modulation formats. optical communication systems are carrier systems. this implies that a wave of a...

Modulation Formats

Optical communication systems are carrier systems. This implies that a wave of a frequency much higher than that of the information ( signal) is used to enable the information to be transported through the channel. The range of wavelength overwhich optical communications operate ranging from , say, 1 to 2 μm. This wavelengthrange corresponds to a frequency range 1.5x102 to 3x102 THertz. Remember, 1 THerz=1x1012 Hertz. The bandwidth of the information sources currently available tous is far away from this number. The carrier features should be suitable to propagate in the channel under consideration and the next question is how does a information carrying signal is “loaded” on a carrier to go through the channel?The process that achieves this objective is called “modulation” and has been a subjectof intensive study since the inception of electronic communications back in the 1920s.

Modulation Formats

Modulation is the process of conveying an information signal inside another signal (carrier) that can be physically transmitted. This is

achieved by varying one or more of the properties of the signal that can be transmitted.

Modulation is the process of conveying an information signal inside another signal (carrier) that can be physically transmitted. This is

achieved by varying one or more of the properties of the signal that can be transmitted.

General

There is two classes of modulation processes; analogue and digital.(1) Analogue modulation; a signal is defined as analogue if it is continuous in both

time and any other parameter that characterised it. Then, if that signal is applied continuously on the carrier the outcome is an analogue modulated signal. Mathematically, the concept is defined through the definition of the continuous function. A function f (x) is continuous at x = a if

Modulation Formats

)f(a)f(xlim3.

exists)f(xlim2.

definedis)f(a1.

ax

ax

(2) Digital modulation; a signal is defined as digital if its parameters are allowed totake values that belong to a discrete set of values. A typical digital signal is

3t2for0

2t1for1

1t0for0

Sdefinitionsignal Digital Dig

General

Then, if this signal is applied continuously on the carrier the outcome is a digital modulated signal.

Mathematically, modulation can be seen as a mapping from one domain to another.The figure below illustrates the mapping and its inverse in recovering the information.

Modulation Formats

Information domain

Carrier domain Channel Carrier

domainInformation

domain

M1 M2 IM2 IM1

M1 x IM1 = 1 and M2 x IM2 = 1

The mappings in the figure above appear to be 1:1 but in a real communication system the noise and other impairments destroy the 1:1 mapping and give rise to detection errors. These concepts are illustrated in the next slide.

General

Modulation is a vast subject and by virtue of necessity we limit ourselves to digital modulation as applied to optical communication systems.

Modulation Formats

The concept of one – to - many mapping in communications.

“0” ●

“1” ● Signal processing and channel

“1” ●

“0” ●

Transmitter

ReceiverOne → Many

One → Many

Input alphabet

Receiver decision space

General

The electric field of a e - m wave is given by

Modulation Formats

θ]tω)rk[(jexpPEθ),r,k,P,ω(t,e c

where E is the peak electric field amplitude, P is the polarisation matrix, k is the wavevector, r is the position vector, wc is the carrier angular frequency, t is the time, and θis the phase. The average density of energy flow in the direction of z , intensity = I,of the wave is defined as the time average of the Poynting vector S = Sez.

area)t(watts/uniAP

)t(z,E2Zn

)HERe(21

)tS(z,I2

0

where n the refractive index of the medium, Z0 the impedance of free space (377 ohms), P the power and A the cross sectional area. The units of the intensity is (watts / unit area). In the communication field the optical device of choice is the semiconductor laser. Therefore, the modulation formats possible with the semiconductor laser are of singular importance

General

The complete equation for an e – m wave can be substantially simplified if we limit ourselves to modulation formats for high capacity transmission. Then,

Modulation Formats

θ]tω)z( β[jexpEθ),ω(t,e c0

where β the propagation constant. In optics the symbol k is used instead of β so one should be aware of the implications in terminology. The equation above indicates thatthere are three parameters that can be used to impart information on the optical carrier. [1] Amplitude, EAmplitude, E00; the format that modulates the amplitude of the optical carrier

iscalled “amplitude modulation”. If the information is digital then the format is known as “ amplitude shift keying” or ASK for short. The format is also

known inoptical communications as “on off keying”, (OOK). In terms of the baseband signal the format is known as “non return to zero”, (NRZ). All these terms

are used in the literature without restrictions. The basics of the ASK format is shown in the next slide for a NRZ baseband format.

General

[2] Frequency, ω; when the baseband signal modulates the frequency of the optical carrier the process is called “frequency nodulation”. For digital basebandsignals it is called “ frequency shift keying”, (FSK). In the FSK format the frequency of the carrier changes between “1” and “0”. The difference between the two frequencies is not big but it is sufficient for the receiver to distinguishthe two frequencies and make the correct decisions.

Modulation Formats

time

≈

Am

plitu

de

TbBaseband signal

≈

time

Am

plitu

de

Carrier Envelope

ASK signal

0

1

0

1

The ASK format with a binary NRZ baseband signal.

General

A typical FSK modulated signal is shown in the diagram below.

Modulation Formats

time

≈

Am

plitu

de

TbBaseband signal

time

Am

plitu

de

Constant envelope

FSK signal

0

1

0

1

≈

f0 carrier f1 carrier

The FSK format with a binary NRZ baseband signal with f0 < f1.

Notice the contact envelope of the format in contrast to that of ASK where the short term power depends on the statistics of the baseband signal. This feature

is helpful in designing the dynamic range of subsystems.

