This chapter presents a simulation study on the performance of the impairments monitoring technique based on overmodulation introduced in the previous chapter. In particular, we consider here the case where the line signal is modulated with NRZ-OOK (non-return-to-zero on-off keying) modulation format. This study considers only linear impairments caused by ASE noise.

First, we introduced the main characteristics of the VPI Photonics simulation® software used in this work. Then, we show the simulation trade-off studies to determine the optimum values for the different design parameters that affect the performance and effectiveness of the proposed monitoring technique: (a) bit-rate of the supervisory signal; (b) modulation depth and extinction ratio of the supervisory signal; (c) overhead of the line coding needed for the line signal. Finally, we conclude this chapter with a summary of the major findings obtained through this simulation study.

2.1 VPItransmissionMaker™Optical Systems

VPItransmissionMaker™Optical Systems accelerates the design of new photonic systems and sub-systems for short-range, access, metro and long haul optical transmission systems.

The combination of a powerful graphical interface, a sophisticated and robust simulation scheduler and realistic simulation models together with flexible optical signal representations at different degrees of abstraction enables accurate and efficient modeling of any transmission system including bidirectional links, ring and mesh networks.

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Sampled signal modeling supports detailed simulation of the optical field in the time domain enabling for instance bit-error-rate estimation and eye-diagram analysis. Time-averaged signal representation facilitates efficient modeling of complex systems without the need to run long-lasting simulations as they allow the tracking, visualization and analysis of signal properties along a link. This sophisticated virtual test-bed environment facilitates the definition of components requirements and risks evaluation in component choice by considering the details of systems design. An unrivaled range of photonic and electronic modules (700+) and design templates (500+) are provided, with regular updates on the VPIphotonics Forum. Interactive Simulation, Macros and Design-Assistants, simulation scripting, data import with automatic file format conversion and cosimulation using standard programming languages streamline and capture design processes. Technical marketing is supported, by providing a dynamic environment to design, evaluate, demonstrate and compare the technical and cost superiority of solutions. This award-winning solution is used by forward-looking groups in more than 100 private companies including service providers, system integrators and equipment manufacturers as well as in 140 public R&D institutions & universities.

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Figure 2.1 Powerful visualization and analysis tools

List of common functionalities available in the

VPItransmissionMaker™/VPIcomponentMaker™ design environment:

• Optical networking simulation

o Evaluate crosstalk and dynamics in reconfigurable DWDM networks due to

power transients and test countermeasures

o Validate network design scenarios using link performance analysis functions and the VPIdesignRules application

o Provide stress-test environment for impairment-aware routing mechanisms • Single and multicarrier modulation (OFDM, Nyquist WDM)

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o Design ultra long-haul amplified systems and submarine systems

o Design high-capacity WDM systems based on Raman, hybrid amplification

or digital-coherent technology

o Quantify fiber-induced signal degradations resulting from CD, Kerr, PMD,

SRS, SBS and reflections

o Dimension FTTx/PON systems including BPON, G(E)PON, WDM-PON, coherent PON and RSOA-based bi-directional PON

o Design analog and digital CATV, radio-over-fiber, and microwave

photonic links

o Equalize DMD-induced distortions in multimode systems o Explore Free-Space Optics (FSO) communication systems

o Select optical amplification scheme (EDFA, Raman, SOA, OPA) in

CWDM /DWDM systems

• Arbitrary constellations in 2 and 4 dimensions including mQAM, CmQAM and 4D set-partitioning formats

• Advanced visualization and analysis tools (BER, EVM, eye-diagram, spectrum, Poincare, ...)

o Design high-performance & cost-effective transceivers for 400G and

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o Develop effective DSP methods for digital adaptive electronic equalization and pre-compensation

o Identify critical design parameters including laser chirp, RIN, amplifier

gain-tilt and noise, path loss, and filtering

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o Define requirements for analog or digital electronics devices (TIA, RF

amplifier, clock, ADC, DAC)

• Quick WDM system design evaluation using link performance analysis functions and engineering design rules

• Realistic physical and behavioral (data-sheet) component model models for various E/O converters such as DML, EML and MZM

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• Analysis of radio over fiber (RoF) and microwave transmissions (SNR, CNR, IMD3, IP3, …)

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2.2 Simulation Setup

The following figure shows the VPI Scheme that we used for the simulations of the impairment monitoring technique.

Figure 2.2 Impairments Monitoring Block Scheme

The next sections show and describe the most important components of the block scheme shown in Figure 2.2.

2.2.1 Continuous Wave Laser:

The LaserCW module models a DFB laser producing a Continuous Wave (CW) optical signal. The module produces a time dependent field

E t

( )

describing the radiation of a CW laser with the specified power, frequency, line width, and polarization. The field E t

( )

represented by a sampled band with bandwidth defined by module parameter Sample Rate and center frequency fc

(which is specified by parameter Emission Frequency). The signal has the power E t

( )

2

equal to parameter Average Power, and polarization specified by parameters Azimuth and Ellipticity. The line width of the generated signal E t

( )

is modeled using a Gaussian

Roberto Proietti 4/23/14 12:17 PM

Commenta [1]: Perche’ mostri il coherent

receiver quando questo schema e’ per il NRZ-‐OOK?

