖𝑚. 𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ = 24 𝑠𝑎𝑚𝑝𝑙𝑒𝑠
 𝑅 𝑏 = 10.7 𝑎𝑛𝑑 42.65 [Gbps]
 𝐵𝐸𝑅 𝑇𝐴𝑅𝐺𝐸𝑇 = 10−3
The number of simulated bits are 211
for the eye diagrams and spectra (qualitative analysis) and 217
for the
error counting; this because we require more precision for the quantitative analysis. The optical field will be
represented in “dual polarization”.
Let us now introduce each of the blocks in the figure in order to understand their working principle. The
blocks that constitute the transmitter are the following:
• Data_seq: generates a pseudorandom sequence of bits which represents the information source
• Driver: generates the ideal electrical pulse for each bit according to the chosen modulation format.
The most important parameter that need to be set is the voltage value for low and high:
o 0 and +5 V for IMDD-NRZ
o -5 and +5 V for PSBT and the DPSK
• LPF: simulates the Bessel filter that is useful for the compensation of the penalty introduced from
the non-matching of the optical filter at the transmitter. It is always kept with 5 and its bandwidth
depends on the modulation format, according to the values provided in the trace of the
Homework2:
o for IMDD-NRZ it is 0.75𝑅 𝑏
o for IMDD-RZ it is 1.3𝑅 𝑏
o for PSBT 0.25𝑅 𝑏
o for DSK 𝑅 𝑏
• Laser: it is an ideal CW Lorenzian laser set at 𝑃𝑇𝑋 = 0 𝑑𝐵𝑚
• External modulator: it is a Mach-Zehnder modulator with sin2
electrical shaped characteristic. It is
properly driven depending on the modulation formats, by the Bessel filter. The Extinction Ratio is
set to 20dB allowing a good aperture of the eye-diagram.
• EDFA: set with output power equal to 0 dBm.
For what concern the channel, the blocks are the following:
• Noisy: it is an AWGN generator that adds on the optical link through a Combiner. In order to have
the required 𝑂𝑆𝑁𝑅, the ASE noise generator has been set through the formula:
𝑃𝐴𝑆𝐸 = 𝑃𝑇𝑋 − 𝑂𝑆𝑁𝑅 − 10 log 𝑅 𝑏
• Dispersive and noisy channel: this block is added in order to insert dispersion in the channel. It is
the ideal Fiber Grating which introduces the parameter 𝐷 𝑎𝑐𝑐
Finally, the receiver:
• OpFilter: it is the second order optical Super Gaussian filter with 𝐵0 = 0.33 𝑛𝑚
• PIN: implements the PIN photodiode that converts the optical power into electrical current. Its
responsivity is set to 0.6 A/W . This will be used for all modulation formats except for the DPSK
which exploits the ideal balanced DPSK receiver that includes the AMZI and the balanced
photodetectors.
• TIA: is the ideal trans-impedance amplifier that converts the current into a voltage value.
• LPF_rx: it is exploited to counteract the penalty introduced by the usage of a non-matched filter at
the receiver side. Its bandwidth depends on the Super Gaussian filter and it has been set to 0.75𝑅 𝑏.

