A Master's Thesis KHALID AABOUCH AZOUGARH MASTER IN ...

Strategies for Efficient Fibre Wireless Networks (FiWiN)

A Master's Thesis

Submitted to the Faculty of the

Escola Tècnica d'Enginyeria de Telecomunicació de

Barcelona

Universitat Politècnica de Catalunya

by

KHALID AABOUCH AZOUGARH

In partial fulfilment

of the requirements for the degree of

MASTER IN TELECOMMUNICATIONS ENGINEERING

Advisor: María Concepción Santos Blanco

Barcelona, January 2021

Abstract

In recent years a growing number of users require wireless communication of access network. This demand requires the incorporation of radio over fibre system, this allows the connection of many users with optical fibre link. Current systems have certain limitations due to fibre dispersion and low efficiency of optical power.

The aim of this thesis is a theoretical study to maximise the number of users from access network through a radio over fiber system. Different configurations of transmitting process using Mach-Zehnder Modulator (MZM) are presented to provide an efficient and configurable radio over fiber system.

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Acknowledgements

I would like to thank my supervisor Maria Concepcion Santos Blanco for giving me the opportunity of this thesis. for her confidence, great patience and helpful discussions. Thanks for the support during this time.

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Revision history and approval record

Revision Date Purpose

0 21/12/2020 Document creation

1 07/01/2021 Document revision



Written by: Reviewed and approved by:

Date 21/12/2021 Date 01/02/2021

Name Khalid Aabouch Azougarh Name María Concepción Santos Blanco

Position Project Author Position Project Supervisor

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Table of contents

Abstract ............................................................................................................................ 0

Acknowledgements .......................................................................................................... 1

Revision history and approval record ................................................................................ 2

Table of contents .............................................................................................................. 3

1. INTRODUCTION ....................................................................................................... 5

1.1. Access network .................................................................................................. 5

1.2. State of the art .................................................................................................... 6

1.3. Project objectives ............................................................................................... 7

1.4. Methodology. ...................................................................................................... 7

1.5. A thesis overviews .............................................................................................. 7

2. ROF FUNDAMENTALS ............................................................................................. 9

2.1. Chromatic dispersion .......................................................................................... 9

2.2. Output Optical Fiber signal ............................................................................... 10

2.3. RF Amplitude fading ......................................................................................... 10

2.4. Optical carrier to signal (OCSR) ....................................................................... 11

2.5. Direct-detection ................................................................................................ 12

2.5.1. NOISE ....................................................................................................... 12

2.5.2. Thermal Noise ........................................................................................... 12

2.5.3. RIN Noise .................................................................................................. 13

2.5.4. Shot Noise ................................................................................................. 13

3. BASICS OF ELECTRO-OPTICAL MODULATION AT OPTICAL FREQUENCIES ... 14

3.1. External modulation .......................................................................................... 14

3.1.1. Phase electrooptical modulators ................................................................ 14

3.2. Mach-Zehnder modulator (MZM) ...................................................................... 15

3.3. MZM-Push-Pull (MZM-PP) ............................................................................... 16

3.3.1. Compression at -1dB ................................................................................. 17

4. TRANSMITTER CONFIGURATION FOR RoF LINKS ............................................. 20

4.1. MZM-PP transmitter configuration for RoF ....................................................... 20

4.1.1. OCSR ........................................................................................................ 20

4.1.2. Dispersions effect ...................................................................................... 21

4.1.3. Electrical Signal detected .......................................................................... 21

4.2. MZM-SSB transmitter configuration for RoF ..................................................... 21

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4.3. MZM-Dual-Drive transmitter configuration for RoF ............................................ 23

4.3.1. OCSR ........................................................................................................ 24



4.4. MZM-Dual-Parallel transmitter configuration for RoF ........................................ 24

4.4.1. OCSR ........................................................................................................ 25



4.5. SUMMARY AND COMPARATIVE .................................................................... 27

5. SIMULATIONS AND RESULTS .............................................................................. 28

5.1. VPIphotinic ....................................................................................................... 28

5.1.1. Design features ......................................................................................... 29

5.2. Simulation of MZM-PP Configuration ................................................................ 30

5.3. Simulation of MZM-DD Configuration ............................................................... 31

5.4. Simulation of MZM-DP Configuration................................................................ 34

5.5. Sumary of the three MZMs configurations ........................................................ 37

6. SENSITIVITY STUDY.............................................................................................. 38

6.1. Design features ................................................................................................ 39

6.1.1. Simulation scenario ................................................................................... 40

6.2. System sensitivity Simulations Results ............................................................. 41

6.2.1. MZM-PP configuration ............................................................................... 41

6.2.2. MZM-DD configuration .............................................................................. 42

6.2.3. MZM-DP configuration ............................................................................... 43

7. Conclusions and future development ....................................................................... 44

8. Referencias ............................................................................................................. 45

9. Annex I .................................................................................................................... 46

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1. INTRODUCTION

1.1. Access network

The imminent advent of the next generation of wireless networks, 5G+, requires the

efficient tackling of several technological challenges to ensure the demand for high

transmission rates and high bandwidth in both fixed and wireless networks communications.

Over the past decade, the number of wireless users and devices has exponentially

increased resulting in the migration towards higher radio-frequency (RF) frequencies to

cover more bandwidth and then more capacity [1]. However, the higher wireless

attenuation produced by the higher frequencies demands the use of cellular architectures

relying on small cells. Figure 1.1 a) shows a cellular system where the base station (BS) of

each cell is connected to the wireless network’s backhaul. A complete BS has several

components that increase the installation costs, especially when migrating to the higher

frequencies. Hence, the economics of setting up a cellular system in which each small cell

is served by a BS is challenging, because of the large number of BSs needed.

Figure 1.1: Comparing the current cellular system (a) to a cellular system employing ROF (b)

Radio over fibre (ROF) is a promising solution to the challenge of handling a large number

of small cells with high-RF frequencies [3]. Figure 1.1 b) shows a cellular architecture

relying on RoF, where multiple cells are served by a single BS through radio access points

(RAPs) that are connected to the BS using optical fibre. The RAP performs minimum signal

processing and is not expensive, while most of the signal processing hardware is retained

in the BS and is shared by multiple cells [4][5]. The advantages of the ROF-aided

architecture include ease of system upgrades, better resource allocation, better wireless

coverage, and higher power efficiency [2], and that allows access for more users. The aim

of this project is to explore how to transmit radio frequency (RF) signals from wireless

networks for serving as many users as possible on a single wavelength over a single fiber,

using minimum power to feed the RAPs while ensuring a minimum Bit Error Rate (BER)

transmission quality.

In looking at the future of optical networks the one obvious common trait is that of

continuous change. That makes the ability to adapt to change a most sought feature in a

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RoF system. In this work we will mainly focus on RoF solutions which may easily

reconfigured to work at different RF bands, taking advantage of the wide bandwidth

inherent to optical components

1.2. State of the art

Figure 2.1 shows the basic scheme of the RoF link that will be considered in this work. The

context is the downlink, from BS to RAP. At the BS we find laser providing the optical carrier.

The standard telecom infrastructure works at C-band or the third window, conventional

band (1530-1565) nm. This band is characterized by a high value of chromatic dispersion

(CD) with a typical CD coefficient D=17ps/nmKm [6], this effect is detrimental in a an typical

RoF system using double-side band modulation because it leads to interference in between

the RF modulation bands that may cause total cancellation the RF signal at the

photodetector for some frequencies [6]. Other optical transmission bands can be

considered such as O-band around 1.3 um with an almost null D value, and hence free of

CD effects. However, the drawbacks associated with the O-band are mainly the high

propagation loss and the lack of convenient solutions for optical amplification such as

Erbium-Doped Fiber Amplifiers (EDFA), whereby, in this work, we focus on RoF systems

in C-band.

Figure 2.1 a basic scheme of a radio over fiber system

The continuous wave emitted by the laser is modulated in an external element, which here

will be considered a kind of electro-optical Mach-Zehnder (MZM) modulator, in different

configurations, as explained in chapter 3. The use of MZM provides wide modulation

bandwidths but requires elements for the control of the input polarization, and is affected

by a voltage bias drift so that voltage control is usually convenient. That is why it is often a

good solution for the RoF link from BS to radio access point (RAP) (downlink). For the RAP-

BS direction (uplink) solutions based on Direct Modulated Lasers (DML) are more

appropriate [7]. The optical output signal travels through an optical fiber link where are

affected by the attenuation and dispersion of the fiber.

The optical signal before or after the optical fiber link can be amplified and the electrical

signal is directly detected by a photodetector. We focus on the downlink direction of the

RoF link, for that, the receiver will consist of a simple direct photodetector which just

provides at its output a photocurrent that is proportional to the intensity of the optical wave.

Coherent receivers could be employed in the uplink direction, or even also in the downlink

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in the more advanced proposals [6b], but these are outside of the scope of the present

work.

It is worth noting that the EDFA found at the photodiode input will not be necessarily present

in a real application, as it would increase the cost of the RAPs. The reason to keep it in our

basic RoF scheme is that since we will be interested in finding optimum configurations that

minimize the power required at the RAP for a given BER quality threshold, in our

simulations we will set the EDFA to maintain a constant optical power despite changes in

the TX configuration parameters. We may just think that the EDFA will actually be placed

at the TX side output to maintain a maximum optical power given by the optical fiber

maximum power threshold, and that this power needs to be distributed over as many users

as possible, thus providing a maximum optical power budget for the RoF network.

1.3. Project objectives

In view of the state of the art, in this section we describe the objectives of the present work

• Review of fundamentals of RoF Systems

Looking at the elements of an RoF system starting from the transmitter, to understand the

effects of fibre dispersion on the optical signal, find the optimum optical carrier to signal

(OCSR) that maximizes the optical power received and show the behaviour of RF signal

fading at the RF output of the photodetector.

• Review of fundamentals of RoF Systems

• Theoretical analysis of TX configurations and identification of optimum parameter

choices

• Build a simulation setup for confirming the theoretical findings and the optimum TX

parameter choices to provide best values of sensitivity for a threshold PRE-FEC

𝐵𝐸𝑅 = 10−3.

1.4. Methodology.

This project makes use of a photonics software which is basically designed for the field of

photonics “VPIPhotonics” which can be referred as VPI. Matlab and python software can

be used to interlink with VPI to either provide or extract data. The entire optimization of the

fiber link such as optical to carrier ratio (OCSR), error probability, power penalty is being

performed using VPI software. This software contains all the necessary tools to a design a

perfect optical communication system, transmission system, optical link configuration and

photonics circuits.

1.5. A thesis overviews

The thesis is organized in the following manner:

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• Chapter 2 gives the theoretical bases of the RoF system, it is shown how the fading

produced by the chromatic dispersion affects the DSB signals.

• Chapter 3 gives the theory about the electro-optical external modulator. the

optimum OCSR value for a basic RoF signal with fixed total optical power, and the

sources and characterization of noise.