General

[3] Phase, θ; the modulation of the phase of the optical carrier is known as “phase modulation”. For digital baseband signals is known as “phase shift keying”, (PSK). In this format the phase of the carrier between “1” and “0” shifts by, say,180o. The actual details depend on the application. The PSK format for a binarybaseband signal is illustrated below.

Modulation Formats

The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 andthe phase of “0” been shifted by π.

GeneralA

mpl

itude

PSK signal

time

≈

TbBaseband signal

time

Am

plitu

de

0

1

0

1

≈

Constant envelopePhase 0 Phase π

The digital modulation formats were presented using a binary baseband signal. However, each format can support multilevel signalling is necessary. For example,A M-ary ASK signal has M -1 discrete “1” levels and the “0” level. Each pulse nowcorresponds to

Modulation Formats

bitsMlogn 2

As a result the M-ary signalling has been reduced to

Bauds/sMlog

BB

2

baryM

With M = 2 the baud rate equals the bit rate, Bb.

General

Modulation FormatsThe constellation conceptUntil now the symbols of “1” and “0” for binary transmission have been defined as levelof, say, voltage or current. There is however an alternative representation that conveys the same amount of information. Consider again a binary signal of “1” and “0” and let us say that they correspond to voltages1 V and 0V that change with time. Then, the complete description is one that contains also the phase, that is, phasors are used for the complete description. The conventional representation is shown below on the left. On the right there is the description using the complex plane. Clearly, both representation contain the same about of information .The representationon the right is called for reason that will become apparent very soon, the “constellation”

“1” (1, angle )V

“0” (0, angle 0)V

Real axisImaginary

axis

●●

Complex plane

1+ j 00+ j 0

(a) Conventional representation. (b) The “constellation” representation

Modulation FormatsThe constellation conceptPerhaps, this example does not demonstrate the power of the new representation. Consider now four voltages corresponding to four signal level represented by ;v1=1+j 0, v2= 0+ j1, v3= -1+ j 0 and v4= 0 – j. The constellation is as shown below andit should be clear now the advantages of the representation. In fact that constellation represents a four level phase shift keying, (PSK), format. Now, let us farther assumethat the PSK four level format encodes bits according the following rule v1=00, v2=01,v3=10 and v4=11. Then, instead of depicting the voltages the symbols can bedirectly represented in the constellation diagram.

Real

Imaginary

●●

●

●

v1

v4

v3

v2

●●

●

●

Imaginary

Real

00

01

10

11

Voltage Symbol

1+ j 0 00

0 + j 01

-1+ j 0 10

0 - j 11

Modulation FormatsThe constellation concept

The constellation diagram in the previous slide showed very clearly the position of thesymbols in the plane. In order to see the impact of transport consider the 4-symbol PSK again but now rotated by 45o and using the unit circle for reference . Notice, thedefined amplitude and phase of each symbol. This is the transmitted constellation.

●●

● ●

00

01

10 11

φ

● 00

01

11

φ

● ●

●

Amplitude

Phase

Amplitude –Random variable

Phase –Random variable

During transmission the constellation has been subjected to random amplitude and phase variations so the receiver has to estimate what was transmitted. See more on the use of signal constellation in assessing performance later.

Intuitively one expects that the available channel bandwidth is efficiently used to transport information. This is achieved by using an efficient modulation format subjectto a number of constrains associated with system design. Some definitions[1] Bit rate; the bit rate defined the rate information is passed forward.[2] Baud (or signalling) rate; defines the number of symbols per second. Each

symbol represents n bits, and has M signal states, where M = 2n. This is calledM-ary signalling. When n = 1, that is, one symbol is used to represents theelements of the alphabet the signal has two states , M = 2. Consider a simple example. A link can transport 50000 bit/s from A to B. The bandwidth of the channel is 4000 Hertz. The spectral efficiency of the link, alsoknown as modulation efficiency, is 12.5 bit/s / Hz.

In spite of the similarity of definitions on spectral efficiency there are two variants that are used; spectral efficiency in bits/Hz and modulation efficiency bits/baud.

Modulation FormatsThe spectral efficiency concept

Consider a system operating at 10 Gbit/s with channel spacing of 50 GHz. The spectral efficiency is 10GBits / 50GHz = 0.2 bits/Hz. In this example the bits/baud is 10GBits/10Gbauds = 1 bit/baud. The effective baud rate (symbol rate) is 10Gbauds.

Modulation FormatsThe spectral efficiency concept

The objective of any communication system is to transfer the maximum amount of information with the minimum bandwidth. The famous Hartley – Shannon law establishes an upper limit for reliable information transmission over a band limited additive white Gaussian noise ,(AWGN), channel. The Hartley – Shannon law can bestated as

Modulation FormatsThe Hartley – Shannon Law

bit/sN

S1logB3.32

2logNS

1logBC 10

10

10

where C the channel capacity in bit/s, B the one sided channel bandwidth in Hz, S/N the signal to noise ratio, (SNR), but not in dB. If the SNR is given in dB it must be converted using the expression

/10SNRdB10NS

The information rate, R, must satisfy the equation

efficiencyspectraltheisNS

1logBR

andbit/sNS

1logBR 22

One useful variant of the Hartley – Shannon law is in terms of the average energy/bit,Eb, (joules /bit) and the AWGN with two – sided noise spectral density N0/2. Then,the signal power is S=Eb R and the noise power N=N0B and


R/B12

NE

bit/s/HzBR

NE

1logBR R/B

0

b

0

b2

Now, Eb/N0 represent the SNR at the receiver in normalise form. The ratio R/B represents the spectral efficiency whose upper limits is C/B. The graph in the next slide illustrates the Harley – Shannon law. The curve corresponding to R = C separates the regions; below the line the spectral efficiencies are potentially achievable but above the curve they are unachievable.