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white noise source with a variance of 2πΔf corresponding to the laser FWHM Line width Δf. The output is multiplied with a complex vector considering the State Of Polarization (SOP), to obtain the x and y polarization components. The baseband signal of the optical output cw-wave is therefore determined by

E t

( )

= P 1− k kejδ ⎛ ⎝ ⎜ ⎞_⎠⎟ ⋅exp j ω τ

( )

0 t

∫

dτ ⎛ ⎝⎜ ⎞ ⎠⎟ (2.1)

The SOP is given by the power splitting parameter k 0

(

≤ k ≤ 1

)

and an additional phase δ . The relations of kand δ with the Azimuth η and the Ellipticity ε are given by

tan 2

( )

η = 2 k 1

(

− k

)

cosδ 1− 2k

(2.2)

sin 2

( )

ε = 2 k 1− k

(

)

sinδ (2.3)

The parameter InitialPhase ϕ0 can be used to define the initial phase of the optical

carrier. The parameter RandomNumberSeed specifies an index of a lookup table for the generation of the laser phase noise. A value of zero produces a unique seed to start the noise generator. This assures that each noise field generated in the simulation is not correlated to all other noise fields, since a unique seed is used for each noise generation. In frequency domain, the average power spectral density of the output signal (2.1) is described by the Lorentzian lineshape:

P f

( )

= 2P πΔf 1+

(

f − fc

)

2 Δf 2

(

)

2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ (2.4)

Note that the laser spectrum on each specific run will depend on the values of the phase which are found using the random process as described above, i.e. the real spectrum will be different from that described by (2.2), but averaged over many iterations, the spectrum of laser emission will tend to that given by (2.2).

Roberto Proietti 4/23/14 12:18 PM

Commenta [2]: Metti questi parametric in

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2.2.2 Pseudo Random Binary Sequence Generator:

The module generates many types of pseudo random data sequences, for example PRBS and De Bruijn sequences of order N, alternate ones and zeros, predefined sequences, all ones, all zeros. A Pseudo Random Binary Sequence (PRBS) is usually required when modeling the information source in simulations of digital communication systems. The binary sequence can be generated with the use of a random number generator, or, alternatively, can be directly specified by the user or read from a specified file. The PRBS module produces a sequence of M bits M = TimeWindow⋅ BitRate with the numbers m and n of zero bits (spaces) preceding and succeeding the generated bit sequence of length M − m − n. The numbers m and n can be set by the user via parameters PreSpaces and PostSpaces, respectively. The sequence of generated bits may be saved to or read from a file. For the binary sequence generation, the following operation modes of the PRBS module can be selected, depending on the setting of the PRBS_Type parameter:

i. PRBS: The modified Wichman–Hill–Generator; ii. PRBS_N: The “classic” PRBS generator; iii. DB_KN: The k-ary De Bruijn generator;

iv. FixedMarkNumber; an exact number of marks l can be specified by the user; v. CodeWord: A user-specified codeword in the form of an int-array, (e.g.,

“1 0 1 1 0 0 0 1”) is used to define the output;

vi. ReadFromFile: the user data and the m leading and n trailing zero bits are read from a file. The filename is given by the parameter InputFilename. The file must be in ASCII-form.

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Figure 2.3.A Sequence of M bits contains m preceding and n succeding zero bits.

2.2.3 NRZ Coder:

The module generates for each input bit, an electrical Non Return to Zero coded signal (see Figure 2.4). A NRZ pulse has a single value over the entire bit length, i.e., the “1” is coded by a high level with non-zero amplitude and the “0” by a low level with zero amplitude. The number of samples per bit is given by the ratio of SampleRate/BitRate and has to be a power of two. The sample rate sets the bandwidth of the electrical signal to be (SampleRate)/2.

Figure 2.4 NRZ coded “1” and “0” bits

2.2.4 Rise Time Adjustment:

The module is a Gaussian filter that transforms, for example, rectangular electrical input pulses into smoother output pulses with a user-defined rise-time. Its effect is to band-limit the modulated optical signal, which is required to avoid numerical artifacts when resampling to higher sample rates. This module is used to generate pulses with a

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user-defined rise-time. An electrical rectangular NRZ/RZ pre-shaped input pulse with pulse duration T0for example is filtered by a linear time-invariant filter with a normalized

Gaussian shaped impulse response:

Where T denotes the _{1 e}-pulse duration. The output pulse y t

( )

I s given as convolution of h t

( )

with the rectangular input time function:

The 10% and 90% amplitude values of y t

( )

define the Rise Time Δt,

see Figure 2.5_{. Provided that the pulse duration T}₀ is long compared

with the filter time constant T , the rise-time is approximately

Δt ≈ 3T 4. For _T0≥ 1.5T the approximation error is less than 10%. In

the frequency domain, the filter is also Gaussian shaped. The_{1 e}

bandwidth Δfeis given by:

Δfe= 4

πT such that for all rise-times Δt ≤ 0.5T0the 1 e

-bandwidth is approximately Δfe ≈

3 πΔt.

2.2.5 Modulator Mach Zehnder:

This module represents a Mach-Zehnder modulator with a single RF drive port as shown in Figure 2.6. The behavior of such modulators depends on their design, and specifically the configuration of the electrodes with respect to the

y t

( )

=1 2 erfc 2 t

(

− T0

)

T − erfc 2t T ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ (2.6) h t

( )

= 2 πTe − 2t T( )2 _(2.5) Figure 2.5 Output pulses with a user-‐ defined rise-‐time Δt are generated by filtering input pulses with a Gaussian-‐shaped filter, in this case a rectangular pulse.

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Niobate crystal. With good design and manufacturing, the modulator will have a large extinction ratio, and a low chirp (dynamic change in frequency under modulation), although redder-leading-edge chirps can be desirable in systems as they lead to pulse compression in SMF at 1550 nm.