• Chapter 4 presents the mathematical development of transmitters configurations, a

brief mention is made to the modulation in SSB [8] using the MZM, the optimal value

of the OCSR is found analytically for each modulation method and compares the

advantages and drawbacks for each configuration.

• Chapter 5 shows the simulations and characterizes the results by giving input

values and analysing the graphs obtained

• Chapter 6 shows the study of the system sensitivity when data are introduced, and

compares the results whit the values found in the previous chapter.

• Chapter 7 closes the thesis with the conclusions obtained and comments on future

research lines.

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2. ROF FUNDAMENTALS

In a conventional RoF System, at the output of the Base Station (BS), the optical

signal consists of an optical carrier and a double sideband (DSB) RF signal, each of these

sidebands travels through the fiber link with a time delay, the double-sideband transmission

of an RF subcarrier will suffer from frequency-dependent fading caused by fiber dispersion,

its effect modifies the behaviour of the signal at the output of the fiber.

2.1. Chromatic dispersion

Chromatic dispersion (CD) is caused by the fact that single mode glass fibres transmit light

of different wavelengths at different speeds. this effect causes signal widening along with

the fiber and is characterized by the CD coefficient D[𝑝𝑠/𝑛𝑚·𝑘𝑚], which gives the delay

between two spectral components separated 1nm when going through 1 km of fiber. A

standard single-mode FO has D=17 𝑝𝑠/𝑛𝑚·𝑘𝑚 at the C-band.

In the mathematical modelling of chromatic dispersion, the propagation constant is the term

that indicates how the phase travels as a function of space, depends on the frequency and

is expressed with 𝛽[10]. considering the carrier frequency 𝜔0 much bigger than the RF

frequency 𝜔𝑅𝐹 , one can develop the propagation constant with the following Taylor

expansion:

𝛽(𝜔 + 𝜔0) = 𝛽0 + 𝛽1 + 𝛽2 + ⋯ EQ (2.1)

𝛽0

= 𝛽(𝜔0); 𝛽1

=𝜕𝛽

𝜕𝜔(𝜔0)(𝜔 − 𝜔0)

𝛽2

=𝜕2𝛽

𝜕𝜔2(𝜔0)

(𝜔 − 𝜔0)2

2

𝛽0 is the term that gives the phase velocity, understood as the speed with which the phase

of a wave propagates in space [6], The second term 𝛽1is the group delay at a frequency 𝜔

defined as the delay per unit length of the envelope, its expression is derived from [6] 𝛽(𝜔 )

𝑣𝑓 =𝛽2𝐿

𝜔0 EQ (2.2)

The higher order terms refer to signal dispersion with 𝛽2 as the most relevant, where Vg is

the group velocity and it is defined as:

𝜐𝑔 = (𝜕𝛽

𝜕𝜔)

−1 EQ (2.3)

Thereby, the frequency dependence of the group velocity causes a widening of the pulse

due to the fact that the different spectral components of the pulse are dispersed during

propagation and do not reach simultaneously the end of the fiber [10]. If Δ𝜔 is the spectral

width of the pulse, the degree of widening after propagating through a fibre of length L is

given by:

Δ𝑇 =𝜕𝑇

𝜕𝜔Δ𝜔 =

𝜕

𝜕𝜔(

𝐿

𝜐𝑔) Δ𝜔 = 𝐿

𝜕2𝛽

𝜕𝜔2 Δ𝜔 = 𝐿𝛽2Δ𝜔 EQ (2.4)

In terms of wavelength, where 𝜔 =2𝜋𝑐

𝜆 is and Δ𝜔 = (−2𝜋𝑐

𝜆2 ) Δ𝜆, the degree of widening can

be written as:

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Δ𝑇 = 𝜕

𝜕𝜆(

𝐿

𝜐𝑔) Δ𝜆 = 𝐷𝐿Δ𝜆 EQ (2.5)

𝐷 =𝜕

𝜕𝜆(

1

𝜐𝑔) = (−

2𝜋𝑐

𝜆2 ) 𝛽2 EQ (2.6)

Where D is the CD coefficient expressed in 𝑝𝑠/𝑛𝑚·𝑘𝑚 [6].

2.2. Output Optical Fiber signal

All frequency components are delayed when they propagate through a medium such as

fiber optics. In our RoF system, there is a modulated RF signal on a carrier so there are

two types of delay, the phase delay, which affects the carrier, and the group delay, which

affects the envelope of the transmitted signal, i.e. the modulated signal.

The low-pass equivalent referred to the optical carrier frequency 𝜔0, with an envelope

modulation at a frequency 𝜔𝑅𝐹 is defined at the output of the modulator with the following

expression:

𝐸𝑜𝑢𝑡 = 1 + 𝑚0

2(𝑒𝑗𝜔𝑅𝐹𝑡 + 𝑒−𝑗𝜔𝑅𝐹𝑡) EQ (2.7)

Note that in the above expression, the field amplitude is normalized to unity optical carrier

amplitude, as it is common practice in optical propagation analysis. The effect of the

different optical elements in the field amplitude can be considered in a separate analysis.

At the output of the optical fibre of length L, our signal will be affected by the propagation

constant 𝛽.Using the Taylor expansion EQ (2.1), the field after a propagates fiber length L

can be written

𝐸𝑜𝑢𝑡 = 1 + 𝑚0

2[𝑒𝑗𝜔𝑅𝐹𝑡𝑒

−𝑗(𝛽0𝜔0𝑡+𝛽1𝜔𝑅𝐹+𝛽22

𝜔𝑅𝐹2)𝐿

+ 𝑒−𝑗𝜔𝑅𝐹𝑡𝑒−𝑗(𝛽0𝜔0𝑡−𝛽1𝜔𝑅𝐹+

𝛽22

𝜔𝑅𝐹2)𝐿

]Q (2.8)

The carrier is affected by phase delay 𝜏𝑓 =𝛽0𝐿

𝜔0, which can be ignored since the receiver

relies on amplitude detection. We may then write the field as

𝐸𝑜𝑢𝑡 = 1 + 𝑚0

2[𝑒𝑗𝜔𝑅𝐹𝑡𝑒

−𝑗(𝛽1𝜔𝑅𝐹+𝛽22

𝜔𝑅𝐹2)𝐿

+ 𝑒−𝑗𝜔𝑅𝐹𝑡𝑒+𝑗(−𝛽1𝜔𝑅𝐹+

𝛽22

𝜔𝑅𝐹2)𝐿

]

𝐸𝑜𝑢𝑡 = 1 + 𝑚0𝑒−𝑗𝛽22

𝜔𝑅𝐹2𝐿cos (𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) EQ (2.9)

𝜙 = −𝛽2

2𝜔𝑅𝐹

2 𝐿 =𝜋𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐 EQ (2.10)

𝐸𝑜𝑢𝑡 = 1 + 𝑚0𝑒𝑗𝜙cos (𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) EQ (2.11)

In the result of the signal at the fiber output, the parameter 𝜙 is introduced, as can be seen

from equation (2.10) it is directly proportional to the length of the fiber and the square of

the RF frequency.

2.3. RF Amplitude fading

The detection of signal is done in terms of intensity, that is proportional to the square of the

modulus of the optical field, the intensity detected is

𝐼𝑃𝐷 = |𝐸𝑜𝑢𝑡|2 = 1 +𝑚0

2

2+ 2𝑚0 cos(𝜙) cos (𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) EQ (2.12)

From here, the transmission S21 parameter can be obtained as:

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|𝑆21| = 2𝑚0 cos(𝜙) = 2𝑚0 cos (𝜋𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐 ) EQ (2.13)

The term |𝑆21| in EQ (2.13) is graphically represented by Matlab to see the amplitude

response. In a frequency sweep of this parameter, nulls appear at specific frequencies, as

shown in Figure 2.3. This phenomenon is called "RF amplitude fading" and is given by

destructive sideband interference.

Figure 2.3 Representation of the theoretical S21 parameter of a SMF fibre at two different distances, in red at

L=20km and in blue at L=40km.

In this representation, the higher the dispersion, the nulls will appear at a lower frequency.

For a fixed dispersion, the other parameter that will affect the fading is the length of the

fibre. in the figure 2.3, it is represented for two different lengths, L=20km (red) and L=40

km (blue). we see that the length of the fibre is proportional to the frequency as doubling

the fiber length causes a reduction of the fading frequency in a factor √2

2.4. Optical carrier to signal (OCSR)

The total optical power from the modulator is distributed between the optical carrier frequency and the laterals mathematically:

𝑃𝑇 = 𝑃𝑐 + 2𝑃𝑆𝐵 EQ (2.14)

Here the ratio of optical carrier to sideband (OCSR) is defined as the ratio of the optical power in the power in the two first-order sidebands:

𝑂𝐶𝑆𝑅 =𝑃𝑐

2𝑃𝑆𝐵 EQ (2.15)

Recalculating the optical power using the OCSR expression in rewritten as:

𝑃𝑇 = 2𝑃𝑆𝐵(1 + 𝑂𝐶𝑆𝑅) EQ (2.16)

And then power the power corresponding to the RF signal is detected is:

𝑃𝑅𝐹 = 2𝑃𝑐𝑃𝑆𝐵 EQ (2.17)

In this mode, we can look for the value that maximises the RF power as a function of the OCSR. The result is:

𝑃𝑅𝐹 = 2𝑃𝑐𝑃𝑆𝐵 = 4𝑂𝐶𝑆𝑅 ∗ 𝑃𝑆𝐵2 = 𝑂𝐶𝑆𝑅

𝑃𝑇2

(1+𝑂𝐶𝑆𝑅)2 EQ (2.18)

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Whereby, the value of the OCSR that maximizes the RF power EQ (2.18) is when OCSR=1,

i.e., when the carrier power contained in the two first-order sidebands 𝑃𝑐 = 2𝑃𝑆𝐵 [8][9].

2.5. Direct-detection

The photodetector is an optical receiver that converts optical signals into electrical signals.

The PIN photodiode is one of the most common photodetectors, has a three-layer structure,

the middle layer being an intrinsic semiconductor, and the outer layers being P-type and

N-type [13]. The intrinsic zone allows the carriers to accelerate under the influence of the

strong field due to the ionized carriers at the edge of the P and N zones.

The process that takes place inside the device is optical absorption, a phenomenon by

which the energy of the photon generates an electron-hole pair in the active zone. The

generated electrons and holes are accelerated in opposite directions due to the electric

field through which the diode is polarized, creating a current flow, which is proportional to

the incident optical power. The output of the photodetector is a photocurrent and is

expressed by the following equation:

𝐼𝑃𝐷 = 𝑅𝑃𝑖𝑛 ≈ |𝐸𝑖𝑛|2 EQ (2.19)

When R in [𝐴/𝑤] is the Responsibility and 𝑃𝑖𝑛 the input power to the photodetector.