Clearly the question now is how do we calculate the [Eb/N0] (dB) for a given system?AS a simple example consider a 10 Gbit/s with an “on-off” NRZ format whose receiverhas a sensitivity of - 20 dBm for 10-9 BER with detector responsivity R = 1.

Graph of the maximum achievable spectral efficiency [Bit/s/Hz ]as function of Eb/N0 (dB).

Modulation Formats

R < C – Accessible areaR < C – Accessible area

The Hartley – Shannon Law

Spe

ctra

l effi

cien

cy (

bit/s

/Hz)

0.1

1

10

-2 0 2 4 6 8 10 12 14 16 18 20

Eb/N0 (dB)

R < C – Accessible areaR < C – Accessible area

10 GBit/s example:BER=10-9

R > C - Out of bounds areaR > C - Out of bounds area

R = CR = C

Step 1 We convert the power (-20 dBm) into the average optical power; thus


520/103aver opt 101.01010P 1

Step 2 Assuming that the optical power is maximum for “1”, zero for “0” and a

50% probability of ”1” and “0” the peak optical power and energy/bit is

Joules10210100102TPEand

A102IW102P2P15125

bpkoptb

-5max

-5averopt pk -opt

Step 3 The value of N0-rms will be found from the BER. For a BER of 10-9 theratio of peak optical power to rms noise is defined by the Q which is

12for 10-9 BER.

W101.6612102

QP

NNI

Q 65

maxrms0

rms0

max


Step 4 The value of N0 will be found by diving the N0-rms by the receiver bandwidth which for the sake of simplicity is 10 GHz; thus

Hz/W1.6610

N6

016

91066.1

1010

Step 5 The value of Eb/N0 is now

dB10.81210logNE

12.0101.66

102NE

10

dB0

b16

15

0

b 11

Step 6 The spectral efficiency of the system is found by dividing the capacity by

the bandwidth occupied by the spectrum ;since it is a NRZ format the effective spectral width is 20 GHz.

bits/s/Hz0.510201010

BR

9

9

Step 7 In the Hartley - Shannon graph the point for this system is at [8.0,0.5].

This point is plotted in the graph. Be aware that the derived noise spectral density was based on the BER.

There are two key features of spectral efficiency:

[1] Fundamental feature; higher signal-to-noise ratio is required for higher ordermodulation.

[2] Practical feature; the implementation penalties are higher for higher constellations and symbol rates.


Historically, the first modulation format is intensity modulation. The reason for this is the simple fact that semiconductor lasers are electrically pumped and they have very short photon lifetimes. The circuit below is the basic circuit used for the intensitymodulation of semiconductor lasers.

Modulation Formats

Laser

Constant current source: BiasConstant current

source: Modulator

Modulating signal

IbiasImod

P1

P0

Ibias

Ithr

Isignal

Output pulses

ILa

ser

outp

ut

Input pulsesThe diagram on the right shows the electronic and optical waveforms.

Intensity modulation

In addition to a simple transmitter an intensity modulated optical carrier offers the useof a very simple receiver for detection. All it requires is a p-i-n or apd detector followedby a low noise electronic amplifier. This combination of intensity modulated carrier anda p-i-n ( apd) receiver is referred to as “intensity modulated direct detection “,(IMDD),system. Optical communications are used in a large number of diverse applications and IMDD systems constitute the majority of systems used. The simplicity of the direct intensity modulation of semiconductor lasers made possiblethe introduction of optical fibre communications at an early date which required theminimum of technical development. Hoverer, this simplicity brought a number of issues such as; turn-on delay, relaxation oscillations, frequency response issues, frequency chirping and unwanted frequency modulation. But continuous progress in device design and material processing made possible to minimise these issues. Directly modulated lasers cannot perform satisfactory for bit rates above 2.4 Gbitsbecause even with the up to date DFB lasers the impairments, especially dispersion, reduce the performance to such an extent that cost effective systems cannot be designed.

Modulation FormatsIntensity modulation

Measured spectrum of a directly modulated laser under 622 MBit/s NRZ modulation with 0.7 mW between ‘1’ and ‘0’ level.


Spectra calculated for the directly modulated laser under 622 MBit/s NRZ modulation.


Chirped spectrum; black.

Theoretically expected spectrum; gray.

The key issue here is that any attempt to directly modulate the laser impairs its ability to function as a very high quality oscillator. The solution to this problem is the use of external modulators. These are devicesmodulate the optical radiation but they are external to the laser cavity and they do not affect to the first order at least the dynamics of the cavity. The use of an external modulator in addition to isolating the function of modulation from that of the generation of very high quality optical radiation makes also possible to use modulation schemes not supported by direct modulation.


The discussion on modulation formats will be based on an external LiNbO3 modulator.There are two reasons for this choice; firstly the devices and technology are mature and deliver excellent performance and secondly it can deliver all the modulation formats to be discussed. The basic outline of a amplitude travelling wave modulator isshown below. The choice of a travelling wave modulator is dictated by bandwidthrequirements.