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The last block is BER_COUNT and it is used for measurements of the Bit Error Rate of an electrical signal,
for a binary modulation (like the standard On-Off intensity modulation). For qualitative analyses it will be
used an Electrical Scope, and an Optical Spectrum at the output of the Super Gaussian filter.
2.1.1 - Optical link with noisy channel: qualitative analysis
As it has been anticipated in the introductive part the qualitative analysis consists into the examination of
the eye-diagram of the received signal and of the optical spectrum after the Super Gaussian filter. The
analysis has been repeated for the two different bit rates (10.7 and 42.65 Gbps).
OSNR has been set at 25 and 100 dB in order to analyze the behavior of the signal in presence of noise for
the different modulation formats.
In the following subsections we will attach the four combination of eye-diagrams (25 dB and 10.7 Gbps, 25
dB and 42.65 Gbps, 100 dB and 42.65 Gbps and 100 dB and 42.65 Gbps) and only two cases for the
spectrum because by varying the OSNR the spectra are pretty similar each other with the exception of a
small scaling factor.
2.1.1.1 - IMDD-NRZ
In the “unipolar” NRZ (Non Return to Zero): bit “1” is coded with 𝑉𝑜𝑛 volts and bit “0” with 0 volts. Bipolar
NRZ instead is not feasible because we need values opposites in sign and optical signal can assume only
positive values. The pulse shape can be easily spotted looking at the eye diagrams in figure 2.2.
The first important difference we can notice in the diagrams is due to the difference in terms of bitrate:
while at 10.7 Gbps the eye diagram looks almost perfect (figures 2.2a and 2.2b), at 42.65 Gbps the effect of
filtering starts to be more evident (figures 2.2c and 2.2d): the optical filter at the receiver has a limited
bandwidth that in this case is almost equal to the transmission rate. The consequence is that some
important spectral components are filtered and that the original waveform shape of the pulse is distorted.
The second difference to notice is the effect of an higher OSNR: it is clear that when the amount of ASE
noise is low w.r.t. the power of the signal the eye in the diagrams are opener.
Let us now consider the spectra in figure 2.3; the NRZ has a narrow spectral occupancy (which can be
defined as the bandwidth occupied by the main lobe). By looking at 10.7 Gbps spectrum (in figure 2.3a),
this corresponds to the bandwidth delimited by the two side peaks, that fall at ±𝑅 𝑏 so that the spectral
occupancy is equal to 2𝑅 𝑏. The central peak at 193THz is caused by the DC bias of the unipolar keying (since
the signal can assume only positive values, the average spectral component is not null).
The spectrum presents just one lobe because the secondary lobes were filtered by the 43.5GHz optical
filter.

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(a) (b)
(c) (d)
Figures 2.2a, 2.2b, 2.2c, 2.2d - Eye diagram of IMDD-NRZ for different OSNR and bit-rates: (a) OSNR=25 and 10.7 Gbps, (b)
OSNR=100 and 10.7 Gbps, (c) OSNR=25 and 42.65 Gbps and (d) OSNR=100 and 42.65 Gbps
(a) (b)
Figures 2.3a, 2.3b - Optical spectrum of IMDD-NRZ for OSNR=100 and different bit-rates: (a) OSNR=100 and 10.7 Gbps,
(b) OSNR=100 and 10.7 Gbps

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2.1.1.2 - IMDD-RZ
For what concerns the unipolar RZ (Return to Zero) the bit “1” is coded with a positive value for half of the
bit time and it comes back to zero for the second half. Bit “0” instead remains at 0 level for the entire pulse
duration. This is clear looking at the eye diagrams in figures 2.4 by looking at the pulse that results smaller
than the NRZ one. This fast transition in an interval that is smaller than the bit duration makes RZ spectral
occupancy wider w.r.t. the one we have seen for NRZ: by looking at the optical spectra in figure 2.5 it is
possible to notice that the main lobe is delimited by the two peaks at ±2𝑅 𝑏 hence the spectral occupancy
is 4𝑅 𝑏 exactly the double.
Obviously, more than NRZ, the filtering effect at 42.65 Gbps is evident: just the main lobe appears in the
optical spectrum. The advantages of NRZ are more robustness to nonlinearities and an easier clock
recovery, because peaks at ±𝑅 𝑏 fall inside the main lobe.
(a) (b)
(c) (d)
Figures 2.4a, 2.4b, 2.4c, 2.4d - Eye diagram of IMDD-RZ for different OSNR and bit-rates: (a) OSNR=25 and 10.7 Gbps, (b)
OSNR=100 and 10.7 Gbps, (c) OSNR=25 and 42.65 Gbps and (d) OSNR=100 and 42.65 Gbps