2.5.1. NOISE

For efficient reception, the useful signal level should be at a certain distance from the noise

level, then, it is necessary to know and compensate the noise power produced in the

system due to various effects.

2.5.2. Thermal Noise

This is the noise generated by electron agitation. Resistive elements correspond to thermal

noise sources of this type, which introduce a root mean square (rms) voltage ⟨ 𝑣𝑡ℎ2 ⟩ = 4𝐾𝑇𝑅

level or intensity ⟨𝐼𝑡ℎ2 ⟩ =

4𝐾𝑇

𝑅 into the system, as shown in Figure 2.4. In our simulations,

the thermal noise is characterized by 10𝑝𝐴

√𝐻𝑧⁄

Figure 2.4 equivalent model of thermal noise sources

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2.5.3. RIN Noise

Relative intensity noise is the result of random intensity fluctuations. The root mean square

intensity is obtained as:

⟨𝐼𝑅𝐼𝑁2 ⟩ = 𝑅𝐼𝑁 𝐼𝐷

2

Where the noise factor RIN is given by the laser used and 𝐼𝐷 is the DC current level in the

photodetector. In our simulations this kind of noise is neglected as it is usual in external

modulation systems.

2.5.4. Shot Noise

This noise is the result of fluctuations in the electric current due to the quantized nature of

the process of electron generation through absorption of photons. The root mean square

(rms) intensity in this case turns out to be:

⟨𝐼𝑆𝐻2 ⟩ = 2𝑞𝐼𝐷

Where 𝑞 is the value of the electron charge q = 1.6 − 10 − 19 C . and 𝐼𝐷 is the discrete

current value of the detected current. It is important to bear in mind, that contrary to the

thermal noise term which only depends on temperature and therefore remains constant at

the ambient temperature value, shot noise increases with the optical power present at the

input of the photodiode.

14

3. BASICS OF ELECTRO-OPTICAL MODULATION AT OPTICAL

FREQUENCIES

This chapter shows the theory about the Electro-optical external modulator and the

Mach-Zehnder modulator (MZM) is introduced, and its linear behaviour showed.

3.1. External modulation

In an external modulation the laser generates an optical intensity constant in time

(continuous wave laser) that later passes through an external optical device to which the

modulating signal is sent. At the output, the radiation is modulated to the desired shape

and coupled to the fibre.

All the modulators used are based on the variation that the properties of a material undergo

with the application of certain signals of different nature. The most popular modulators, in

terms of both performance and design economy, are the electro-optical type, where an

electrical signal causes a change in the refractive index of the material, and thus, it can

modulate the phase of the optical signal with a voltage applied in the right direction [10].

Through the use of interferometry, the phase modulation may be translated into an

amplitude modulation. The most common kind of interferometer is the Mach-Zehnder.

It is within this group that the Mach-Zehnder modulators are found, however, to better

understand the operation of Mach-Zehnder amplitude modulators, electro-optical phase

modulators are introduced.

3.1.1. Phase electrooptical modulators

Figure 3.1: Basic structure of the operation of an optical phase modulator [10]. The design corresponds to the

commonly known structure of a capacitor: an embedded dielectric between two conductive surfaces on which

an external electrical voltage is applied.

A properly oriented electro-optical crystal can modulate the phase and intensity of the

optical signal with a voltage applied in the correct direction. Lithium Niobate (𝐿𝑖𝑁𝑏𝑂3) is

the most common electro-optic crystal used to manufacture electro-optic type external

modulators. There is an optimal direction of the electro-optical waves for which it is most

efficient. In a LiNbO3 crystal, if we apply an electric field along the x-axis of the waveguide,

as shown in figure 3.1, the refractive index of the material changes by a value given by the

expression:

∆𝑛 =1

2𝑛0

3𝑟33𝐸𝑥 EQ (3.1)

15

Where 𝑟33 es the EOM coefficient with a value of 328 ∗ 10−6 𝜇𝑚𝑉⁄ for LiNbO3, 𝑛0 is the

material refractive index of the waveguide with zero voltage and 𝐸𝑥 is the electric field

applied to the width of the guide (x-axis), as shown in figure 3.1. The phase shift of the

optical input signal, after travelling a length 𝐿𝑖 is [8]:

∆∅0 =2𝜋∆𝑛𝐿𝑖

𝜆0= 𝜋𝑛𝑟

3𝑟33𝑉𝐿𝑖

𝑑𝜆0 EQ (3.2)

Where 𝜆0 is the wavelength of the optical signal in vacuum, 𝐿𝑖 and 𝑑 are the geometric

dimensions of capacitor (see figure 3.1) the voltage required to cause a 180° phase shift is

defined as:

𝑉𝜋 =𝑑𝜆0

𝑛𝑟3𝑟33𝐿𝑖

EQ (3.3)

It will be a fundamental design parameter in the phase modulator.

In the design of a phase modulator, one of the main objectives is to reduce the value of the

voltage 𝑉𝜋 in order to consume as little electrical power as possible during modulation. This

would be achieved by increasing the coefficient 𝐿𝑖/𝑑 which would in turn increase the

internal capacity of the modulator causing a slower temporary response to its input. This is

known as the Bandwidth-sensitivity trade off [11].

3.2. Mach-Zehnder Modulator (MZM)

Mach-Zehnder is an external amplitude modulator that generally provides better quality

than DML, provides high modulation bandwidths to the generated signal, and reaches high

transmission speeds, making these devices fundamental elements in high-capacity optical

networks.

Electrode

Wave guide

Figure 3.2 Diagram of an amplitude modulator based on the Mach-Zehnder interferometer

Figure 3.2 illustrates an amplitude modulator based on a Mach-Zehnder interferometer

(MZI) structure. The optical input signal is divided into two paths by a Y junction. A signal

is obtained whose amplitude and phase will depend on the phase shift introduced between

both branches of the interferometer, i.e. the result is a signal that is modulated both in

phase and amplitude. The output of the MZM can be written as:

𝐸𝑜𝑢𝑡(𝑡) = 𝐸𝑖𝑛(𝑡)ℎ(𝑡) EQ (3.4)

Where h(t) represents the MZM transfer function given by

ℎ(𝑡) =1

√2

𝑌𝑠𝑝𝑙𝑖𝑡𝑢𝑝𝑝𝑒𝑟𝑒𝑗(

𝜋𝑉1(𝑡)𝑣𝑐

)+𝑌𝑠𝑝𝑙𝑖𝑡𝐿𝑜𝑤𝑒𝑟𝑒

𝑗(±𝜋𝑉2(𝑡)

𝑣𝑐)

𝐴𝑡𝑡𝑒𝑛𝑢𝑎𝑡𝑖𝑜𝑛 EQ (3.5)

The parameters that characterize this transfer function are V1(t) and V2(t) as a voltage

applied to the microwave contacts. The junction has excess extinction ratio (ER) losses,

the power ratio between the maximum and minimum transmission:

16

𝑌𝑠𝑝𝑙𝑖𝑡𝑢𝑝𝑝𝑒𝑟 = 𝑎 = √0.5 + 𝜀

𝑌𝑠𝑝𝑙𝑖𝑡𝐿𝑜𝑤𝑒𝑟 = √1 − 𝑎2

𝐸𝑅 =𝑃𝑚𝑎𝑥

𝑃𝑚𝑖𝑛= (

𝑎+√1−𝑎2

𝑎−√1−𝑎2)

2

= (1

𝜖2) EQ (3.6)

The term ε represents the difference in the upper and lower power split ratios. For a perfect

50/50 split in between the MZM branches ε = 0 This allows the MZ structure to have an

infinite ER. However, in real Mach-Zehnder devices, a perfect split cannot be obtained, due

to fabrication tolerances. This means that the device will have a finite ER. This is known as

the intrinsic extinction ratio of the device, and is normally measured at very low speeds.

For typical off-the-shelf high-speed Lithium Niobate Mach-Zehnder modulators, the intrinsic

extinction ratio is usually in the 35 to 55 dB range. This effectively unbalances an ideal MZ

device introducing some chirp.

There are mainly two different structures for coupling the electrical modulating signal to the

optical guide, single-drive and dual-drive. In a single drive modulator, the two paths of the

MZI are phase modulated with antipodal phase shifts ±𝜋𝑉(𝑡)/2𝑉𝜋, which guarantees that

for ideal infinite ER the modulator has a null chirp factor. Dual-drive structure a different

voltage is applied to each branch.

3.3. MZM-Push-Pull (MZM-PP)

Push-Pull, is the conventional MZM configuration where the two paths of the MZI are phase

modulated with antipodal phase shifts ±𝜋𝑉(𝑡)/2𝑉𝜋, that can be achieved with the single-

drive structure or with the dual-drive structure feeding the lower arm with the opposite sign

than the upper arm.

MZM

-

Figure 3.2 Conventional MZM-Push-Pull (MZM-PP)

In this project The MZM structures are assumed ideal with 0dB insertion loss and very high

Extinction Ratio (ER). The equation field at the output of the modulator has the following

expression:

𝐸𝑜𝑢𝑡 =𝐸𝑖𝑛

2√𝐿𝑀𝑍𝑀(𝑒

𝑗𝜋𝑉 (𝑡)

2𝑉𝜋 + 𝑒−𝑗𝜋𝑉 (𝑡)

2𝑉𝜋 ) = 𝐸𝑖𝑛 cos (𝜋

2𝑉𝜋𝑉(𝑡)) EQ (3.7)

Where 𝐸𝑖𝑛 is the optical carrier wave and the 𝑉(𝑡) voltage at the port of the MZM (see

Figure 3.2) is composed of a bias voltage 𝑉𝐵 and the RF signal of amplitude 𝑉𝑅𝐹 and

frequency 𝜔𝑅𝐹. Mathematically it is written as:

𝑉(𝑡) = 𝑉𝐵 + 𝑉𝑅𝐹 cos(𝜔𝑅𝐹𝑡)

17

QP

Figure 3.3 MZM transfer function (blue), the small RF signal (red) has as an 𝑉𝑅𝐹 index modulation m and is biased at the quadrature point.

By applying the transfer function of the MZM it is the optical power at the output yields

𝑃𝑜𝑢𝑡 = | 𝐸𝑜𝑢𝑡|2 = 𝑃𝑖𝑛 cos (𝜋

2𝑉𝜋𝑉(𝑡))

2

=𝑃𝑖𝑛

2[1 + cos(𝜃𝐵 + 𝑚 cos(𝜔𝑅𝐹𝑡))]

Using the basic trigonometric identity, the previous equation can rewritten as:

𝑃𝑜𝑢𝑡 =𝑃𝑖𝑛

2[1 + cos(𝜃𝐵) cos(𝑚 cos(𝜔𝑅𝐹𝑡)) − sin(𝜃𝐵) sin(𝑚 cos(𝜔𝑅𝐹𝑡))] EQ (3.8)

Where 𝜃𝐵 = 𝑉𝐵𝜋

𝑉𝜋 and 𝑚 =

𝑉𝑅𝐹𝜋

𝑉𝜋 are the expressions of the phase of the bias and the

modulation index respectively. The operating point is determined by the bias phase shift of the modulator 𝜃𝐵. The difference between the voltage for which the first maximum and the first zero of the function is 𝜃𝐵 = 𝜋, i.e when 𝑉𝐵 = 𝑉𝜋. Figure 3.3 shows the transfer function where the bias voltage is applied at the quadrature point, whereby, the transfer function has a linear behaviour.