This model strikes a balance between including important effects and ease of use. It includes chirp and the extinction ratio degradation due to the drive voltage being less than required for full extinction, but does not give direct control over Vπ , or extinction ratio

degradation due to imbalances in the optical splitters and couplers. It is, however, easy to use because it can be driven directly from the output of NRZ or RZ Coder. This version includes a choice on specifying the chirp (the optical frequency shifts during the leading and trailing edges of a pulse). The Symmetry Factor method relates to the physical design of the modulator, whereas the Alpha Factor method relates to measured behavior (assuming certain measurement conditions). The optical power Poutat the output of MZM, depends on the phase difference ΔΦ between the two

modulator branches Pout= Pin

( )

t ⋅ d t

( )

= Pin

( )

t ⋅cos 2 _{ΔΦ t}

( )

⎡⎣ ⎤⎦ (2.7) With ΔΦ t

( )

= ΔΦ1

( )

t − ΔΦ2

( )

t 2 (2.8)

W_{here d t}

( )

_{is the power transfer function and ΔΦ}₁

( )

t _{, ΔΦ}₂

( )

t are the phase changes in each branch caused by the applied modulation signal data(t). The phase changes take place due to the electro-optical effect. Requiring a power extinction ratio of Figure 2.6 Schematic of Mach-‐Zehnder modulator

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fextinct= dmax dmin(see Figure 2.7) and assuming a “quadrature” operating point (the bias

phase shift of

ΔΦQP=π 4) , the dependence of the phase difference _ΔΦ

( )

t on the

electrical input data signal data(t) is given by: ΔΦ = π 2 1 2− ext data(t) − 1 2 ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (2.9) With ext= 1− 4 πarctan 1

(

fextinct

)

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The extinction ratio can be specified in dB units according to ε = 10log f

(

extinct

)

by

setting the parameter Extinction. Note that this extinction ratio is due to the modulator being under-driven by the RF input. The extinction ratio can also be degraded by imbalances in the optical splitter and optical coupler regions of the device, so that the two arms contribute different powers to the output signal, and so do not cancel perfectly when the device is driven to its off state. This intrinsic extinction ratio also gives rise to phase modulation and increased chirp. The ModulatorDiffMZ_DSM module includes the intrinsic extinction ratio. Unless correctly designed and accurately manufactured, MZ modulators will exhibit chirp. Because of the physics of a MZ modulator (compared with a semiconductor laser, for example), the chirp occurs on the power transients (turn-on and turn-off), and is called transient chirp.

The sense of the transient chirp (whether the frequency increases/decreases or decreases/increases during a turn-on/turn-off) depends on the imbalance of the drive-induced phase shifts in the two arms of the MZ. To understand how the input parameters relate to the chirp, we have to examine the physics of the device. The total phase change occurs at the modulator output if the individual phase changes of the modulator branches are not anti-symmetrical, i.e., if . ΔΘ t

( )

= ΔΦ⎡⎣ 1

( )

t + ΔΦ2

( )

t ⎤⎦ 2

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Figure 2.7 MZM power transfer function showing a degraded extinction ratio.

To characterize the chirp behavior of the MZM, the parameter SymmetryFactor k is used: k= ΔΦ2 ΔΦ1 for ΔΦ₂ ≤ ΔΦ₁ (2.11) k= ΔΦ1 ΔΦ2 for ΔΦ2 > ΔΦ1 (2.12)

From the above definitions, k may assume any value within −1,1⎡⎣ ⎤⎦. Some special cases explain the meaning of k:

i. k = 1, results in ideal intensity modulation, with zero chirp. Physically this means that the phase shifts induced by the drive signals in the two arms are of the opposite sense, but equal in magnitude.

ii. k = 0, results in intensity modulation with chirp. Physically, this case implies that one arm is being driven by the onput signal and the other not driven.

iii. k → 1, corresponds to ideal phase modulation, with zero intensity modulation.

Physically this means that both arms are being driven to give the same phase shift, in the same sense. Therefore, ΔΦ = 0, so the operation of the modulator

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at the quadrature point ΔΦ

(

bias=π 4

)

is impossible. For this reason, the value

k = +1 is excluded from the valid parameter range of SymmetryFactor.

Most modulator designs operate with k between -1.0 (chirp-less) and 1.0 (single-arm driven). The sense of the frequency chirp is determined by the sign of parameter ChirpSign σ: ChirpSign=σ= sgn ΔΦ1+ ΔΦ2 ΔΦ1− ΔΦ2 ⎛ ⎝⎜ ⎞ ⎠⎟ (2.13)

A positive ChirpSign gives a negative frequency excursion during turn-on of the modulator (during its leading edge). This normally leads to pulse compression in Single Mode Fiber at 1550 nm. Using Equations (2.7), (2.8) and (2.13), the electrical field of the output signal is

E_out

( )

t = E_in

( )

t ⋅ d t

( )

⋅ejσ1+k1−kΔΦ t( )

= Ein

( )

t ⋅ d t

( )

⋅e

jσΔΘ t( )

(2.14)

An arbitrary polarization state is allowed for the input optical signal. The output polarization is the same as the input one. The chirping behavior of modulators is often characterized by the “α-factor” defined as the ratio of phase and intensity changes of the modulator’s output signal. These measurements should be taken under small-signal conditions with the modulator biased at quadrature.

From Equations (2.7) and (2.14) it follows that for our model of MZM the α-factor is given by α≡ 2 dΔΘ dt 1 P_out dP_out dt (2.15)

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α ≡ −σ1+ k 1− k 1 tanΔΦbias (2.16)

Since the operating point is set to ΔΦbias=π 4 the expression above becomes

Alternatively, the SymmetryFactor and ChirpSign may be written as a function of the AlphaFactor:

k= α +σ

α −σ (2.18)

α = −1.0sign

( )

α (2.19)

It would appear that having two parameters, SymmetryFactor and ChirpSign to replace the one parameter AlphaFactor would allow two combinations of SymmetryFactor and ChirpSign to describe a single value of AlphaFactor. This is true, however, restricting the range of SymmetryFactor to between -1.0 and 1.0, means that there is a 1:1 mapping of all three parameters over all values of AlphaFactor except for AlphaFactor = 0.0. For AlphaFactor = 0.0 the ChirpSign is irrelevant.

2.3 Simulation Results

This section discusses the way to implement the above Impairments Monitoring Technique with emphasis on the more sensitive design parameters, such as the bit-rates of the Line and Supervisory Signals, and the value of the Extinction Ratio of the Mach-Zehnder modulator used for imposing the overmodulation on the line signal. We first consider, for the line signal, a PRBS order equal to 7 and we run a set of simulations to choose the optimum values for the bit-rate and the Extinction Ratio of the Supervisory signal, in order to guarantee a good correlation between the BER of the Line and

α = −σ 1+ k

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Supervisory monitor signal. Note that, as already mentioned in Chapter1, the main goal of this monitoring technique is to obtain a BER of the low-speed Supervisory Signal that is as close as possible to the BER of the high-speed Line Signal.