Modulation Formats

Waveguide

Electrical Contacts

Ein Eout

Ein / 2

kEin / 2

v1(t)

v2(t)

))V)/(tv(j πkexpV)/(tvexp((j π2

E)(texp(j φk)(texp(j φ

2E

E π2π1in

21in

out

The equation of the operation of an amplitude modulator also known as Mach-Zehnder(MZ) is given by,

Technology - Modulators

With k = 1 the normalised output is written

Modulation Formats

(chirp(modulationphase

π21

modulationampitude

21π

out V(t))/v(t)(vπexp(j(t))v(t)(v2Vπ

cose

and with v1(t) = - v2(t) the phase term is removed and

)(tv

Vπ

cosPP)(tvVπ

cose 1π

2inout1

πout

The details of the operation of a MZ amplitude modulator depend on the bias point of the device. In the next slide the power vs. input signal is shown. In the simplest application the device is biased at the point where the output power is half. This pointis also known as the quadrature point. Then a drive peak-to-peak signal of Vπ is applied and the output swings between zero and full power. Different bias points enable the use of different modulation formats.


One word of caution regarding the biasing point. Because of the material the bias pointdrifts and careful design is necessary for ensuring the stability of the bias point. One of the key features of modulation schemes is the bandwidth after modulation.

Modulation Formats

Vπ 4Vπ

3Vπ2Vπ

0 π● ● ●●

Drive voltage

M -

Z M

odu

lato

r o

utp

ut

Quadrature point

Power

Field

The field and power output vs. drive voltage of a M - Z modulator.


Modulation FormatsTechnology - Modulators

The architecture of a Mach – Zehnder modulator; from Photline

Left ; the basic modulator.

Right ; the modulator with driver, terminating load and monitoring

photodiode.

The architecture of an optical transmitter using an external modulator is, as expected,more complex than that of a direct modulated one. The block diagram of a frequencystabilised laser with a co-packaged external modulator is shown below.

Modulation Formats

Frequency stabilised DFB laser

Optical isolator

External modulator

Electronic amplifier

Data

High quality optical connector

Device fibre tail

Laser TE Controller

Transmission fibre TE element

Constant current bias source

Laser package

Tem

pera

ture

Pow

er to

TE

Power monitorBias current


The ASK format is a very popular formats because of its simplicity and flexibility. In some of the literature the term “on-off keying”, (OOK), is used instead. Starting with a binary baseband signal one distinguishes two classes of ASK signalling:

[1] Non - return to zero format , (NRZ).[2] Return to zero format, (RZ).

[1] Non – return to zero format; in this format the duration of the pulse (Tp) equals the signalling interval (Tb) which is the inverse of the bit rate, Bb. A unity amplitude NRZ pulse is shown below.

Modulation FormatsASK signalling format

Tp

Tb

time

A

Tb/2-Tb/2

For a NRZ pulse the MZ is biased at quadrature and the input signal swings themodulator drive voltage between zero and Vπ.


0

0.2

0.4

0.6

0.8

1

2.6 3.6 4.6 5.6 6.6 7.6 8.6 9.6 10.6 11.6 12.60 Vπ 4Vπ3Vπ2VπDrive voltage

M -

- Z

pow

er

tran

smis

sion

● ● ● ●

Bias

Vπ / 2

Signal drive

Phase 0 Phase π

The biasing and drive of a M-Z modulator for the NRZ format ASK format.

Biasing the M-Z at the quadrature point and driving with a signal of Vπ amplitude the optical carrier swings between zero and the maximum value E0.


One of the most important features of a carrier system is the bandwidth after modulation. This feature is particular important in the context of WDM systems. For arandom binary stream of data in the baseband with equal probability for “1” and “0”and with each pulse modelled as a rectangular pulse the baseband signal powerspectral density, (PSD), is given by the two sided function,

,-:fwith)δ(f

4A

)Tf( π)Tf( πsin

T4A

)(fS

spectrum tingDeterminis

2

spectrumContinuous

2

b

bb

2

baseb

The one sided PSD of this function is shown in the next slide with A = Tb = 1. Notice that the impulse at f = 0 carries half the power on the baseband signal and this is oneof detrimental features of NRZ format because the power Is not used for information transmission.

The PSD of the random unipolar signal for a NRZ rectangular pulse stream.


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2 2.5 3

2

b

2

)f( π)fsin( π

T2

A

)δ(f2

A2

1 bTA

f

PS

D

21

)Pr(0)Pr(1

When the baseband signal modulates the carrier the combined signal can berepresented as

Modulation Formats

)t)exp(j ωa(tE)(ts c0c

The two - sided PSD of the modulated carrier is now given by

0kwith)Tk

(fδ)Tk

(sinc8TE

)fδ(f)fδ(f8

E)f(fsinc)f(fsincT

8E

)(fS

bk b

2

b

20

cc

20

c2

c2

b

20

carrier

Since sinc2(f ± fc) = 0 the summation over k is zero. The one sided PSD of the ASK signal is shown in the next slide. The bandwidth after modulation is ≈ 2Bbase. This should not be a surprise because this a key feature of amplitude modulation ingeneral.

ASK signalling format


The PSD of a binary ASK signal in the optical domain.

fc f

Bandwidth ≈ 2Bbase

Scarrier(f)

90% of power

95% of power

fc = optical carrier

Deterministic signal

Stochastic signal

4E2

0

b

20 T

4E

The modulation spectrum of a Mach – Zehnder modulator at 2.5 Gbit/s.


It is very instructive to construct the state and constellation diagram for the binary ASK signalling format.