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(a) (b)
Figures 2.5a, 2.5b - Optical spectrum of IMDD-RZ for OSNR=100 and different bit-rates: (a) OSNR=100 and 10.7 Gbps,
(b) OSNR=100 and 10.7 Gbps
2.1.1.3 - DPSK
DPSK (Differential Phase Shift Keying) is an optical “phase modulation” scheme. In line of principle a phase
modulation needs coherent receivers (they are particular receivers able to measure the absolute phase of a
signal) but in this simple case, for the reason why it is used a differential precoding, is possible to
implement phase keying with ordinary direct detection receivers . It has to be highlighted that the precoder
has been omitted because we are doing a simulation and for this reason we are not interesting in a specific
sequence to transmit but only in the PRBS.
In DPSK the transition between different bits is coded with a phase shift of 𝜋 and in this way it is possible to
obtain an electric signal with positive and negative values. However, when in optical domain, the electric
signal is converted in light intensity that is only positive. To overcome this problem differential precoding is
applied at TX so that the launched optical signal looks like a sequence of positive values interrupted by fast
variations to zero.
The received power is split in two equal signals and one of them is a bit time delayed using an AMZI
(Asymmetric Mach-Zehnder Interferometer). Using two Balanced Photodectors (BPD), these two signals are
summed up and the original bit stream is obtained.
Similarly to IMDD-NRZ the spectral occupancy is 2𝑅 𝑏 (figure 2.7a) with the exception that here the peaks
are not present. Furthermore, also in this case only the main lobe is filtered at 42.65 Gbps rate (figure
2.7b).

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(a) (b)
(c) (d)
Figures 2.6a, 2.6b, 2.6c, 2.6d - Eye diagram of DPSK for different OSNR and bit-rates: (a) OSNR=25 and 10.7 Gbps, (b) OSNR=100
and 10.7 Gbps, (c) OSNR=25 and 42.65 Gbps and (d) OSNR=100 and 42.65 Gbps
(a) (b)
Figures 2.7a, 2.7b - Optical spectrum of DPSK for OSNR=100 and different bit-rates: (a) OSNR=100 and 10.7 Gbps, (b)
OSNR=100 and 10.7 Gbps

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2.1.1.4 - PSBT
PSBT (Phase-Shaped Binary Transmission) is an implementation of duobinary signaling. In this modulation
set a certain amount of bit correlation is introduced in the signal to be transmitted. Also in this case a
differential precoder is used. At each symbol time, due to the interference with the previous symbol pulse,
the resultant sum makes the electrical signal to have three levels -1, 0, +1. Moreover, in optical domain, it
becomes only positive, so that differential precoding has to be used as seen in DPSK (and also in this case
the precoder is omitted in the simulation setting).
When pulse shape is carefully optimized, PSBT can perform about 1 dB better than standard NRZ in terms
of OSNR performance. In terms of spectral occupancy it is the best modulation scheme we have seen until
now because it is equal to 𝑅 𝑏 (figure 2.9).
But the most important fact for PSBT and DPSK is that they show high robustness to chromatic dispersion
because of the π phase shift. It makes PSBT more robust w.r.t. the dispersion.
(a) (b)
(c) (d)
Figures 2.8a, 2.8b, 2.8c, 2.8d - Eye diagram of PSBT for different OSNR and bit-rates: (a) OSNR=25 and 10.7 Gbps, (b) OSNR=100
and 10.7 Gbps, (c) OSNR=25 and 42.65 Gbps and (d) OSNR=100 and 42.65 Gbps

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(a) (b)
Figures 2.9a, 2.9b - Optical spectrum of PSBT for OSNR=100 and different bit-rates: (a) OSNR=100 and 10.7 Gbps, (b)
OSNR=100 and 10.7 Gbps

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2.1.2 - Optical link with noisy channel: quantitative analysis
This section focuses on the BER vs OSNR performance and on the evaluation of the 𝑂𝑆𝑁𝑅𝑡, that is the
minimum OSNR required at the receiver in order to achieve a 𝐵𝐸𝑅𝑡 ≥ 103
. The optical link has been
evaluated for each modulation format and both bitrates. In order to obtain more precise results, the
following simulation has been realized with 217
bits.
In the following set of figures (figures 2.10) are shown the decreasing functions of BER in function of the
OSNR:
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figures 2.10a, 2.10b, 2.10c, 2.10d, 2.10e, 2.10f, 2.10 g, 2.10h - BER vs OSNR curves of NRZ, RZ, DPSK and PSBT for different bit-
rates: (a) NRZ with 10.7 Gbps, (b) NRZ with 42.65 Gbps, (c) RZ with 10.7 Gbps, (d) RZ with 42.65 Gbps, (e) DPSK0 with 10.7 Gbps,
(f) DPSK with 42.65 Gbps, (g) PSBT with 10.7 Gbps, (h) PSBT with 42.65 Gbps.