Using the optimum parameters obtained from the above study, we increased then the order of the PRBS used for the Line Signal in order to simulate a more realistic scenario.

2.3.1 Parameters settings for the simulation of the Impairments

Monitoring Technique Based on Overmodulation

The first thing to determine is what values to use for the ER and bit-rate of the

Supervisory Signal. Note that, while the Supervisory Signal bit-rate value does not affect the BER of the Line Signal, there are constraints on the maximum ER value in order to not cause significant penalty for the Line Signal. So, as first, we run a set of simulations to study the effect of the ER on the BER of the line-signal. After choosing the range of acceptable ER values, we vary then the bit-rate of the Supervisory Signal to determine the best correlation between the BER of the Line and Supervisory signals.

2.3.1.1 Extinction Ratio

The Extinction Ratio is defined as the ratio of two optical power levels of a digital signal generated by an optical source. The Extinction Ratio (re) may be expressed as a

fraction, in dB, or as a percentage. It may be given by re=

P1

P0

, where P1 is the optical

power level generated when the light source is on, and P0 is the power level generated

when the light source is off. The output of the Mach-Zehnder Modulator, after the Overmodulation is as shown in Figure 2.9(a) and Figure 2.9(b), which represent a 10 Gb/s NRZ-OOK Line Signal for ER=1.5 dB and 0.4 dB respectively. The higher the ER the higher will be the BER of the Line Signal due to the high closure caused by the overmodulation. This penalty can be quantified from the simulation results shown in

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Figure 2.8 BER curve of Line Signal when it is simulated without Overmodulation (red line) and with Overmodulation for several values of ER.

Assuming that we can accept a penalty up to 2dB, we can conclude that the maximum acceptable ER is 1.0 dB.

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b)

Figure 2.9 a)Modulated Signal With E.R.=1.5 dB .b) Modulated Signal with E.R.=0.4 dB.

The next parameter to determine is the bit-rate of the Supervisory Signal. In our VPI simulations, we set the bit-rate of the Line Signal equal to 10 Gb/s while the bit-rate of the Supervisory Signal varies from 20 Mb / s to 240Mb / s . Also the value of the Extinction Ratio is variable in the range_{[0.4,0.8,1.2,1.6]dB}.

By using the block “Set OSNR” (Figure 2.10), already implemented in VPI, it was possible to vary the Optical Signal-to-Noise Ratio. This module adds ASE noise (depolarized noise), emulated as a Gaussian-distributed optical white noise, to the input signal in order to reach the specified OSNR and optionally applies a linear polarization filter at the output. The input signal is assumed to be noise-free and consist of one or several WDM channels; in this second case, all channels are assumed to have identical power. The OSNR expressed per channel and in dB is defined as follows:

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(2.20)

b)

Figure 2.10.VPI Set OSNR module.

Where is the channel power (total power divided by the number of WDM channels N), is the bandwidth for ASE measurement, and is the power spectral density of the added ASE noise in both polarizations.

We varied the OSNR in a range from 5 dB to 20 dB; the following figures show the simulation results for the BER of the Line and Supervisory Signals as function of the OSNR, for different ER values. Each figure refers to a different bit-rate of the Supevisory Signal (i.e. 20 Mb/s, 40 Mb/s, 60 Mb/s … 180 Mb/s and 200 Mb/s).

OSNR = 10 log10 Pch BASE⋅WASE " # $ % & ' Pch BASE WASE

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a)

b)

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c)

Figure 2.11 a) BER of the Line Signal (@ 10Gb / s) and BER of the Supervisory Signal as function of the OSNR, for different values of the Supervisory Signal bit rate (@ 20Mb / s, @ 40Mb / s, @ 60Mb / s, 80Mb / s) and Extinction Ratio (0.4, 0.8, 1.2, 1.6); b) BER of the Line Signal (@ 10Gb / s) and BER of the Supervisory Signal as function of the OSNR for different values of the Supervisory Signal bit rate (@ 100Mb/s, @ 120Mb/s, @ 140Mb/s, 160Mb/s) and Extinction Ratio (0.4, 0.8, 1.2, 1.6); c) BER of the Line Signal (@ 10Gb / s) and BER of the Supervisory Signal as function of the OSNR, for different values of the Supervisory Signal bit rate (@ 180Mb/s, @ 200Mb/s, @ 220Mb/s, 240Mb/s) and Extinction Ratio (0.4, 0.8, 1.2, 1.6);

From this first set of simulations, it is easy to see that for a Line Signal at 10 Gb/s and Supervisory Signal at 20 Mb/s, a goof value of the Extinction Ratio of the Mach-Zehnder Modulator is equal to 0.4 dB. If we increase the bit-rate of the Supervisory Signal it is intuitive that the extinction ratio parameter needs to be increased in order to keep the two BER curves close to each other. Since, as explained above, the lower the ER the better the BER of the Line signal, we decided to set the ER=0.4 and use 20 Mb/s as bit-rate for the Supervisory Signal.

In two successive sets of simulations, carried out exactly as the first set, the bit rate of the Line Signal was set equal 20 Gb/s and then 40 Gb/s; as expected, we found the following relationship between the bit-rate of the Line Signal and the bit rate of the Supervisory Signal when the Extinction Ratio is kept constant: “At constant extinction ratio of Mach-Zehnder Modulator, if the bit rate of the Line Signal is doubled, it is

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necessary to double also the bit rate of the Supervisory Signal in order the keep the same relation between the two BER curves.”

We can therefore conclude that the optimal choice for the parameters necessary to implement the monitoring technique, in case of OOK Line Signal, are:

Table 2.1 Optimum Choice of the design parameters.