One of the disadvantages of the external modulation as compared to DML is its intrinsic nonlinear character. It is necessary to know these limits to avoid distortion of the RF signal.

3.3.1. Compression at -1dB

Modulators are mainly used within the linear range, i. e. small modulation index, m, so that

the small signal approximation may be applied. Beyond this range, nonlinear effects begin

to appear. In this section we will be looking for these limits, usually quantified as the 1 dB

gain compression point, which is the input RF voltage for which the slope of the transfer

function is reduced by 1 dB. To find this limit it is necessary to know the real behaviour of

the optical power, whereby, Equation EQ (3.9) is rewritten taking into account the terms of

the Jacobi-anger expansion (table 3.1) [12] as:

cos(𝑚 cos(𝛼)) = 𝐽0(𝑚) + 2 ∑ (−1)𝑛𝐽2𝑛(𝑚) cos(2𝑛𝛼)𝑛=∞

𝑛=1

18

Sin(𝑚 cos(𝛼)) = −2 ∑ (−1)𝑛𝐽(2𝑛−1)(𝑚)𝑛=∞𝑛=1 cos((2𝑛 − 1)𝛼)

𝑒𝑗𝑧 cos 𝜃 = ∑ 𝑗𝑛𝐽𝑛(𝑧)𝑒𝑗𝑛𝜃

𝑛=∞

𝑛=−∞

𝑒𝑗𝑧 sin 𝜃 = ∑ 𝐽𝑛(𝑧)𝑒𝑗𝑛𝜃

𝑛=∞

𝑛=−∞

Table 3.1 Jacobi-anger Expansion

𝑃𝑜𝑢𝑡 =𝑃𝑖𝑛

2[1 + cos(𝜃𝐵)(𝐽0(𝑚) + 2 ∑ (−1)𝑛𝐽2𝑛(𝑚)𝑛=∞

𝑛=1 cos(2𝑛𝜔𝑅𝐹𝑡))…

… − 𝑠𝑖𝑛(𝜃𝐵)(−2 ∑ (−1)𝑛𝐽(2𝑛−1)(𝑚)𝑛=∞𝑛=1 cos((2𝑛 − 1)𝜔𝑅𝐹𝑡))]

𝑃𝑜𝑢𝑡 ≈𝑃𝑖𝑛

2𝐿𝑀𝑍𝑀

[cos(𝜃𝐵)𝐽0(𝑚) − 2𝑠𝑖𝑛(𝜃𝐵)𝐽1(𝑚) cos(𝜔𝑅𝐹𝑡) EQ (3.9)

The 𝐽𝑛 refers to terms related to the amplitude of the Bessel function for each harmonic

[15]. In EQ (3.9) only terms up to the first order are considered relevant, in figure 3.4 it can

be seen that for small input values 𝐽0(𝑚) can be approximated as a constant and 𝐽1(𝑚) as

a linear function.

Figure 3.4 harmonic content riven by Bessel function

Table 3.2 Bessel approximations

Table 3.2 shows the approximations for small values of the modulation index. The objective

is to find the limit value of the modulation index m where the difference between the real

value and the approximate value is 1dB. The following figure shows the compression at -

1dB.

𝐽0(𝑚) ≈ 1

𝐽1(𝑚) ≈𝑚

2

19

Figure 3.5 Theoretical representation of the compression point at -1dB

In figure 3.5 all the values are expressed in dB, we see that the term affects the RF signal

has the compression at -1dB in m=0dB, therefore m=1. Therefor the maximum voltage

amplitude of the modulation index that guarantees to work in the linear zone is when

𝑉𝑅𝐹 =𝑉𝜋

𝜋.

20

4. TRANSMITTER CONFIGURATION FOR RoF LINKS

Once the theory about the behaviour of an optical field signal in an RoF system has

been consolidated and we know how the external modulator MZM works and shown

analytically is mathematical expressions it is time to talk about the different transmitter

configurations for an RoF system.

4.1. MZM-Push-Pull transmitter configuration for RoF

The first transmitter configuration considered is MZM-PP, taking the conventional MZM into

an RoF system, where continuous wave (CW) optical source produces an optical signal

that is inserted into the MZM, is phase and amplitude modulated with an RF signal. The

optical output field travels over a fibre link to the RAP as seen in figure 4.1

MZM

LD

SMF

- -

Figure 4.1: Radio over Fiber system with MZM-PP configuration

The result at the output of the modulator has been introduced in the previous chapter, here

it is rewritten whit the corresponding small-signal approximations:

𝐸𝑜𝑢𝑡 ≈𝐸𝑖𝑛

√𝐿𝑀𝑍𝑀[cos (

𝜃𝐵

2) − sin (

𝜃𝐵

2)

𝑚

2cos(𝜔𝑅𝐹𝑡)] EQ (4.1)

4.1.1. OCSR

The Optical carrier to signal ratio can be calculated extracting from the optical field of the

modulator the component of power corresponding to the optical carrier and the RF signal.

In the DSB system, half of the optical field amplitude has to be taken into account when

calculating the RF signal power.

𝑃𝑇 = 𝑃𝑐 + 2𝑃𝑆𝐵 EQ (4.2)

For a conventional MZM-PP, the optical carrier and sidebands power levels are given

respectively by:

𝑃𝐶 = cos (𝜃𝐵

2)

2 EQ (4.3)

𝑃𝑆𝐵 = |−1

2sin (

𝜃𝐵

2)

𝑚

2|

2 EQ (4.4)

Which takes to the following OCSR expression

𝑂𝐶𝑆𝑅 =𝑃𝐶

2𝑃𝑆𝐵

21

𝑂𝐶𝑆𝑅 = 8

𝑚2 tan(𝜃𝐵

2)

2 EQ (4.5)

From here, the RF power detected is maximum when OCSR = 1, whereby the optimum

bias voltage will be:

𝑉𝐵_𝑜𝑝𝑡 =2𝑉𝜋

𝜋tan−1 √8

𝑚 EQ (4.6)

4.1.2. Dispersion effect

The optical field 𝐸𝑜𝑢𝑡 is transmitted through the optical fiber cable where it is affected by

the attenuation and dispersion. For a standard SMF the attenuation is 0.2dB/km in C-band,

although, it is not taken into account for the study since can be included into the power

budget that we focus on chromatic dispersion, the optical field at the output of the fiber is:

𝐸𝐿 =𝐸𝑖𝑛

√𝐿𝑀𝑍𝑀(cos (

𝜃𝐵

2) −

m

2sin (

𝜃𝐵

2) 𝑒−𝑗∅ cos(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿))) EQ (4.7)

The result adds to the signal the propagation constant 𝛽1 and the phase dispersion

∅ which is directly proportional to the RF frequency and the optical fiber cable length

4.1.3. Electrical Signal detected

The signal at the output of the optical fibre is amplified with an optical amplifier EDFA to

obtain the power 𝑃𝑇. At the photo detector output, the 𝐼𝑃𝐷 current in the electrical domain

is obtained as

𝐼𝑃𝐷 =ℜ𝐸𝑖𝑛

2

𝑃𝑇[cos2 (

𝜃𝐵

2) +

𝑚2

4sin2 (

𝜃𝐵

2) cos2(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) − 𝑚𝑐𝑜𝑠 (

𝜃𝐵

2) sin (

𝜃𝐵

2) cos(𝜙)𝑐𝑜𝑠(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿))]

EQ (4.8)

For small RF amplitude value of the modulation index m higher order than one can be

neglected. In addition, fading only affects the RF signal, hence at the output of the

photodetector, 𝐼𝑅𝐹 has the following expression:

𝐼𝑅𝐹 =ℜ𝐸𝑖𝑛

2

𝑃𝑇𝑚𝑐𝑜𝑠 (

𝜃𝐵

2) sin (

𝜃𝐵

2) cos(𝜙)𝑐𝑜𝑠(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) EQ (4.9)

Equation (4.9) shows the amplitude of the RF signal is affected by the phase bias (𝜃𝐵), as

well as by the dispersion parameter 𝜙 may be maximized by tuning the voltage bias, as it

will be seen later, but the dispersion at the frequency of work is independent of the bias,

whereby with the configuration of the MZM-PP it is not possible to compensate the

amplitude loss due to fading.

4.2. MZM-SSB transmitter configuration for RoF

Theoretically, we study a configuration of the MZM-SSB, intending to analytically see how

this configuration avoids the CD effect in an RoF system.

22

MZM

90ºHybrid

Coupler

Figure 4.5 RoF System with SSB configuration

The chromatic dispersion can be avoided using a single-sideband (SSB) modulation.

Taken the dual-drive structure of the MZM, seen in Figure 4.5, the RF signal is applied to

both electrodes with 90º phase shift. A DC bias voltage is also applied to one arm at the

quadrature point, while the other DC terminal is grounded [7]. The optical field 𝐸𝑜𝑢𝑡(𝑡) from

the MZM has the following expression:


2 √𝐿𝑀𝑍𝑀

(𝑒𝑗𝑉1𝜋

𝑉𝜋 + 𝑒𝑗𝑉2𝜋

𝑉𝜋 )

𝑉1 = 𝑉𝐵 + 𝑉𝑅𝐹 cos(𝜔𝑅𝐹𝑡)

𝑉2 = 𝑉𝑅𝐹 cos (𝜔𝑅𝐹𝑡 − 𝜋

2) = 𝑉𝑅𝐹 sin(𝜔𝑅𝐹𝑡)

𝜃𝐵 = (2𝑛 − 1)𝜋

2 ; 𝑚 =

𝜋𝑉𝑅𝐹

𝑉𝜋


2 √𝐿𝑀𝑍𝑀[√2𝑒𝑗

𝜋

4 − 𝑚𝑒𝑗𝜔𝑅𝐹𝑡] EQ (4.10)

The result of the optical field at the output of the modulator is shown in EQ (4.10), (see

development in (Annex I) It can be seen that there is only one phasor component

corresponding to the RF signal. The power spectral density stands for the optical carrier

while the second term represents one of the sidebands at the frequency of work, as can be

seen in the figure 4.6:

Figure 4.6 Power spectral density for the optical carrier and the sidebands at the RF signal

23

keeping up with the mathematical development, the electrical current of the RF signal component is obtained as:


2

2√𝐿𝑀𝑍𝑀√2𝑚 𝑐𝑜𝑠 (𝜔𝑅𝐹(𝑡 − 𝛽1𝐿) − ∅ −

𝜋

4) EQ (4.11)

Where it is seen that the dispersion parameter ∅ does not affect the amplitude, which remains constant regardless of the working frequency.