●●

State “1”State “0”

“0” “1”

“1 to 0”

“0 to 1”

“0” “1”

“0” 0.5 0.5

“1” 0.5 0.5

State diagram

Transition probabilities

State diagram and transition probabilities for binary ASK signalling.

Constellation diagram for binary ASK signalling.

●●

Symbol “0”

real

Symbol “1”E0

imaginary

threshold

The PSD of a binary NRZ ASK signal for 10 Gbit/s data without filtering.


DC impulse

Spectral nulls.

The spectral of NRZ modulation at 10 and 40 Gbit/s.

10 Gbit/s. 40 Gbit/s.


The key features of ASK signalling is that there is a DC term whose energy is not usedand it is difficult to recover timing information with long strings of “1” and “0”. The fact that there will be long strings of “1” and “0” can be deduced from the state diagram of NRZ format. Additionally, NRZ pulses are sensitive to the fibre dispersion.

[2] Return to zero format, (RZ); in this format the pulse width (Tp) is less than thesignalling interval ( Tb). Three typical RZ formats are shown below.


Tb

Tp

time

A

Tp

time

A

Tb

Tp= 50% Tb

Tb

Tp

time

A

Tp= 67% Tb Tp= 33% Tb

The reasons for using RZ pulses are:[1] High timing content.[2] Reduced sensitivity to fibre dispersion.

However, these advantages are not without a price. The bandwidth of RZ pulses is broader than that of NRZ and uses therefore more fibre bandwidth. This becomes anissue in dense WDM,(DWDM), systems. In order to generate RZ optical pulses the M - Z is biased at quadrature and the device is driven with a pulse of appropriate width. For 50% duty cycle the M - Z is biased as per NRZ format. However, as the pulse width is reduced it becomes progressively difficult to generates the narrowpulses required. An alternative approach has been developed using two M - Z in tandem and driven by different pulse streams. The concept is illustrated in the nextslide. The duty cycle of the output format depends on the bias and driving voltage of the sinewave drive. Of course the transmitter is more complicated now but thegeneration of RZ pulses with arbitrary duty cycle is much easier.


In order to generate RZ50 pulses ( RZ pulse of 50% duty cycle) the pulse carver is bias at quadrature and driven by a sinusoid of Vπ peak-to-peak voltage at the data rate. The output pulses have an approximate 50% duty cycle and no additional phase flipping. A RZ33 pulse is created by driving the pulse carver with a 2Vπ voltage (peak to peak) sinusoid at half the data rate, Bb/2, which is biased at the maximum of the transfer curve. Again, there is no phase flipping in the output.


The concept of pulse carver modulator.

CW light

NRZ data

NRZOptical RZ

format

Data MZ Pulse carver MZ

Clock or sinusoid

RZ67 is created by driving the pulse carver with a 2Vπ voltage (peak to peak) sinusoidat half the data rate, Br /2, which is biased at the null of the transfer curve. The key effect of this type of pulse carving is that adjacent pulses always have alternating zero and phase. In other words, the DC tone averages to zero since alternating bits have opposite phase. As a result, the carrier is suppressed on average and harmonic tones at +/- Br / 2 appear . The format is also known as Carrier Suppressed RZ. The state diagram and the constellation for RZ formats is shown below.


State ”0” State ”1”

”0” “1”Tb / D

RZ67 D = 1.5RZ50 D = 2RZ33 D = 3

The state diagram and the constellation for RZ formats.

Symbol “0”

real

Symbol “1”

E0

imaginary

The bias and drive requirements for generation of RZ pulses using the carver concept.


0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10

●

●

●

Phase 0 Phase π

M - Z voltage

M -

Z p

owe

r ou

tput

Vπ/2 2VπVπ 3Vπ 4Vπ

0

Bias

Bias

Bias

RZ67 signal drive

RZ50 signal drive

RZ33 signal drive

The two sided PSD of RZ33 and RZ50 format is given by


The pulses of various RZ formats.

kbb

2

b

b

b

20

carrier )kBδ(fB1/2Tfπ

/2)Tfsin( π16BE

)(fS

For RZ67 the PSD is given by


kbb

2

b

b

b

20

carrier )B2

12kδ(fB1

/2Tfπ/2)Tfsin( π

16BE

)(fS

The PSDs for RZ33, 50 and 67 from computer simulations are shown below.

Mod

ulat

ion

For

mat

s C

onve

rsio

n fo

r F

utur

e O

ptic

al

Net

wor

ks:

Javi

er C

ano

Ada

lid M

Sc

The

sis

, T

UD

, 20

09

In order to understand how the carrier is suppressed with RZ67 one has to consider the impact of phase. The optical pulses and their phase relationship is shown below.


Modulation Formats Conversion for Future Optical Networks:

Javier Cano Adalid MSc Thesis , TUD, 2009

The sign of the carrier is changing at every bit transition and they are completeindependent of the information carrying part of the signal. On average therefore The filed has a positive sign for half the ”1” bits and negative for the other half. This phase changes results in a zero mean optical field envelope. As a result the carrier at the optical centre frequency vanishes giving the format its name.

The concept of ASK can also be used for multilevel transmission. A typical 4-level NRZ ASK format is shown below where the original pulse width is Tb.


A typical 4-level ASK format.

With four levels of signalling the number of bits, n, transmitted by one symbol is lbits/symbo24logn4MforMlogn 22

A typical encoding scheme for a 4 - level ASK is Binary Symbol Binary Symbol

00 0 10 2

01 1 11 3

1

2

3

0

Amplitude levels

time

Tb

The generation and decoding of multilevel signals.