The figures below show the simulation results when the bit rate of Line Signal is equal to 20 Gb/s and 40 Gb/s.

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a)

b)

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c)

a)

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b)

c)

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2.3.1.2 Changing the PRBS order

For the initial study carried out above, we used a PRBS order = 7 for the Line Signal. However, to emulate a real communication system and account for any pattern-dependent effect, it is required to use higher PRBS order values (the designed system should work up to a PRBS order = 31). By increasing the PRBS order to 8, 9 etc… we soon realized (see Figure 2.15) that the above technique, designed as above, cannot work. In fact we have, until now, considered the Line Signal with a PRBS of order 7, but this is a situation very far from reality: this sequence is characterized by a very short word length, and it is therefore inevitable that in the simulation, the periodicity of the Line Signal creates an ideal and particular situation where there is not spectrum overlap between the two signals and therefore no energy from the Line Signal falls within the Supervisory Signal RX bandwidth. The real signals, however, are obviously not periodic. Therefore, it becomes essential to test our technique for longer PRBS sequences that represent better a real scenario.

2.3.1.2.1 Overview of Pseudo Random Bit Sequence

A Binary Sequence is a sequence a0, a1,..., aN−1 of N bits, i.e. aj∍ 0,1

{ }

for

j = 0,1,..., N −1. A Binary Sequence consists of m = aj

j

∑

ones and N − m zeros.

A Binary Sequence is a Pseudo-Random Binary Sequence (PRBS) if its autocorrelation

function C v

_{( )}

= ajaj+v j=0 N−1

∑

has only two values: C v

_{( )}

= m, if v ≡ 0 mod N

(

)

mc, otherwise " # $ , where c = m −1

N −1 is called the duty cycle of the PRBS, similar to the duty cycle of a continuous

time signal. A PRBS is “pseudorandom”, because, although it is in fact deterministic, it seems to be random in a sense that the value of an aj element is independent of the

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stretched to infinity by repeating it after N elements, this in contrast to most random sequences, such as sequences generated by radioactive decay or by white noise, that are “infinite” by nature. The PRBS is more general than the maximum length sequence, which is a special Pseudo-Random Binary Sequence of N bits generated as the output of a linear shift register. A maximum length sequence always has a 1 2 duty cycle and its number of elements N = 2k

−1 . PRBS's are used in telecommunication, encryption, simulation, correlation technique and time-of-flight spectroscopy. Pseudorandom binary sequences can be generated using linear feedback shift registers. In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. However, an LFSR with a well-chosen feedback function can produce a sequence of bits which appears random and which has a very long cycle. Both hardware and software implementations of LFSRs are common. The mathematics of a cyclic redundancy check, used to provide a quick check against transmission errors, are closely related to those of an LFSR. The bit positions that affect the next state are called the taps. In the following diagram the taps are [16,14,13,11]. The rightmost bit of the LFSR is called the output bit. The taps are XOR'd sequentially with the output bit and then fed back into the leftmost bit. The sequence of bits in the rightmost position is called the output stream; the bits in the LFSR state which influence the input are called taps (white in the diagram). A maximum-length LFSR produces an

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m-sequence (i.e. it cycles through all possible 2n − 1 states within the shift register except the state where all bits are zero), unless it contains all zeros, in which case it will never change. As an alternative to the XOR based feedback in an LFSR, one can also use XNOR. This function is an affine map, not strictly a linear map, but it results in an equivalent polynomial counter whose state of this counter is the complement of the state of an LFSR. A state with all ones is illegal when using an XNOR feedback, in the same way as a state with all zeroes is illegal when using XOR. This state is considered illegal because the counter would remain "locked-up" in this state. The sequence of numbers generated by an LFSR or its XNOR counterpart can be considered a binary numeral system just as valid as Gray code or the natural binary code. The arrangement of taps for feedback in an LFSR can be expressed in finite field arithmetic as a polynomial mod 2. This means that the coefficients of the polynomial must be 1's or 0's. This is called the feedback polynomial or reciprocal characteristic polynomial. For example, if the taps are at the 16th, 14th, 13th and 11th bits (as shown), the feedback polynomial is x16+ x14+ x13+ x11+1. The 'one' in the polynomial does not correspond to a tap — it corresponds to the input to the first bit (i.e. x0_{, which is equivalent to 1). The powers of}

the terms represent the tapped bits, counting from the left. The first and last bits are always connected as an input and output tap respectively.

The LFSR is maximal-length if and only if the corresponding feedback polynomial is primitive. This means that the following conditions are necessary (but not sufficient):

• The number of taps should be even.

• The set of taps taken all together, not pairwise (i.e. as pairs of elements) must be relatively prime. In other words, there must be no divisor other than 1 common to all taps.

Output-stream properties are:

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of five runs of lengths 1,2,1,1,2, in order. In one period of a maximal LFSR, 2n −1

runs occur (for example, a six bit LFSR will have 32 runs). Exactly half of these runs will be one bit long, a quarter will be two bits long, up to a single run of zeroes n − 1 bits long, and a single run of ones n bits long. This distribution almost equals the statistical expectation value for a truly random sequence. However, the probability of finding exactly this distribution in a sample of a truly random sequence is rather low

ii. LFSR output streams are deterministic. If you know the present state as well as the positions of the XOR gates in the LFSR, you can predict the next state. This is not possible with truly random events. With minimal-length LFSRs, it is much easier to compute the next state, as there are only an easily limited number of them for each length.

iii. The output stream is reversible; an LFSR with mirrored taps will cycle through the output sequence in reverse order.

In the next set of simulations, we consider the Line Signal bit-rate equal to 10 Gb/s and the Supervisory Signal at 20 Mb/s, Note that in this simulation the Line Signal and the supervisory Signal are generated in the same scheme with two different transmitter and modulated by a Mach-Zehnder Modulator with an ER = 0.4 dB. From these simulations we conclude that, for PRBS orders ≥ 9, the system does not work. Figure 2.15 shows the simulation results. With N = 9, the BER of the Line Signal has already a clear error floor at 10-2 _{as consequence of the spectrum overlap and crosstalk caused by the Line Signal}

on the Supervisory Signal. Therefore, the proposed system, as is, can work only for PRBS ≤ 8, which means that the system cannot work in a real scenario, for the motivations explained above.