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By referring to the previous plots it has been possible to extract the 𝑂𝑆𝑁𝑅𝑡 values that are gathered in the
following table:
Modulations
𝑶𝑺𝑵𝑹 𝒕 measured in [dB]
𝑅 𝑏 = 10.7 𝐺𝑏𝑝𝑠 𝑅 𝑏 = 42.65 𝐺𝑏𝑝𝑠
NRZ 10.7 10.2
RZ 9.2 10.1
DPSK 8.8 6.58
PSBT 13.63 9.7
Table 2.1 - OSNRt for different modulation schemes and different bit rates
By analyzing the data on the table 2.1 is possible to notice that the DPSK is the modulation format with
better performance for both bitrate values. Another important remarks must be done about RZ that is the
only scheme where is present an improvement of target OSNR at the higher rate. This result depends on
the relation between the bandwidth of the considered modulation format and the bandwidth of the optical
filter.
The reason for this improvement is that at the rate of 42.65 Gbps the optical filter approaches to be a
matched filter for the link, since its bandwidth of 43.5GHz is comparable to the bandwidth occupied by
NRZ, DPSK, PSBT modulation. At 10.7 Gbps instead, the optical filter selects also a lot of noise that is
outside the bandwidth of the interesting signal. This is proved also by the fact that the higher target OSNR
at 10.7 Gbps is with PSBT (13.63 dB). This modulation in fact has a narrower spectral occupancy so that the
optical filter lets pass more noise with respect to the other modulation formats.

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2.2 - Optical link with noisy and dispersive channel
In this second part we are going to analyze an optical system with a channel where is introduced an
additional impairment: the chromatic dispersion. This phenomenon depends on the refractive index of the
optical fiber that varies with the wavelength. If we consider the power spectrum of a transmitted
rectangular pulse we, qualitatively, are in front of a shape as the following:
Figure 2.11 - Qualitative representation of the spectrum of a rectangular pulse for a better comprehension of the chromatic
dispersion effect
So each spectral “slice” (or component) of the signal has a different group delay and a different phase
delay. If we reconstruct the overall signal at the end of the fiber we can clearly notice that it is “out of the
synch”. Dispersion alters the pulse by:
 delaying each spectral “slice” in a different way according to the “local” group delay
 adding a phase mismatch between each spectral component
What we aspect from the following analysis is a clear impact on the performance (especially for higher
bitrates). On the other hand this phenomenon has a positive impact on the system because it makes the
transmission more robust against non-linear distortions. The chromatic dispersion is a linear effect and it is
cumulative with the length of the fiber. The parameter that is used to “quantify” the dispersion is 𝐷; it can
be expressed in [𝑝𝑠/𝑛𝑚] or in [𝑝𝑠/(𝑛𝑚 ∗ 𝑘𝑚)] if normalized to one kilometer.
Generally, the “rule of thumbs” for the determination of a maximum accumulated dispersion 𝐷 𝑎𝑐𝑐,𝑚𝑎𝑥 is
the following:
𝐿 ≤ 𝐿 𝑚𝑎𝑥 =
1
10|𝐷|𝑅 𝑏
2
From which is possible to determine the maximum accumulated dispersion that the system is able to
tolerate without significant loss:
𝐷 𝑎𝑐𝑐 = 𝐷𝐿 ≤ 𝐷 𝑎𝑐𝑐,𝑚𝑎𝑥 =
1
10 𝑅 𝑏
2
The In the simulation context the emulation of the dispersive channel has been done by using an ideal fiber
grating, set to introduce a specific 𝐷 𝑎𝑐𝑐 value [ps/nm]. The block diagram used for the analysis is the
following one:

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Figure 2.12 - Block diagram of the simulated link (from OptSim
TM
)
2.2.1 - Optical link with noisy and dispersive channel: qualitative analysis
In order to analyze the impact on the performance we will use the following two metrics: 𝐵𝐸𝑅 and
𝑄 𝑓𝑎𝑐𝑡𝑜𝑟. The second parameter is called “quality factor” and it has a one-to-one relationship with BER:
𝑄 = √2 𝑒𝑟𝑓𝑐−1
2𝐵𝐸𝑅
The adopted strategy is the following one: for each modulation format, with the OSNR fixed to the target
value previously established, 𝑂𝑆𝑁𝑅𝑡, we derive the 𝐵𝐸𝑅 (and 𝑄) vs. 𝐷 𝑎𝑐𝑐 curve, varying 𝐷 𝑎𝑐𝑐 in the ideal
fiber grating. In the case of 𝑅 𝑏 = 10.7 𝐺𝑏𝑝𝑠, we simulate the system with 𝐷 𝑎𝑐𝑐 varying in the range: [0
1600 ps/nm], with step ∆ 𝐷 𝑎𝑐𝑐 = 100 𝑝𝑠/𝑛𝑚 and for 𝑅 𝑏 = 42.65 𝐺𝑏𝑝𝑠, [0 200 ps/nm], with step
∆ 𝐷 𝑎𝑐𝑐 = 10 𝑝𝑠/𝑛𝑚(sections 2.2.1.1 and 2.2.1.2 with a particular focus on PSBT).
A second step is the computation of the 𝑂𝑆𝑁𝑅𝑡,𝑑𝑖𝑠𝑝 that includes the penalty due to dispersion: it has been
obtained by adding to the previously calculated target 𝑂𝑆𝑁𝑅𝑡 a margin 𝑂𝑆𝑁𝑅 𝑝𝑒𝑛𝑎𝑙𝑡𝑦 in order to reach the
target BER fixing the accumulated dispersion to the value that makes the Q factor 2 dB lower than its
maximum (sections 2.2.2).

33. Pietro Santoro
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2.2.1.1 - BER curves and Q-factor vs Dacc curve
Let us comment on the following curves:
(a)
(b)
Figure 2.12a, 2.12b - BER vs Dacc curves of NRZ, RZ, DPSK and PSBT for different bit-rates: (a) 10.7 Gbps and (b) 42.65 Gbps
At both rates, DPSK and PSBT are the modulations which perform better. As said, the 𝜋 phase transition
makes this systems much robust with respect to distortion of the pulse caused by dispersion. In particular
PSBT maintains low BER values so far in dispersion axis. Worse performance instead has been noticed for
the RZ modulation that have the worst performance: the main reason of the vulnerability against
dispersion is the wider spectral occupancy.
If we consider the curves at higher rate (figure 2.12b) we notice a more decreasing trend for the BER
curves. If we instead focus on the Q-factor curves is possible to extract similar information because the two
parameters are bounded.

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(a)
(b)
Figure 2.13a, 2.13b - Q-factor vs Dacc curves of NRZ, RZ, DPSK and PSBT for different bit-rates: (a) 10.7 Gbps and (b) 42.65 Gbps
2.2.1.2 - BER curves and Q-factor vs Dacc curve: focus on the PSBT
For what concerns the PSBT modulation scheme it has been required to repeat the simulation by
considering different bandwidth for the transmission filter:
 𝐵 = 0.24 𝑅𝑏
 𝐵 = 0.25 𝑅𝑏
 𝐵 = 0.26 𝑅𝑏
In plots of figures 2.14 and 2.15 it has been attached the 𝐵𝐸𝑅 and 𝑄 − 𝑓𝑎𝑐𝑡𝑜𝑟 vs 𝐷 𝑎𝑐𝑐 curves for the two
different values of 𝐵 and different values of 𝑅 𝑏. The reason of this further analysis on PSBT depends on the
pulse shape optimization that is main point for this modulation scheme in order to obtain best
performances.
We can see that at 10.7 Gbps, using a bandwidth of 0.24 ·Rb we have the worst performance (figures 2.14a
and 2.15a) while the other two systems present a similar behavior. Similar comment can be done for higher
bitrate at 42.65 Gbps (figures 2.14b and 2.15b).