V1

V2

V3

timethresholds

00

01

10

11

V1

V2

V3

timethresholds

00

01

10

11 D-FF 3Q

Q

Q

Q

Q

QD-FF 2

D-FF 1

V3

V2

V1

A

BZPower splitter

D-FF 3Q

Q

Q

Q

Q

QD-FF 2

D-FF 1

V3

V2

V1

A

BZPower splitter

D-FF 3Q

Q

Q

Q

Q

QD-FF 2

D-FF 1

V3

V2

V1

A

BZPower splitter

Power combiner

Stream A

Stream BZ

A B Z

0 0 0

0 1 1

1 0 2

1 1 3(a) Multilevel signal generation.

(a) Multilevel signal decoding.

Experimental eye diagrams for 4-ary ASK signalling; notice how the inner eye shapes and the different optimum sampling times change with distance .


Because the pulse width in the 4 – level ASK is twice that of the initial binary data the symbol rate has been halved to B r /2.Generalising this result to M – level waveforms in which blocks of n-bits are represented by one of the M – level waveform with


n2MNow, each pulse corresponds to

lbits/symboMlogn 2

and as a result the M – ary signalling rate has be reduced to

bauds/sMlog

BB

2

bsymbol

On the face of it by reducing the signalling rate through M - ary transmission we have reduced the requirements on the system parameters..

The bandwidth reduction can be staggering at least theoretically. The table below summarises the reduction in bandwidth.. The B stands for the bandwidth of the originalbinary signal. The ± implies the bandwidth around an notional optical carrier.


Levels of M-ary

Bandwidth

2 ± B

4 ±B/2

8 ±B/3

16 ±B/4

32 ±B/5

64 ±B/6

All seem to be easy, but is it? In order to understand what we have done we have to go back to the binary transmission format and investigate its subtle features.

For a binary format the transmitted constellation and the constellation in the receiverbefore decision are shown below with the effect of noise exaggerated. .


“0” “1”

opt2P

Symbol dynamic range “0” “1”

Noise processes

Detection threshold

Space of “0” Space of “1”

Transmitted constellation Constellation at the receiver decision point

At the receiver decision point noise has been added to the transmitted constellation And in order to minimise the errors in detection the threshold should be set in the middle of the receiver dynamic range. The overlap between the two noise processes give rise to detection errors. Consider now the case of a 4-level ASK with the same power. The new transmitterand receiver constellations are shown in the next slide.

In order to achieve the same detection errors with the reduced dynamic symbol range as in the binary case either the variance of the noise processes must be reduced, unlikely, or the power must increase. The latter usually happens and it is for this reason that M-ary ASK is not as wide spread as perhaps expected. In optical power required for a M - ary ASK format is


“00” “01” “10”

Symbol dynamic range for 4-ary

“11”

Symbol dynamic range for binary

“00” “01” “10” “11”

Noise processes

Detection thresholds

Transmitted constellationConstellation at the receiver decision point

Mlog

1MP

2

M

For example with M=4 the optical power required is 3.3 dB more than that for M = 2( binary).

The basic features of the “phase shift keying”, (PSK), format as shown below.

Modulation FormatsPSK signalling format

Am

plitu

de

PSK signal

time

≈

TbBaseband signal

time

Am

plitu

de

0

1

0

1

≈

Constant envelopePhase 0 Phase π

The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 andthe phase of “0” been shifted by π.

Conceptually, an optical phase modulator is one of the simplest devices. The next slide illustrates the concept of an optical phase modulator.


Driving voltage V0;N peaks of wave.

Driving voltage V1;N+1 peaks of wave.

A travelling wave phase modulator: from: Sumitomo Osaka Cement Co. Ltd.

Basic concept; waveguide 3 - 9 μm depth.

Actual device.

The electrode configuration for phase modulator.

Electrical contacts

x

zy waveguide

X - cut

signal

ground ground

waveguide

Z - cut

zy

x


The phase shift induced by the applied voltage is given by


ΓgV

rnλLπ

Δφ 333e

where L; the length of the device, ne; the extraordinary index, r33; the electro-optic coefficient , V; the applied voltage, g; the distance between the two electrodes and Γ; the overlap integral value. For LiNbO3 at 1550 nm ne = 2.15; r33=30.8 x 10-12 m/V and Γ ~ 0.3 to 0.5. With symmetric drive V is replaced by V/2. Defining Vπ as the value for which the phase shift is π

L)r(n/ gλV 333eπ

the phase shift can be written as

πVV

2π

Δφ

For fibre communication modulators Vπ ~ 4 - 5 V.

The transmitter for “Binary PSK” (BPSK) with coherent detection is very simple.


.

CW optical source

Binary phase modulator

Binary data

Phase modulated light

On the phase of it seems that nothing more is required for BPSK with coherent detection. However the issues will emerge if one looks at the details of the operation of the modulator. For this the relation between voltage and phase shift is required;

ΓgV

rnλLπ

Δφ 333e

πVV

πΔφ

It is clear that to get a phase shift of π rads V=Vπ is required. But, if the voltage fluctuates around Vπ or if the phase of the carrier changes it will distort the constellation of BPSK. If unchecked the fluctuations will have a serious impact on detection.


The impact of a fluctuating phase of an optical carrier.