For PRBS of order N = 7 , N = 8 or N = 9 , the word length of the sequence is very short, respectively equal to L7= 2 7 −1 = 127bits , L8= 2 8 −1= 255bitsand L9= 2 9_{−1= 511 bits.}

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a)

b)

Figure 2.15 a) BER curves of the Supervisory Signal (@20 Mb/s) and of the Line Signal (@10Gb/s) when it is simulated using different PRBS of order N = 7, N = 8, N = 9, respectively. b) Eye Diagram of Supervisory Signal when the Line Signal is simulated using PRBS order N = 9.

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Considering that the Line Signal bit time, TbLS, is equal to the inverse of the bit-rate of

the Line Signal RbLS, the signals generated with the PRBS orders above have a spectrum

composed by lines with a spacing equal to (Figure 2.16):

TbLS= 1 R_b LS = 100ρs ⇒ f7= 1 L₇⋅ TbLS = 1 27 −1

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⋅100 ×10−12 = 78, 750MHz TbLS= 1 RbLS = 100ρs ⇒ f7= 1 L8⋅ TbLS = 1 28 −1

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⋅100 ×10−12 = 39, 375MHz TbLS= 1 RbLS = 100ρs ⇒ f9= 1 L9⋅ TbLS = 1 29 −1

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⋅100 ×10−12 = 19, 687MHz a)

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Figure 2.16 a)Electrical Spectrum of Line Signal at 10Gb/s generated by PRBS of Order 7; b)Electrical Spectrum of Line Signal at 10Gb/s generated by PRBS of Order 8; c)Electrical Spectrum of Line Signal at 10Gb/s generated by PRBS of Order 9;

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Looking at the spectrum above it is now clear why the maximum PRBS order that we can use is only N = 8: increasing the order of the PRBS, the frequency components of the Line Signal become important at low frequencies, like in a real signal, producing interference in the Supervisory Signal receiver and causing the closure of the Supervisory Signal eye diagram, and strong BER degradation. To overcome this problem, we decided to study and test the use of line coding techniques for spectral shaping like 8B/10B, 9B/10B, etc…, as explained in the next section.

2.3.2 Line Coding for spectral shaping

In this section, we investigate the use of line coding to deplete the low-frequency spectral contents of the signal and thus to alleviate the degradation of the Supervisory Signal; for that reason we examine various line codes (8B/10B, 9B/10B, 5B/6B and 7B/8B).

2.3.2.1 8B/10B, 9B/10B, 5B/6B, and 7B/8B

Directly modulated laser (DML)-based optical transmitters offer many advantages over external modulator-based counterparts, including small footprint, cost-effectiveness, high output power, and low driving voltage. However, directly intensity-modulated lasers have two major drawbacks: small extinction ratio and large frequency chirp. The main problem is that DMLs exhibit highly non-uniform response at low frequencies, which in turn causes severe pattern dependency. Different approaches have been reported to combat this problem such as pre-equalization of the laser driving signal and the use of multi-electrode laser diodes. Nevertheless, these methods require either a complicated implementation or replacement of the conventional lasers with those having modified structures. Recently, Baroni et al. have proposed the use of 8B/10B line coding to deplete the low-frequency spectral content of the signal; however, 8B/10B coding has a large overhead of 25%, which requires 25% larger bandwidth for the transmission devices (e.g., drivers, DML, receiver).

Roberto Proietti 5/1/14 6:51 AM

Commenta [3]: Recently? When? La

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The 8B/10B, 9B/10B, 5B/6B and 7B/8B codes are based on mapping blocks of data into predefined code words that maintain the run length and DC-balance constraints. For example, 8B/10B code translates each source byte into a predefined 10-bit code word with a maximum run length of 5 and a disparity of either 0 or ± 2 in each 10-bit code word. The run length is defined as the number of identical contiguous ‘1’s or ‘0’s which appear in the signal stream and the disparity is the difference between the number of 1’s and 0’s in the code word. Since the disparity is bounded, the 8B/10B code is DC-balanced, i.e., provides a low DC content. Similarly, 9B/10B, 5B/6B and 7B/8B codes map 9-bit, 5-bit and 7-bit blocks into predefined 10-bit, 6-bit and 8-bit code words, respectively. Table 2 summarizes the basic characteristics of the line codes.

Table 2.2. Line-‐Codes Properties 2.3.2.1.1 The 8B/10B Code

Albert X. Widmer and Peter A. Franaszek of IBM Corporation proposed the 8B/10B Code in 1983. The code defines the mapping from an 8-bit byte (256 unique data words) and an additional 12 special (or K) characters into a 10-bit symbol, hence the name 8B/10B encoding. It has been widely used in high speed serial communication standards that need a run-length limited, charge balanced data stream for reliable data transmission and clock recovery. Because of its many feature, the code has been used in the physical layer (PHY) of a number of current and emerging standards, including Fiber Channel, Gigabit Ethernet, and Rapid I/O, to name a few.

Understanding them clearly is crucial to a successful implementation of the encoder. The most important terminology to understand for this assignment is Disparity. The

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Disparity of any block of data is defined as the difference between the number of ones and zeros in the block. Positive and negative refer to an excess of 1s over 0s, or 0s over 1s, respectively. Each encoded symbol can be considered to be a block. The code scheme guarantees that an encoded symbol's disparity is always either 0 (five ones, five zeros), +2 (six ones four zeros) or -2 (four ones, six zeros). Some byte inputs will have more that one potential symbol encoding with the encoded symbol pattern determined by the "Running Disparity". Running Disparity is simply a record of Disparity for the aggregate of all the previously encoded symbols. For packet-based networking applications, the Running Disparity is typically tracked from the start of a packet. The code scheme stipulates that the running disparity at the end of any symbol (block) is always +1 or -1. To ensure that this rule is maintained, the Encoder will track the current Running Disparity. If the currently encoded byte produces a symbol of Zero Disparity, the Running Disparity remains unchanged. When the input byte produces a Nonzero Disparity symbol, the Encoder will encode the data such that the Running Disparity is swapped, for example, [+1 + (-2) = -1] or [-1 +(+2) = +1]. See Table 3 for an example of the two possible encoded symbol patterns for the D31.1 data symbol.