However, electrical phase shifters or hybrid couplers were required to achieve a 90º phase shift in the SSB modulation, which only works at a fixed frequency band and so it lacks flexibility because it makes the frequency of work as a hardware characteristic and this limits the RoF system [13].

4.3. MZM-Dual-Drive transmitter configuration for RoF

The second transmitter configuration considered is MZM-DD. Using the dual-drive structure

of the MZI. the upper branch is fed by the amplitude RF signal and the lower branch by the

bias voltage, while the other terminals are grounded, as seen in figure 4.7

MZM

LD

SMF

Figure 4.7 Radio over Fiber system with MZM-DD configuration

The optical field at the output of the MZM-DD is given by:


2 (𝑒

𝑗𝑉1𝜋

𝑉𝜋 + 𝑒𝑗𝑉2𝜋

𝑉𝜋 ) ; 𝑉1 = 𝑉𝑅𝐹 cos(𝜔𝑅𝐹𝑡) ; 𝑉2 = 𝑉𝐵

V1 and V2 corresponds to the RF signal and VB is the bias voltage respectively. The optical

field output can rewritten as:


2 (𝑒𝑗𝑚 cos(𝜔𝑅𝐹𝑡) + 𝑒𝑗𝜃𝐵) EQ (4.12)

By means of the Bessel functions approach we may arrive to:


2 √𝐿𝑀𝑍𝑀(𝐽0(𝑚) + 2𝐽1(𝑚) cos(𝜔𝑅𝐹𝑡) + 𝑒𝑗𝜃𝐵) EQ (4.13)

Same as the MZM-PP the index modulation is small enough to apply a small signal

approximation, whereby Jacobi-Anger is applied to consider the first harmonic and the

Bessel function for small argument is approximated, the equation result is:

𝐸𝑜𝑢𝑡 = 𝐸𝑖𝑛𝑒𝑗𝜃𝐵

2 (cos (𝜃𝐵

2) + 𝑒

−𝑗(𝜃𝐵

2−

𝜋

2) 𝑚

2cos(𝜔𝑅𝐹𝑡)) EQ (4.14)

24

4.3.1. OCSR

The optical carrier and sidebands power levels are given respectively by:

𝑃𝐶 = cos (𝜃𝐵

2)

2 EQ (4.15)

𝑃𝑆𝐵 = |−1

2𝑒

−𝑗(𝜃𝐵

2−

𝜋

2) 𝑚

2|

2

=𝑚2

16 EQ (4.16)

The OCSR in this configuration, has the following expression:

𝑂𝐶𝑆𝑅 = 8 cos(

𝜃𝐵2

)2

𝑚2 EQ (4.17)

The optimal voltage maximize the RF power detected is.

𝑉𝐵−𝑜𝑝𝑡 =2𝑉𝜋

𝜋cos−1 𝑚

√8 EQ (4.18)

4.3.2. Dispersions effect

The result of the optical field after travelling over the fibre link is:

𝐸𝐿 ≈ 𝐸𝑖𝑛𝑒𝑗𝜃𝐵

2 (cos (𝜃𝐵

2) +

𝑚

2𝑒

−𝑗(𝜃𝐵

2−𝜙−

𝜋

2)

cos(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿))) EQ (4.19)


The electrical current at the output of the photodetector shows the result of the setting

parameters. The amplitude of the RF signal is affected by the phase bias (𝜃𝐵), as well as

by the dispersive parameter 𝜙.

𝐼𝑅𝐹 = ℜ𝐸𝑖𝑛2

𝑚𝑐𝑜𝑠(𝜃𝐵

2)

𝑃𝑇

sin (𝜃𝐵

2− 𝜙) 𝑐𝑜𝑠(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿)) EQ (4.20)

In this case, if the RF frequency is greatly affected by the dispersion of the fibre, is

compensated with the voltage bias. The condition is:

sin (𝜃𝐵

2− 𝜙) = ±1 ;

𝜃𝐵

2− 𝜙 = ±(2𝑛 − 1)

𝜋

2→ 𝜃𝐵 = ±(2𝑛 − 1)𝜋 + 2𝜙 = ±(2𝑛 − 1)𝜋 + 2

𝐷𝜆02𝑓𝑅𝐹

2 𝜋𝐿

𝑐

𝑉𝐵_𝑁𝑜𝑐ℎ = 𝑉𝜋 [±(2𝑛 − 1) +2𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐] EQ (4.21)

Where 𝑉𝐵_𝑁𝑜𝑐ℎ is the value of the bias voltage that increases the frequency response of the

𝐼𝑅𝐹 current and keeps it constant in a certain bandwidth around the frequency of work. This

modification also alters the power level and the power is no longer maximum as compared

to the MZM-PP, however, makes it possible to transmit the signal at frequencies wherein

the MZM-PP configuration is completely cancelled.

4.4. MZM-Dual-Parallel transmitter configuration for RoF

The last optical transmitter scheme introduced in this project is the Mach-Zehnder

Modulator Dual-Parallel (MZM-DP), this method adds more complexity than the previous

configurations, the structure is a MZM with two small nested MZM-PP configurations in

25

each of its branches, Figure (3.9) The RF signal and the first bias voltage (𝑉𝐵1) are applied

to the upper MZM-PP. An optical phase shift may be applied between the two MZMs

outputs through the third bias voltage (𝑉𝐵3) while the second bias voltage (𝑉𝐵2) is applied

in the lower MZM.

Figure 4.8 Radio over Fiber system with MZM-DP configuration

The optical field at the output of the MZM 𝐸𝑜𝑢𝑡, shows 𝐸1 and 𝐸2 as an expression similar

to the MZM-PP:

𝐸𝑜𝑢𝑡 =1

2[𝐸1 + 𝑒

𝑗𝑉3𝜋

𝑉𝜋 𝐸2] EQ (4.22)

𝐸1 =𝐸𝑖𝑛

2 [𝑒

𝑗𝜋

2𝑉𝜋𝑉1 + 𝑒

− 𝑗𝜋

2𝑉𝜋𝑉1] = 𝐸𝑖𝑛 cos (

𝜋

2𝑉𝜋( 𝑉𝐵1 + 𝑉𝑅𝐹 cos(𝜔𝑅𝐹𝑡)))

𝐸2 =𝐸𝑖𝑛

2 [𝑒

𝑗𝜋2𝑉𝜋

𝑉2 + 𝑒−

𝑗𝜋2𝑉𝜋

𝑉2] = 𝐸𝑖𝑛 cos (𝜋

2𝑉𝜋 𝑉𝐵3 )

Using the basic trigonometric identity, the previous equation can rewritten as:


2 [cos (

𝜃𝐵1

2) cos (

𝑚

2cos(𝜔𝑅𝐹𝑡)) − 𝑠𝑖𝑛 (

𝜃𝐵1

2) 𝑠𝑖𝑛 (

𝑚

2cos(𝜔𝑅𝐹𝑡)) + 𝑒𝑗𝜃𝐵3 cos (

𝜃𝐵2

2)] EQ (4.23)

Applying the respective approximations for small amplitude signals, the output optical field

expression of the MZM-DP looks like:


2 [cos (

𝜃𝐵1

2) − 𝑠𝑖𝑛 (

𝜃𝐵1

2)

𝑚

2cos(𝜔𝑅𝐹𝑡) + 𝑒𝑗𝜃𝐵3 cos (

𝜃𝐵2

2)] EQ (4.24)

The amplitude of the RF signal can be maximized, taking advantage of the appearance of

the new adjustment parameters, the first bias voltage is set at a null-point, i.e., equalling

the value of 𝜃𝐵1 =𝜋

2. In this way, it is possible to eliminate the contribution of the optical

carrier it whose amplitude will be controlled through the bias applied to the other nested

MZM. As a result, the optical field 𝐸𝑜𝑢𝑡(𝑡) has the following expression:


2 [𝑒𝑗𝜃𝐵3 cos (

𝜃𝐵2

2) −

𝑚

2cos(𝜔𝑅𝐹𝑡)] EQ (4.25)

4.4.1. OCSR

Optical Carrier-to-Signal in this configuration, has the following expression:

𝑂𝐶𝑆𝑅 =8 cos(

𝜃𝐵22

)2

𝑚2 EQ (4.26)

26

In this configuration the voltage Bias 𝑉𝐵2 is used to maximize the RF power detected, it

may be written as:

𝑉𝐵2−𝑜𝑝𝑡 =2𝑉𝜋

𝜋cos−1 𝑚

√8 EQ (4.27)

4.4.2. Dispersions effect

The result of the optical field after travelling over the fibre link is:


2 𝑒

𝑗𝜃𝐵32 [𝑒

𝑗𝜃𝐵32

cos (𝜃𝐵2

2) −

𝑚

2𝑒−𝑗(

𝜃𝐵32

−𝜙) cos(𝜔𝑅𝐹(𝑡 − 𝛽1𝐿))] EQ (4.28)


The electrical current is detected at the output of the photodetector. As it can be seen the

𝐼𝑅𝐹 current is affected by two different bias voltages:

𝐼𝑅𝐹 ≈ℜ𝐸𝑖𝑛

2

4

𝑚𝑐𝑜𝑠(𝜃𝐵2

2)

𝑃𝑇cos (

𝜃𝐵3

2− 𝜙) cos (𝜔𝑅𝐹(𝑡 − 𝛽

1𝐿)) EQ (4.29)

The phase bias 𝜃𝐵2 is used to maximise the amplitude leaving the 𝜃𝐵3 free to eliminate the

CD effects at the frequency of work, as follows:

cos (𝜃𝐵3

2− 𝜙) = ±1

𝜃𝐵3

2− 𝜙 = ±𝑛𝜋 → 𝜃𝐵3 = ±2𝑛𝜋 + 2𝜙 = ±2𝑛𝜋 + 2

𝐷𝜆02𝑓𝑅𝐹

2 𝜋𝐿

𝑐

𝑉𝐵3 = 2𝑉𝜋 [±𝑛 +𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐] EQ (4.30)

The MZM-DP transmitter is the most complete of the three and offers full reconfigurability in an RoF system, it can transmit at the maximum RF signal independently of the frequency of work with the most efficient power.