For the BPSK format the optical field is given by

)))(tφtj( ωexp(E)e(t cc0

where only the phase φc(t) is modulated by the data

n

bnc )nTp(tαπ)(tφ

where the random variable αn= 0 or 1 depending on the data sequence. For αn= 0

))tj( ωexp(E)(te c01

Ideal constellation. Perturbed constellation.

π π0 0φ1

φ2φ3

threshold


and for αn= 1)(te-))tj( ωexp(E-))πtj( ωexp(E)(te 1c0c00

The state diagram of a BPSK format is shown below. Some key observations can now be made.

0 1

1

0

Phase

Intensity

Time

For a genuine random source of information the number of consecutive “1” and “0” can be very large and consequently the phase of the source will fluctuate leading to detection problems. One other key feature of the BPSK with a phase modulator is that it is a continuousenvelope format. Yes, the phase changes from “1” to “0” but the power, Popt, stays the same per bit and the energy per bit, Eb, is


b

bcb

2c

b

2c

opt T2E

AT2

AE

2A

P

Also, from the information point of view BPSK is a symbol per bit format. It will be more productive to reassigned the set of the input bit set {1,0} to the symbol set (1,-1},that is, phase for “1”= 0 and phase for “0” = π. Another key feature of using a phase modulator in the chirping introduced as the drive signal changes. This chirping forces the optical way to move along the unit circle rather than straight from 0 → π and π→ 0. It is customary to express the constellation in terms of the energy /bit; see next slide. The signalling for NRZ and RZ pulses is shown in the next slide.

The constellation in terms of energy per bit. The Euclidean distance is now twice that in ASK signalling leading to a better S/N ratio.


0 1

1

0

Phase

Time

bEbE

d

Euclidean distance bE2d

The power spectral density of the BPSK - NRZ format is


≈

+1

-1

≈

+1

-1

time time

1 1

-1 -1

1 111

BPSK – NRZ format BPSK – RZ format

e(t) e(t)

2

2cbase Tfπ

TfπsinTA(f)S

The important observation is that because the average phase is zero there is no DC term which means that all the power is available for signalling. When the baseband modulates the carrier again there is no power in the carrier. This form of signalling isknown as “suppressed carrier signalling.”

The single sided PSD of a BPSK – NRZ format; bandwidth ~ 2Rb.


fc f

Bandwidth ≈ 2Bbase

Scarrier(f)

90% of power

95% of power

fc = optical carrier

Stochastic signal

b

20 T

2E

The PSD of a RZ-50% BPSK pulse is shown in the next slide together with the PSD of BPSK with NRZ format.

The spectra of BPSK with NRZ and RZ - 50% pulses.


22c

base T/2fπT/2fπsin

2TA

(f)S

0

0.2

0.4

0.6

0.8

1

-3 -2 -1 0 1 2 3fT

Scarrier(f)

BPSK - RZ 50%BPSK - NRZ

The spectral densities for BPSK have been calculated for rectangular pulses, without filtering before modulating the carrier and modulators without frequency chirping.If these conditions apply then the electrical and optical spectral are the same. However, if this is not the case then the electrical and optical spectra differed to adegree that depends on the filtering and the chirping. The absence of the carrier inthe BPSK format makes the carrier recovery in the receiver difficult. The BPSK format can be slightly modified by transmitting a residual carries element. This is achieved by not modulating the carrier by π- rads but at say 0.9 π rads. Then the constellation becomes;


Suppressed carrier constellation

Residual carrier constellation

Φ=π

Φ < π

0

The architecture of a RZ BPSK transmitter is similar to the one used in ASK.


CW light

NRZ data

NRZOptical RZ

format

Pulse carver MZ

Clock

Phase modulator

Schematic of a RZ BPSK transmitter architecture.

The key assumption underlining the development of the concept of BPSK is that thephase of the carrier evolves as a constant vs. time. This implies an optical oscillator ofzero linewidth and a great stability. In general these conditions cannot be met in practice and a solution has emerged through signal processing.

The study of PSK signalling will be concluded with the study of the differentiallyencoded PSK, (DPSK). With the PSK format the information is embedded in thephase of the carrier so in order to retrieve the information a detection system sensitiveto the phase must be used. Such a system is refer to as “coherent” and the receiver isvery complex compared to the ASK receiver. One way to recover informationembedded in the phase of the carrier without a coherent receiver is to encode theinformation before modulation “differentially”. To understand the process consider adata stream that for PSK signalling the “1” are associated with 0 - phase and the “0”with π – phase. Then,


Data 1 0 1 1 0 1 0 0

Transmitted phase 0 π 0 0 π 0 π π

The key feature of this table is that the data set the phase.

To demodulate a binary PSK signal the receiver has to have a local oscillator synchronous with the oscillator in the transmitter. However, the carrier phase can be recovered only with a synchronous receiver but also by using the phase of the transmitted carrier itself. This is the basic idea behind the differential PSK.The basic algorithm for DPSK is


addition2moduloindicateswherexyy i1ii

where xi the current bit (symbol) and yi-1 the last transited symbol (bit). Now all the x’s arriving to be transmitted are independent but the encoding process introduces a correlation between the y’s and x’s at the output of the transmitter. At the receiver thedecoding is simply,

quanityestimatedanindicatesxwhereyyx i1ii~~~~

Now, xi depends not one the absolute value of y’s but on their difference. That means that if the constellation is rotated for some reason in the channel the correct data can still be detected if the difference does not change. The circuit diagram of a differential encoder / decoder is shown overleaf.