Table 2.3.Example Encoding of D31.1 for both running disparity (RD) cases

The code scheme actually partitions the input byte into 5-bit and 3-bit sub-blocks, which in turn are encoded into 6- and 4-bit blocks respectively. The original nomenclature defines the symbols in terms of these sub-blocks. The five input bits are defined as A, B,

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C, D and E (A is Least Significant Bit) and the 3-bit block is F, G and H (F is LSB). A prefix of D or K is used to distinguish between data and special characters respectively. For example, D31.1 is a data symbol with all ones on the 5-bit block (11111) and a single one as the LSB of the 3-bit block (100) (see Table 3). Note that the 5-bit sub-block precedes the 3-bit sub-sub-block and the ordering (LSB to MSB) is ABCDE_FGH. The encoded sub-blocks are described with lowercase letters a, b, c, d, e, i (i is LSB) and f, g, h, j (j is LSB) respectively, and the ordering is (LSB to MSB) jhgf_iedcba. See Appendix A for the mapping between input bytes and output bits.

The encoder assumes a negative RD- (-1) at start up. When a 8-bit data is encoding, the encoder will use the RD- column for encoding. If the 10-bit data been encoded is disparity neutral, the Running Disparity will not be changed and the RD- column will still be used. Otherwise, the Running Disparity will be changed and the RD+ column will be used instead. Similarly, if the current Running Disparity is positive (RD+) and a disparity neutral 10-bit data is encoded, the Running Disparity will still be RD+. Otherwise, it will be changed from RD+ to RD- and the RD- column will be used again.

At this point we elaborated a Matlab script for the implementation of an 8B/10B Encoder to apply the 8B/10B coding to a PRBS sequence of order N = 17. The coded sequence will be then used for the Line Signal. The simulation results, using the encoded 8B10B sequence, setting the Line Signal bit-rate and the Supervisory Signal bit-rate to the usual value of 10 Gb/s and 20 Mb/s respectively, and the Mach-Zehnder Modulator Extinction Ratio at 0.4, are shown in Figure 2.17.

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Figure 2.17 BER curve of Line Signal (@10Gb/s) without Overmodulation and BER curves of the Supervisory Signal (@20 Mb/s) when the Line Signal is modulated using PRBS’s of order N=7 (blue line), N=8 (green line), N=9 (light blue line) and an encoded PRBS with the 8B/10B Code (purple line).

The monitoring technique exploiting 8B/10B coding works now, no matter which PRBS order is used for the line signal. This is because the 8B/10B Code carves the Line Signal at the low frequencies, strongly reducing the in-band crosstalk caused by the Line Signal at the Supervisory Signal receiver. We can clearly see this by observing the optical spectrum of the Line Signal when using 8B/10B encoded sequence (see Figure 2.18) and the Supervisory Signal eye diagram in Figure 2.19.

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Figure 2.18 Optical Spectrum of Line Signal simulated with an 8B/10B encoded PRBS.

Figure 2.19 Eye Diagram of Supervisory Signal when the Line Signal is simulated using an encoded PRBS with the 8B/10B Code.

2.3.2.1.2 The 9B/10B Code

Prior art in the Ethernet technology has shown that 8bit-10bit (8B/10B) coding has advantages over scrambling, in that the code output is DC balanced over a very short time horizon, and a maximum run length of 5 bits. This code was originally defined to enable the use of very low cost transceivers for point-to-point applications. However, it has proven even more useful in EPON, because the DC balance and short run length makes burst mode reception of 8b10b code much easier than scrambled code. On the other hand, 8B/10B code does come at the price of a 25% overhead in bandwidth. The common application of the code takes a 1.00 Gb/s user data-stream, and transforms it into a 1.25 Gb/s coded stream. In data communications, this overhead is acceptable; however, in telecom networks it is bordering on being excessive. Additionally, the DC-balance and run length properties of 8B/10B code seem to be overkill for practical optics today. For these reasons, there is good cause to seek a line code that strikes a middle ground between 8B/10B code and pure scrambled code, while maintaining as much

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compatibility to existing protocol and physical layers as possible.

The goal is to define a block code that takes 9 bits of payload data and encodes it into a 10 bits transmission pattern. The code can be generated as follows:

i. Considering all the combinations of 10b patterns, and grouping the patterns by the number of 1’s in each pattern, we find the simple binomial distribution of bit patterns:

Table 2.4. 9B/10B Code Properties

Of the possible 1024 bit patterns, we choose to discard those with excessive disparity (greater than 2 bits disparity in absolute value.) This leaves us with 252 balanced code-points, and a number of slightly imbalanced code-points.

ii. To address the imbalance present in the code-points of +/-1 and +/-2 bits, we use the principle of running disparity control. The transmitter keeps track of the running disparity (the sum of all prior code-points disparity). If the transmitter has a positive running disparity, then it will only transmit a code-point that has zero or negative disparity. If the transmitter has a negative running disparity, then it will only transmit a code-point that has a zero or positive disparity. In this way, the running disparity will be bounded, and tend towards zero always. There are 252 code-points that are balanced, 210 code-point pairs with disparity of 1, and 120 code-point pairs with disparity 2. Therefore, the total number of code-points is 582, which is more than needed to encode 9 bits of arbitrary user data.