27

4.5. SUMMARY AND COMPARATIVE

Regarding the three transmitter configurations for RoF we are now in a position to make a

comparative analysis where the advantages and disadvantages of each method are

highlighted. The relevant equations of each configuration have been gathered in table 4.1

MZM-PP MZM-DD MZM-DP

𝐸𝑂𝑈𝑇 cos (

𝜃𝐵

2) − sin (

𝜃𝐵

2)

𝑚

2cos(𝜔𝑅𝐹𝑡) cos (

𝜃𝐵

2) + 𝑒

−𝑗(𝜃𝐵2

−𝜋2

) 𝑚

2cos(𝜔𝑅𝐹𝑡) 𝑒𝑗𝜃𝐵3 cos (

𝜃𝐵2

2) −

𝑚

2cos(𝜔𝑅𝐹𝑡)

|𝐼𝑅𝐹| 𝑚

𝑐𝑜𝑡𝑔 (𝜃𝐵2

)

+𝑚2

8tg (

𝜃𝐵2

) cos(𝜙) 𝑚𝑐𝑜𝑠 (

𝜃𝐵2

)

cos (𝜃𝐵2

)2

+𝑚2

8

sin (𝜃𝐵

2− 𝜙)

𝑚𝑐𝑜𝑠 (𝜃𝐵2

2)

cos (𝜃𝐵2

2)

2

+𝑚2

8

cos (𝜃𝐵3

2− 𝜙)

OCSR 8

𝑚2 tan (𝜃𝐵2

)2 8 cos (

𝜃𝐵2

)2

𝑚2 8 cos (

𝜃𝐵22

)2

𝑚2

𝑉𝐵−𝑜𝑝𝑡 2𝑉𝜋

𝜋tan−1 √8

𝑚 2𝑉𝜋

𝜋cos−1

𝑚

√8

2𝑉𝜋

𝜋cos−1

𝑚

√8

𝑉𝐵−𝑛𝑜𝑐ℎ ---------- 𝑉𝜋[±(2𝑛 − 1) + 2𝜙] 2𝑉𝜋[±𝑛 + 𝜙]

Table 4.1 the relevant equation in the modulations MZM-PP, MZM-DD and MZM-DP

𝜙 =𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐 ; 𝜃𝐵𝑛 =

𝜋𝑉𝐵𝑛

𝑉𝜋 ; m=

𝜋𝑉𝑅𝐹

𝑉𝜋

The first column shows the equations corresponding to the configuration in MZM-PP. The

value of 𝑉𝐵−𝑜𝑝𝑡 makes the electrical current response to 𝐼𝑅𝐹 to reach its maximum value,

however, the bias does not have an effect on the frequency at which CD nulls occur for a

certain fiber length and therefore we will be limited to work at frequencies where we may

have a flat response, with no control of the RF operative band

In the central column, there is the equation of the MZM-DD configuration, like the previous

one, we put the bias value in 𝑉𝐵−𝑜𝑝𝑡 to maximize the 𝐼𝑅𝐹 signal, on the other hand, we can

adjust the bias voltage to 𝑉𝐵−𝑛𝑜𝑐ℎ to avoid the dispersion produced by the fading, as this

change modifies the amplitude of the signal. This will allow to work at the notch frequencies

at which the PP cannot possibly work but at the price of a lower gain than the maximum

possible because the bias to avoid the notch does not allow to reach the optimum OCSR

condition.

The third column shows the MZM-DP configuration, in which more variables are added for

the control of the bias, 𝑉𝐵3−𝑛𝑜𝑐ℎ is used to move the notch and ensure a flattened response

the 𝑉𝐵2−𝑜𝑝𝑡 may achieve the maximum OCSR Making this option the most recommended

configuration to offer a fully reconfigurable RoF system.

28

5. SIMULATIONS AND RESULTS

Now that the mathematical feasibility of the proposed transmitters configurations for

RoF system has been analysed from a theoretical point of view is time to move on to

present the results that were obtained using a simulation-based study employing realistic

systems parameters.

5.1. VPIphotinic

In this chapter the different functions and blocks of the software VPIphotinic are presented,

where the characteristics of the design are chosen and the previous three configurations

of the RoF system are simulated taking the values according to the mathematical

development.

The simulation scenario built in VPI photonics resembles very closely the basic scheme of

an RoF system. Figure 5.1 shows the different parts of the system into relevant stages.

1.CW

5.OCSR

2.TX

3.SMF4. RAP

5.1 VPIphotonic diagram of MZM-DP transmitter for RoF

CW is the continuous wave laser, generates an optical carrier in C-Band and has as input

parameter the optical power level. In Figure 5.1 The TX stage represents the most complex

of the structures studied, the two nested MZM-PP configuration and a phase stage in

between the two arms of the big MZM-DP structure. From there, the others transmitters

configuration may be straight forwardly derived by eliminating some elements and

rearranging their parameters.

SMF is a single mode fiber whose relevant parameters are length and dispersion parameter.

The RAP stage is where the amplifier EDFA raises the signal to the desired power and the

electrical RF signal is detected by a photodetector PIN, who introduce both shot and

thermal noise. The last block is an analyser that represents graphically the amplitude of

|𝐼𝑅𝐹| as a function of a frequency sweep.

OCSR is calculated by VPI photonics, takes the optical signal at the Tx stage, and

separates the optical and RF power using bandpass filters and then a mathematical

operator calculates the OCSR.

29

5.1.1. Design features

In table 5.1 some parameters of design are presented. The selection criterion has been in

accordance with the constraints proposed in the theoretical analysis and to comply with the

small-signal approximations, a small value of the modulation index has been chosen.

The input power level to the optical source and the EDFA amplifier is kept fixed at the same

value for all simulations, thus making it easy to compare them with each other.

In the MZM, a high value for ER (ER=65dB) and 0 dB for insertion loss has been selected

to simulate ideal behaviour, the design value of 𝑉𝜋 has been normalised to unity.

For a realistic RoF system, the CD parameter is the standard for C-band SMF and the

length of the fibre cable (L=25Km) remain fixed for all simulations, keeping the frequency

of work as a variable parameter.

The rest of the parameters such as thermal noise are kept by default, as VPI is a very good

program for simulating optical circuits and its default parameters match the standards of

optical systems. A summary of all relevant parameters is presented in table 5.1

Parameter Definition Value

Optical Source Pin Optical power input 1 [𝑚𝑊] (0 𝑑𝐵𝑚)

𝜆0 Wavelength carrier 1.55 [𝜇𝑚]

𝑓0 Optical frequency carrier 193.1 [𝑇𝐻𝑧]

MZM 𝑉𝜋 For each voltage port 1 [𝑣]

ER Extinction ratio 55 dB

IL Insertion Loss 0 dB

m Index modulation 0.15

𝑉𝑅𝐹 RF Amplitude voltage 𝑉𝑅𝐹 =𝑚

𝜋𝑉𝜋 [𝑣]

VB Bias voltage “Design”

𝑓𝑅𝐹 RF carrier [0 to 30 ]GHz

SMF L Fiber Length 𝐿 = 25 [𝑘𝑚]

D Fiber Dispersion parameter 17 [𝑝𝑠

𝑘𝑚 ∗ 𝑛𝑚⁄ ]

Amplifier EDFA Power controlled 1 [𝑚𝑊](10 𝑑𝐵𝑚)

Photodetector Shot Shot Noise On

Th Thermal noise 10 𝑝𝐴

√𝐻𝑧⁄

Table 5.1 relevant parameters selected for RoF simulations

30

To illustrate the theoretical results, all simulations will be done in a frequency sweep

between 0 and 30GHz and with the bias voltage around its optimum value, as given by

equations EQ (4.6), EQ (4.18) and EQ (4.27) for each configuration.

5.2. Simulation of MZM-PP Configuration

The first simulation run is the conventional configuration of the MZM-PP, where the bias

voltage is set at quadrature point. To comply with the formulas of the MZM-PP structure,

𝑉𝜋 must be a half-wave, so the null value point is 0.5 v. Therefore, for the quadrature bias:

𝑉𝐵 =𝑉𝜋

2= 0.25𝑣

Figure 5.2 MZM-PP frecuency respons of |I-RF| signal at Quadrature Point

Figure 5.2 shows the signal at the I-RF output. The bias voltage at the quadrature point

VB=0.25v. As shown, it reaches a maximum amplitude of -10dBm, and at 12.12 GHz, the

signal is completely cancelled out by the fading produced by the dispersion of the fibre.

The simulator is used to find graphically the optimal bias value that is maximizes the RF

power detected, in figure 4.4 a scan is made with the bias voltage parameter and the OCSR

graph is represented.

31

Figure 5.3 MZM-PP Represent The OCSR in funtion of bias voltage.

This graph shows that for VB=0.5v, i.e. 𝑉𝐵 = 𝑉𝜋 it is OCSR=0 since this cancels out the

optical power of the carrier This confirms that for MZM-PP the null point is achieved with a

push-pull voltage of 0.5 V. The optimal bias value is when OCSR=1 is when VB=0.483 v

thus confirming the calculated theoretical value.


𝜋tan−1 √8

𝑚 = 483.13𝑚𝑉

The simulation is run again with VB-opt, figure 5.3 (red) shows that the I-RF achieves the

maximum amplitude.

Figure 5.3 Comparative between |I-RF| VB=0.25v at QP (blue) and VB=0.483v (red)

Figure 5.3 shows the results of the I-RF current, adjusting the bias voltage to the

Quadrature point (blue) compared with its optimum value (red), we can conclude that we

have a gain of 10dB with its optimum value, but the signal nulls are produced at the same

frequencies independently of the bias value.

In an RoF system, the MZM-PP configuration is easy to implement and presents low

complexity but it is limited, as it can be seen in figure 4.5, it only can guarantee the

maximum capacity if our frequency of work is below 9GHz or in a range from 15GHz to

20GHz for example. If the frequency of work is 12.12GHz, the MZM-PP configuration is

completely useless.

5.3. Simulation of MZM-DD Configuration

As well as the MZM-PP simulation the optimal value of the bias voltage is sought with the

OCSR representation, in this case, in the dual-drive configuration, the null carrier point is

found at a bias voltage 𝑉𝐵 = 𝑉𝜋 = 1 𝑉.

32

Figure 5.4 MZM-DD Represent The OCSR in funtion of bias voltage

Similar to the previous case the bias voltage optimum is when OCSR=1. In figure 5.4 this

value is found in VB = 0.965 V. It is verified that it coincides with its theoretical value:


𝜋cos−1 𝑚

√8 =

2

𝜋cos−1 0.15

√8 = 966.2 𝑚𝑉

Now, the frequency response of the I-RF current with 𝑉𝐵−𝑜𝑝𝑡 is simulated

Figure 5.5 MZM-DD frecuency respons of |I-RF| signal with optimal bias voltage

Figure 5.5 shows that the I-RF current achieves the maximum amplitude, but it presents

attenuations at the same frequencies as in the case of the MZM-PP. however, with the

MZM-DD configuration, these attenuations can be avoided by adjusting the bias voltage.

To study how the signal is modified with these settings, the bias voltage 𝑉𝐵 − 𝑛𝑜𝑐ℎ is

adjusted using the theoretical equation:

𝑉𝐵2 − 𝑛𝑜𝑐ℎ = 𝑉𝜋 [(2𝑛 + 1) +2𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐]

33

The frequencies selected are one with a certain amplitude and another with a null signal,

Table 5.2 shown the result of the 𝑉𝐵2 − 𝑛𝑜𝑐ℎ calculated at these frequencies.