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(a)
(b)
Figure 2.14a, 2.14b - BER vs Dacc curves of PSBT for different bandwidth of the transmitted filter and different bit-rates: (a) 10.7
Gbps and (b) 42.65 Gbps
(a) (b)
Figure 2.15a, 2.15b - Q-factor vs Dacc curves of PSBT for different bandwidth of the transmitted filter and different bit-rates: (a)
10.7 Gbps and (b) 42.65 Gbps

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2.2.2 - Optical link with noisy and dispersive channel: quantitative analysis
In this final section we are gathering all the numerical results we have obtained in the previous simulations
in order to compute the OSNR penalty due to dispersion: 𝑂𝑆𝑁𝑅 𝑝𝑒𝑛𝑎𝑙𝑡𝑦. The 𝑂𝑆𝑁𝑅𝑡,𝑑𝑖𝑠𝑝 that is the 𝑂𝑆𝑁𝑅
target when dispersion occurs has been obtained by adding to the target 𝑂𝑆𝑁𝑅𝑡 (obtained from
simulations in section 2.2.1) a margin 𝑂𝑆𝑁𝑅 𝑝𝑒𝑛𝑎𝑙𝑡𝑦 in order to reach the target BER fixing the accumulated
dispersion to the value that makes the 𝑄 − 𝑓𝑎𝑐𝑡𝑜𝑟 2 dB lower than its maximum.
Rb Modulation format
𝑸−𝟐𝒅𝑩
[dB]
𝑫 𝒂𝒄𝒄,−𝟐𝒅𝑩
[ps/nm]
𝑶𝑺𝑵𝑹 𝒕
[dB]
𝑶𝑺𝑵𝑹 𝒕,𝒅𝒊𝒔𝒑
[dB]
𝑶𝑺𝑵𝑹 𝒑𝒆𝒏𝒂𝒍𝒕𝒚
[dB]
10.7
Gbps
NRZ 8.63 689.35 10.7 11.92 1.15
RZ 9.25 496.23 9.2 10.46 1.26
DPSK 9.85 979.9 8.8 9.3 0.5
PSBT (0.24𝑅 𝑏) 10.06 3139.5 13.43 14.4 1.01
PSBT (0.25𝑅 𝑏) 8.87 3112.8 13.63 14.62 0.99
PSBT (0.26𝑅 𝑏) 9.12 3068.5 13.8 14.9 1.11
42.65
Gbps
NRZ 8.87 60.45 10.22 11.43 1.21
RZ 8.98 57.59 10.1 11.34 1.24
DPSK 8.44 103.2 6.58 8.21 1.63
PSBT (0.24𝑅 𝑏) 9.18 175.2 9.79 10.84 1.05
PSBT (0.25𝑅 𝑏) 9.33 173.17 9.77 10.75 0.98
PSBT (0.26𝑅 𝑏) 9.29 173.65 9.74 10.86 1.12
Table 2.2 - All the most important parameters for different modulation schemes and different bit rates
Regarding OSNR penalties, at 10 Gbps the lowest are DPSK and PSBT with 𝐵 = 0.25𝑅 𝑏 probably because of
their similar spectral occupancy. DPSK, in particular, has just 0.5 dB of penalty, which makes it a good
choice in some environments.
For what concerns the higher bitrate 42.65 Gbps, the increments of target OSNR in presence of dispersion
have the same trend of the one without dispersion. In any case the best case is represented by the use of
PSBT with a filter bandwidth 𝐵 = 0.25𝑅 𝑏 with a penalty of only 0.99 dB at 10.7 Gbps and of 0.98 dB at
42.65 Gbps.
The worse performance is obtained with RZ modulation with a penalty of 1.26 dB at 10.7 Gbps and of 1.24
dB at 42.65 Gbps.