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iii. The question then is how to choose the 70 extra code-points that we do not need, such that the maximum run length is minimized. We find that this is possible by considering the beginning and ending run lengths of each code. For example, the code-point 0010111111 has an ending run length of 6 and a beginning run length of 2. If the 582 code-points are analyzed in this way, we find the distribution of ending and beginning run lengths are as follows:

Table 2.5. 9B/10B Code Run Length

Knowing that we have 70 extra codes, we can start by dropping all the codes that have beginning and trailing runs of 5 or more. This amounts to 32 code-points eliminated, because actually there are two code-points that fall into both lists: 0000011111 and 1111100000. So, this measure leaves us with 550 code-points, and the maximum run length is 8, since a code-point that ends with a run of 4 and be followed by a code that begins with a run length of 4. We cannot drop all the beginning and ending runs of 4, because that would cost too many code-points. Therefore, we can choose to remove either the ending runs of 4, or the beginning runs of 4, but not both. The simple count above suggests that 31 code-points would be used. However, it so happens that exactly one of these 31 code-points (0000001111) was already counted when we eliminated the run of 6 code-points. So, 30 code-points are consumed, and we arrive at a set of 520 code-points. That is, 582 – 32 – 30 = 520. The 520 code-points is the largest set that guarantees that the maximum run length is 7. The value of 7 happens also to match the

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largest run that can occur inside a single code-point (since the longest internal run of 8 is not a legal code-point, since it has a disparity of +/-3). Therefore, this set of codes is optimized in a sense. However, we may select 8 additional code-points to eliminate to reach a set of 512. We can do this by considering the running disparity inside of each code-point. The construction of the basic code of 582 code-points guarantees that after each code-point the disparity will be -2, -1, 0, 1, or 2. However, inside of the code-point there can be excursions outside of this range. Considering the set of 520 code-points, it so happens that there are exactly 8 code-points that have the maximum running disparity excursion of 4. These are all balanced codes that have a beginning run of 4 bits. Since they are balanced codes, they can be used even when the running disparity coming into that code-point is the worst case of -2 or 2, and then the beginning run of 4 can take the disparity that much further. By eliminating these 8 codes, we arrive at our code that maps exactly 9 bits of user data into 10 bits on the line, and this code has a maximum run length of 7 and a maximum disparity excursion of 3.5.

Therefore we implement a 9B/10B Encoder based on the procedure described above.

The simulation results, using the encoded 9B/10B Sequence, setting the Line Signal bit rate and the Supervisory Signal bit rate to the usual value of 10 Gb/s and 20 Mb/s respectively, and the Mach-Zehnder Modulator Extinction Ratio at 0.4, are shown in the following Figure 2.20. The Figure shows a comparison between the BER of the Line Signal (red line) and the BER of Supervisory Signal when the Line Signal is simulated using the 9B10B coded Sequence (light blue line) and using PRBS of order N = 7 (blue line), N=8 (green line) and N=9 (turquoise line). It is clear that the 8B/10B Code attenuates the low frequencies components of the Line Signal a little bit more than the 9B/10B Code: the difference between these codes are not enough to require a changing of the parameters obtained in the 8B/10B code case. For that reason, we can continue to use a Supervisory Signal equal to 20 Mb/s and a value of Mach-Zehnder Modulator Extinction

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Ratio equal to 0.4, furthermore we obtain an improvement in terms of spectral efficiency. In fact as mentioned above the 9B/10B has an overhead a little bit more of the 11% while the 8B/10B has an overhead equal to 25% exactly.

Figure 2.20 BER curve of Line Signal (@10Gb/s) without Overmodulation and BER curves of the Supervisory Signal (@20 Mb/s) when the Line Signal is modulated using PRBS’s of order N=7 (blue line), N=8 (green line), N=9 (light blue line) and an encoded PRBS with the 9B/10B Code (purple line).

The Figure 2.22 and Figure 2.221 show the optical spectrum of the 9B/10B coded Line Signal

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Figure 2.21 Optical Spectrum of Line Signal simulated with a 9B/10B encoded PRBS.

Figure 2.22 Eye Diagram of Supervisory Signal when the Line Signal is simulated using an encoded PRBS with the 9B/10B Code.

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2.4 Conclusions

From the results discussed so far, we can conclude that the monitoring technique, in the case of a Line Signals modulated with OOK format, can work only if a proper line coding is applied to the data modulating the Line Signal. Our simulation results show that the 8B/10B coding guarantees good performance, allowing to obtain a BER of the Supervisory Signal which well represents the BER of the Line Signal. Unfortunately, 8B/10B introduces a high overhead (25%), which is not a desired feature since it decreases the effective number of bits that can be transmitted over a certain bandwidth. For this reason we implemented also the 9B/10B coding, which, as explained above, it requires an overhead of 11.1%, less than half compared to 8B/10B case. The figure below shows experimental data for the electrical spectrum of the Line Signal binary sequence in the case of no coding, 8B/10B coding and 9B/10B coding. As we can see, both coding techniques strongly reduce the low frequency components of the Line Signal. Note that, in the range 0-30 MHz, the results obtained with the two codes are almost the same (as also shown in ). So, we can expect, as confirmed by the simulation results below (Figure 2.223), that the optimum parameters of ER and bit-rate for the Supervisory Signal (ER=0.4 dB and bit-rate= 20 Mb/s) do not change.

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Figure 2.23 Line Signal BER Vs. Supervisory Signal BER for 8B/10B coding.

Table of Contents

Chapter 2

2 Impairments Monitoring Technique for NRZ-­‐OOK Signals

2.1 VPItransmissionMaker™Optical Systems

2.2 Simulation Setup

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2.2.2 Pseudo Random Binary Sequence Generator:

2.2.3 NRZ Coder:

2.2.4 Rise Time Adjustment:

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2.2.5 Modulator Mach Zehnder:

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2.3 Simulation Results

2.3.1 Parameters settings for the simulation of the Impairments

Monitoring Technique Based on Overmodulation

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2 Impairments Monitoring Technique for NRZ-‐OOK Signals

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