D=17ps/km*nm ; 𝜆0 = 1.55𝜇𝑚; L=23km ; 3 ∗ 108𝑚/𝑠 and 𝑉𝜋 = 1𝑣; n=0

𝑓𝑅𝐹 = 9𝐺𝐻𝑧 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧

𝑉𝐵−𝑛𝑜𝑐ℎ 1.5514 v 1.999 v

Table 5.2 numerical values of 𝑉𝐵−𝑛𝑜𝑐ℎ calculated at 𝑓𝑅𝐹 = 9𝐺𝐻𝑧 and 𝑓𝑅𝐹 = 9𝐺𝐻𝑧

Figure 5.6 MZM-DD compares VB-optima (Red) with VB-noch at 12.12GHz (Black) and with VB-noch at 9

GHz (Green)

Analyzing the comparisons in figure 5.6 shows that by modifying the bias value to avoid

attenuation at a selected frequency, the behavior of the signal amplitude is affected, and

therefore it is no longer maximum.

In Figure 5.6 (red) we see that at the frequency where there was a null, now the amplitude

has been improved to reach the value around -10dBm figure 5.6 (Black), however, in

Figure 5.6 (Green), it can be observed that the change is not more favorable than the

original signal.

In conclusion, the MZM-DD configuration may avoid the cancellation of the signal at our

frequency of work, but if the frequency shows a small attenuation, it is more efficient the

MZM-PP configuration. However, the advantage of the MZM-DD configuration is a flat

response around the operating frequency, making it possible to transmit the signal over a

wider bandwidth.

34

5.4. Simulation of MZM-DP Configuration

The third RoF system simulated is the MZM-DP configuration, which consists of nesting

two small MZMs with the same structure as the MZM-PP each.

the upper drives the RF signal with the first bias voltage 𝑉𝐵1, the second bias voltage 𝑉𝐵2 is

connected to the DC voltage of the lower MZM, at the output from this the third bias voltage

𝑉𝐵3 is connected.

This design is more complex than the others, adds more bias voltage variables giving more

freedom of configuration to obtain a better frequency response at the output of the

photodetector.

The first design criterion is to eliminate the carrier frequency coming from the upper MZM,

for this purpose, the first bias voltage is fixed at a null point, i.e, 𝑉𝐵1 = 𝑉𝜋. Figure 5.6 shows

the spectral density showing only the two sidebands are presented at the output of the

upper MZM.

Figure 5.6 MZM-DP shows the spectral density at the output of the first MZM whit 𝑓𝑅𝐹 = 10𝐺𝐻𝑧 and 𝑉𝐵1 = 𝑉𝜋

Same as the previous configurations, the optimal bias voltage which meets OCSR=1 is

calculated.

𝑉𝐵2−𝑜𝑝𝑡 =2𝑉𝜋

𝜋cos−1

𝑚

√8 =

2 ∗ 0.5

𝜋cos−1

0.15

√8 = 483.11𝑚𝑉

Now with 𝑉𝐵1 at a null point and 𝑉𝐵2 at the optimal value, the firs simulation is run with

𝑉𝐵3 = 0𝑉 . The resulting frecuency response of the electrical current |I-RF| is represented

as.

35

Figure 5.7 MZM-DP result of frecuency response of |I-RF| signal with optimal bias voltage and 𝑉𝐵3 = 0𝑉

Figure 5.7 shows the same optimal frequency response as the previous methods. In this

case, the third bias voltage is released for avoid attenuation at the selected frequency whith

its corresponding theoretical equation

𝑉𝐵3−𝑛𝑜𝑐ℎ = 2𝑉𝜋 [±𝑛 +𝐷𝜆0

2𝑓𝑅𝐹2 𝐿

𝑐]

D=17ps/km*nm ; 𝜆0 = 1.55𝜇𝑚; L=25 km ; c= 3 ∗ 108𝑚/𝑠 and 𝑉𝜋 = 1𝑣; n=0

𝑓𝑅𝐹 9 𝐺𝐻𝑧 12.12𝐺𝐻𝑧

𝑉𝐵3−𝑛𝑜𝑐ℎ 1.2757 V 1.5 V

Table 5.3 MZM-DP numerical values of 𝑉𝐵−𝑛𝑜𝑐ℎ calculated at 𝑓𝑅𝐹 = 9𝐺𝐻𝑧 and 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧

36

Figure 5.8 MZM-PD whit VB-opt (red) , VB3-noch=1.27V at 𝑓𝑅𝐹 = 9𝐺𝐻𝑧 (Green) and VB3-noch=1.5V at

𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧 (Black)

Figure 5.8 (red) shows the original frequency response. The bias voltage 𝑉𝐵3−𝑛𝑜𝑐ℎ is used

to avoid attenuation of signal at two selected frequencies 𝑓𝑅𝐹 = 9 𝐺𝐻𝑧 and 𝑓𝑅𝐹 =

12.12 𝐺𝐻𝑧 respectively. It is seen that all of them achieve the maximum amplitude.

37

5.5. Sumary of the three MZMs configurations

Finally, as a summary and for comparison, the frequency response of the |I-RF| signal of

the three MZM configurations is shown in figure 5.9. In blue, the MZM-PP configuration is

shown, with the bias voltage it can be optimized to reach its maximum amplitude but it

shows attenuations and nulls of the signal always at the same frequencies. In red we

feature the MZM-DD configuration whereby adjusting the bias voltage, the nullity of the

signal at the frequency of work can be avoided, but this modification affects the amplitude

of the signal and it no longer reaches its maximum value. Finally, we have in green the

MZM-DP configuration where more bias control variables are added to avoid the null to any

frequency of work keeping the amplitude at its maximum value.

Figure 5.9 Comparison between MZM-PP, MZM-DD and MZM-DP configurations

38

6. SENSITIVITY STUDY

The results obtained in the previous chapter are highly encouraging, especially for

the RoF system with the MZM-DP configuration. In this chapter we will confirm those

expectations in a digital transmission, through measures of BER. The RF signal comes

whit a QAM modulation. The goal will be to find the minimum optical power that guarantees

the correct operation of the different RoF systems proposed. This value will provide the

PONs power budget and hence the number of users that may share a common passive

optical Network (PON).

Figure 6.1 VPIphotonic diagram of RoF whit QAM signal

Figure 6.1 shows a diagram of one of the RoF configuration when the QAM modulation

signal is introduced, in this case the main difference from the previous configuration is the

presence of the new digital block that add the data to the RF configuration.

Simulations are performed over a range of values of optical power at the input of the optical

source and at the EDFA output. The received signal is considered valid for a threshold

𝐵𝐸𝑅 = 10−3 adds because with this threshold there are Soft FEC methods able to reduce

the system BER beyond 10−12 [15]

39

6.1. Design features

Before explaining how these simulations are performed, let us have a look at the design

parameters in table 6.1.

Parameter Value

Bitrate 1Gbps

Sample Rate 64*BitRate

Number of Bits (Nbis) 217

Bits per second (Bps) 2

Bandwibth Bitrate/ Bps = 500MHz

Roll-Off factor 0.18

Up/Down Sample factor 𝑒

𝑆𝑎𝑚𝑝𝑙𝑒𝑅𝑎𝑡𝑒∗𝐵𝑝𝑆𝐵𝑖𝑡𝑅𝑎𝑡𝑒

Input code [I,Q,BitSeq]=IQ_TX(Nbits,BpS,a)

Output code p=IQ_RX(I,Q,BitSeq,BpS)

Optical power Range [-40 to 0] dBm

Table 6.1 properly value of QAM signal

In Figure 6.2 Matlab code takes from table 6.1 as input parameter Bps and Nbits and

generates the sequence of bits corresponding to the IQ components of the QAM

modulation, this sequence is Up sampled to achieve the required sample rate, then

connected to a square root raised cosine pulse with a roll-off factor and fed into the system

with the RF carrier, phase-shifted by 90° for the quadrature component.

Figure 6.2 input data for QAM modulation

40

Figure 6.3 shows the process of IQ component recovery. At the output of the receiver, the

electrical carrier from each component after being mixed with the RF tone at phase and

quadrature is low-pass filtered, goes through square root raised cosine pulse shaping, and

the symbol sequences are down Sampled, the separate bit sequences enter another

Matlab code together with the original BitSeq, the code obtains the received bit sequence,

compares it with the sent data sequence and the probability P is returned.

RoF

Figure 6.3 output data for QAM Modulation

6.1.1. Simulation scenario

As shown in figure 6.4, the simulation is run with a two-level sweep, the first iteration with

the bias voltage. In the second iteration, it searches the power level and displays those

which have a BER less than 10−3 . A matrix of these values is exported from the

VPIphotonic and a short code of Matlab is run to choose the value of optical power that is

closer to 𝑃𝑒 = 10−3. Finally, the optical power level is plotted as a function of bias voltage.

Figure 6.4 Screenshot of simulation sweeps

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6.2. System sensitivity Simulations Results

The systems are reconfigured with the new parameters for data input, and we have run

different simulations setting the working frequency for each of them.

Figure 6.5 frequency response of |I-RF| for all configurations (a) and for MZM-DD and MZM-DP configuration

(b)

Figure 6.5 shows the selected frequencies, for all simulations the frequencies 𝑓𝑅𝐹 = 4𝐺𝐻𝑧

and 𝑓𝑅𝐹 = 10𝐺𝐻𝑧 have been chosen. Already known from the previous study is a fact that

they presents a different power level for the optimum bias voltages shown in figure (a). For

the MZM-DD and MZM-DP configurations figure 6.5 (b), simulations have also been made

at 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧 with corresponding VB-noch tuning. Now we are going to display the

results of power sensitivity for each configuration.

6.2.1. MZM-PP configuration

Figure 6.6 shows the bias sweep as a function of power in the MZM-PP configuration, it is

seen that 𝑓𝑅𝐹 = 4𝐺𝐻𝑧 (Blue) is more efficient than 𝑓𝑅𝐹 = 10𝐺𝐻𝑧 (Orange) but both have

the minimum power around at VB=0.47v. As expected, the simulations at the exact

frequency of the notch did not yield any valid result for sensitivity.

This confirms that with this bias value, the RoF System with the MZM-PP configuration

achieves its maximum efficiency but with restrictions on the operating frequency.

Figure 6.6 Sensitivity response of MZM PP at 𝑓𝑅𝐹 = 4𝐺𝐻𝑧 (Blue) and 𝑓𝑅𝐹 = 10𝐺𝐻𝑧 (Orange)

42

6.2.2. MZM-DD configuration

In the MZM-DD configuration, first, the simulations are performed at the same

frequencies selected in the previous case. Figure 6.7 shows the simulation results

confirming once again that the minimum power is at the optimum bias value, taking

into account that for the dual-drive structure the 𝑉𝜋 is doubled as compared to the

Push-Pull, the optimum bias is at VB=0.96v.

Figure 6.7 Sensitivity response of MZM DD at 𝑓𝑅𝐹 = 4𝐺𝐻𝑧 (Blue) and 𝑓𝑅𝐹 = 10𝐺𝐻𝑧 (Orange)

The second simulation is run setting the bias sweep around the theoretical value that avoid

null at 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧. Figure 6.8 shows the result of the power sensitivity,

Figure 6.8 Sensitivity response of MZM DD at 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧

Figure 6.8 shows that the minimum value is around -21dBm. This power level is too high,

because at this bias value the frequency response of |I-RF| shown in figure 6.5 (b) the signal

remains flat at a higher bandwidth compared to the level of 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧 in figure 6.5 (a).

This may be due to the fact that little bandwidth has been considered for a significant

change to be appreciated, or it may also be because in a simulation scenario the EDFA is

ideal and for a study in the laboratory the results may be different.

43

6.2.3. MZM-DP configuration

Finally, in MZM-DP configuration the simulations are run at 𝑓𝑅𝐹 = 4𝐺𝐻𝑧 and 𝑓𝑅𝐹 =

12.12𝐺𝐻𝑧 the latter with its corresponding bias parameters 𝑉𝐵3−𝑛𝑜𝑐ℎ = 1.27𝑣 . Show the

power level depending on the bias voltage (see figure 5.1). We appreciate that the power

level is minimum at VB=0.47v in both cases as shown in figure 6.9.

Figure 6.9 Sensitivity response of MZM DP at 𝑓𝑅𝐹 = 4𝐺𝐻𝑧 (Blue) and 𝑓𝑅𝐹 = 12.12𝐺𝐻𝑧 (Orange)

This corroborates that the RoF system with the MZM-DP configuration achieves its

maximum efficiency without restrictions on operating frequency.

44

7. Conclusions and future development

As a summary of this work, we have carried out a review of radio over fibre (RoF) systems intending to propose a system that allows reconfigurability and with the lowest possible sensitivity.

We have started with research on the main elements building into an RoF system, the RF signal fading and the dispersive fiber link, and focusing on the transmission process where three transmission configurations have been proposed and mathematically characterised MZM-PP, MZM-DD, and MZM-DP.

A key parameter in order to achieve low values of sensitivity that may allow to extend the power budget of RoF access networks, is the OCSR. We have shown that the optimum value is OCSR=1, and have provided expressions for OCSR for the three transmission configurations studied. Also, expressions for the optical field and Rx photocurrent have been derived and for the fading frequencies and the voltage condition that avoids it.

At the simulation level, the study has comprised setting up and optimizing two simulation scenarios with VPI, one with pure RF signals to compare and confirm the main conclusions steaming from the analytical study and a second one including digital data in QAM format in order to explore the sensitivity values that may be obtained with each Tx. As a main conclusion, we have demonstrated with calculations and simulations that, the optical power can be optimised at a certain frequency for all transmission configurations proposed. MZM-DD configuration can avoid the RF fading for a specific frequency of work, but at the expense of a very poor sensitivity. Also, it has been demonstrated that the MZM-DP configuration can optimise the optical power without frequency restrictions.

Second conclusion, with the sensitivity study we have verified the minimum power that guarantees the correct operation of the three systems. But for the case of the MZM-DD, configured to avoid RF fading, we expected a better response than what we have obtained since it offers higher bandwidth compared to another frequency at a linear level of the signal, however, the power obtained is much higher. This may be due to the fact that little bandwidth has been considered for a significant change to be appreciated, or it may also be because in a simulation scenario the EDFA is ideal and for a study in the laboratory the results may be different.

Here a reduced number of simulations could be presented, but the designed setup could be exploited for obtaining more results with higher data bandwidth, more realistic ER, or higher modulation indices, in order to explore the limits and effects of nonlinearities. Also of interest is the study of coherent receivers and the demonstration of the results of this study in a laboratory setup.

45

8. Referencias

[1] Rappaport, T., Sun, S., Mayzus, R., et al.: ‘Millimeter wave mobile

communications for 5G cellular: it will work!’, IEEE Access, 2013, 1, pp. 335–349

[2] Thomas, V., El-Hajjar, M., Hanzo, L.: ‘Performance improvement and cost

reduction techniques for radio over fiber communications’, IEEE Commun. Surv.

Tutor., 2015, 17, pp. 627–670

[3] Thomas, V., El-Hajjar, M., Hanzo, L.: ‘Millimeter-wave radio over fiber optical

upconversion techniques relying on link non-linearity’, IEEE Commun. Surv.

Tutor., 2015, PP, early access

[4] Beas, J., Castanon, G., Aldaya, I., et al.: ‘Millimeter-wave frequency radio over

fiber systems: a survey’, IEEE Commun. Surv. Tutor., 2013, 15, pp. 1593–1619

[5] Koshy, B., Shankar, P.: ‘Spread-spectrum techniques for fiber-fed microcellular

networks’, IEEE Trans. Veh. Technol., 1999, 48, pp. 847–857.

[6] S. Mas Gomez, J. Caraquitena Sale y P. Sanchis Kilders, “Control de la dispersión cromática en guías

ranuradas nanofotónicas”, Tesis Maest., Esc. Téc. Sup. Ing. de Telecomunicación, Univ. Pol. Valencia,

Valencia, 2009.

[7] B. G. Kim, S. H. Bae, H. Kim and Y. C. Chung, "RoF-Based Mobile Fronthaul Networks Implemented by

Using DML and EML for 5G Wireless Communication Systems," in Journal of Lightwave Technology, vol. 36,

no. 14, pp. 2874-2881, 15 July15, 2018, doi: 10.1109/JLT.2018.2808294.

[8] I. N. Cano, M. C. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol. 25, no. 13, pp. 1242–1245, Jul. 2013.

[9] C. Lim, M. Attygalle.A. Nirmalathas, D. Novak and R. Waterhouse, “Analysis of Optical Carrier-to-Sideband Ratio for Improving Transmission Performance in Fiber-Radio Links”, IEEE Trans. Microwave Th. And Techniques, Vol. 54, No 5, May 2006.

[10] BETTS, Gary E. LiNbO3 external modulators and their use in high performance analog links. Cambridge, UK: Cambridge Univ. Press, 2002.

[11] Fuste, J. A. I., & Blanco, M. C. S. (2013). Bandwidth–length trade-off figures of merit for electro-optic traveling wave modulators. Optics letters, 38(9), 1548-1550.

[12] Zhao, L., Benesty, J., & Chen, J. (2016). Design of robust differential microphone arrays with the Jacobi–

Anger expansion. Applied Acoustics, 110, 194-206.

[13] G. H. Smith, D. Novak, and Z. Ahmed, “Technique for optical SSB generation to overcome dispersion

penalties in fibre-radio systems,” Electron. Lett., vol. 33, no. 1, pp. 74–75, Jan. 1997.

[15] A. Leven, F. Vacondio, L. Schmalen, S. ten Brink and W. Idler, "Estimation of Soft FEC Performance in Optical Transmission Experiments," in IEEE Photonics Technology Letters, vol. 23, no. 20, pp. 1547-1549,

Oct.15, 2011, doi: 10.1109/LPT.2011.2162725.

46

9. Annex I

Single-side Band Configuration

MZM

90ºHybrid

Coupler

𝑉1 = 𝑉𝐵 + 𝑉𝑅𝐹 cos(𝜔𝑅𝐹𝑡)

𝑉2 = 𝑉𝑅𝐹 cos (𝜔𝑅𝐹𝑡 − 𝜋

2) = 𝑉𝑅𝐹 sin(𝜔𝑅𝐹𝑡)

𝜃𝐵 = (2𝑛 − 1)𝜋

2 ; 𝑚 =

𝜋𝑉𝑅𝐹

𝑉𝜋



(𝑒𝑗𝑚 cos(𝜔𝑅𝐹𝑡)𝑒𝑗𝜃𝐵 + 𝑒𝑗𝑚 sin(𝜔𝑅𝐹𝑡))

Jacobi-Anger expansion

𝒆𝒋𝒛 𝐜𝐨𝐬 𝜽 = ∑ 𝒋𝒏𝑱𝒏(𝒛)𝒆𝒋𝒏𝜽

𝒏=∞

𝒏=−∞

n=0, +1

𝒆𝒋𝒛 𝐜𝐨𝐬 𝜽 ≈ 𝑱𝟎(𝒛) + 𝟐𝒊𝑱𝟏(𝒛) 𝐜𝐨𝐬 𝜽

𝒆𝒋𝒛 𝐬𝐢𝐧 𝜽 = ∑ 𝑱𝒏(𝒛)𝒆𝒋𝒏𝜽

𝒏=∞

𝒏=−∞

n=0, +1

Bessel-function

𝑱𝒏(𝒛) = (−𝟏)𝒏𝑱𝒏(𝒛)

𝑱𝟎(𝒛) ≈ 𝟏

𝑱𝟏(𝒛) ≈𝒛

𝟐

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𝒆𝒋𝒛 𝐬𝐢𝐧 𝜽 ≈ 𝑱𝟎(𝒛) + 𝟐𝒊𝑱𝟏(𝒛) 𝐬𝐢𝐧 𝜽



[(𝐽0(𝑚) + 2𝑖𝐽1 (𝑚)cos(𝜔𝑅𝐹𝑡))𝑒𝑗𝜃𝐵 + 𝐽0(𝑚) + 2𝑖𝐽1 (𝑚)sin(𝜔𝑅𝐹𝑡)]



[(1 + 𝑖𝑚 cos(𝜔𝑅𝐹𝑡))𝑒𝑗𝜃𝐵 + 1 + 𝑖𝑚 sin(𝜔𝑅𝐹𝑡)]

𝜃𝐵 =𝜋

2



[cos (𝜋

4) 𝑒

𝜋4 + −𝑚(cos(𝜔𝑅𝐹𝑡) + 𝑖 sin(𝜔𝑅𝐹𝑡))]



[√2𝑒𝑗𝜋4 − 𝑚𝑒𝑗𝜔𝑅𝐹𝑡]



[√2𝑒𝑗𝜋4 − 𝑚𝑒𝑗(𝜔𝑅𝐹(𝑡−𝛽1𝐿)−∅)]

𝐼𝑃𝐷 =ℜ𝑃𝑖𝑛

2

𝑃𝑇[2 + 𝑚2 − √2𝑚 (𝑒𝑗(𝜔𝑅𝐹(𝑡−𝛽1𝐿)−∅−𝜋

4) + 𝑒−𝑗(𝜔𝑅𝐹(𝑡−𝛽1𝐿)−∅−𝜋

4))]


2

2√𝐿𝑀𝑍𝑀

√2𝑚 𝑐𝑜𝑠 (𝜔𝑅𝐹(𝑡 − 𝛽1𝐿) − ∅ −𝜋

4)

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