Differential encoder.

Logic circuit for differential encoder.

Delay Tb

iy~ix~

1-iy~

i1ii yyx ~~~

Delay Tb

xi yi

yi - 1

i1ii xyy

Differential decoder.

I1 I2 Out

0 0 0

0 1 1

1 0 1

1 1 0

Modulo-2 addition - Exclusive OR

i1ii xyy i1i1 yyx ~~~ Sometimes the expressions are found in the literature.and

Delay flip-flop

xi

yi

yi - 1

XORAND

Negative AND

i1ii1ii xyxyy

Delay flip-flop

xi

yi

yi - 1

XORAND

Negative AND

i1ii1ii xyxyy

.


K -1 0 1 2 3 4 5 6 7

Xk 1 0 1 1 0 1 0 0

Yk 1 0 0 1 0 0 1 1 1

1 0 0 1 0 0 1 1 1

1 0 1 1 0 1 0 0

where k-1 the reference digit, and the estimated yk and xk. If for some reason the channel inverts the polarity , that is, the y - sequence is the one’s complement then the original signal can still be recovered ( next slide).

Consider the following table as an example of differential encoding

Decoding with correct channel polarity.

ky~

kx~

ky~ kx~

If the PSK format is used to transmit a binary sequence without differential encodingthe format is known as “binary PSK” ( BPSK). When differential encoding is added then it becomes “differential binary PSK” ( DBPSK).

k -1 0 1 2 3 4 5 6 7

Xk 1 0 1 1 0 1 0 0

yk 1 0 0 1 0 0 1 1 1

y*k 0 1 1 0 1 1 0 0 0

x*k 1 0 1 1 0 1 0 0


Sequence invertedReference digit

Decoding with inverted channel polarity.

It is now straightforward to translate this encoding scheme to PSK. The basic rule isthat if the current input signal and the previous encoded signal are the same ( no change) the phase of the carrier does not change. If they are different the phase changes. The table below summarises the encoding and decoding process.


k -1 0 1 2 3 4 5 6 7

xk 1 0 1 1 0 1 0 0

yk 1 0 0 1 0 0 1 1 1

Phase 0 0 π 0 0 π π π

Received signal

1 1 0 1 1 0 0 0

Complement 0 0 1 0 0 1 1 1

Decoded 1 1 0 1 1 0 1 0 0

The architecture of a DBPSK transmitter is shown below.


CW light

Synchronisation

NRZOptical RZ

format

Pulse carver MZ

DBPSK encoder

Phase modulator

Data

Tb

Clock or RF

The constellation and state diagram is shown overleaf.

The constellation and state diagram of the DBPSK format.

1 1

0

0

Phase

Intensity

Time


The phase modulator is a simple device but its features do not lead to a simple transmitter because of the control circuits required. However, the MZ amplitude modulation can also be used for phase modulation.

The additional processing in the transmitter required for the DBPSK format pays dividend at the receiver where the simplicity for a phase modulated format is staggering. Consider the following example.


From: Iidefonso M. Polo1 October 2009SUNRISE TELECOM. com

Direct detection receiver for the DBPSK format.


1/Tb

A

BDI

tran

smis

sion

Optical frequency

Tb

Delay interferometer

A

B

Direct detection receiver


modulationPhase

π21

modulationAmplitude

21π21out )/2V))(tv)(t(v(j πexp))(tv)(t(v)/2V( π(cos))(tv,)(t(ve The transfer function of the MZM is given by

With v1(t) = - v2(t) the phase modulation is removed and ))(t(v)/V( π(cosPP))(t(v)/V( π(cos))(tv,)(t(ve 1π

2optopt1π21out

For phase modulation the MZ is biased for zero output without signal and then drivenby 2Vπ. The phase modulation is induced as the drive moves the modulator right and left of the bias. However, as the modulator moves from 0 to π phase a dip in the intensity occurs as it crosses the 0 - power line. The operation is similar to that of a MZ driven by a duobinary signal. The next view graph summarises the operation of the MZ as a phase modulator. It must be born in mind that the operation described is the theoretical one and the performance could deteriorate with real drive signal. However, because of the nonlinear transmission function of the MZ ameliorates the impact of overshoots and undershoots in sharp contrast to a phase modulator here all the imperfections pass on straight on the phase of the carrier.

The operation of the MZ modulator as phase modulator.

Vπ 4Vπ3Vπ2Vπ

π

time

0 ππ

Out

put

pow

er

Drive voltage

Difference v1(t) - v2(t)

Intensity dips

Optical power

Optical field

time

2Vπ


v1(t)

- v1(t)

CW light Phase modulated light

Vπ for zero transmission

The use of DBPSK offers the possibility of simple good performance systems but it also offers further possibilities if combined with advances in technology. Consider the MZ configuration shown below.


VPM =-Vπ/2

vQ(t)

- vI(t)

Phase modulator

CW light

Phase modulator I

Phase modulator Q

DQPSK modulator

vI(t)

- vQ(t)

Each individual MZ modulator ( I & Q) operates as a phase modulator. The phase modulator after the Q-modulator introduces a rotation of π/2 rads that give rise to theterm “channel in quadrature”, (Q – channel ), the other channel is known as “ channelin phase”, ( I - channel). This form of signalling is known as “Differential Quadrature PSK”, (DQPSK). To see how the modulator works assume that the transfer function ofeach MZ is given by


πinout V

)v(tπcose)(te

π

I

π

Q

1

π

Q2

π

I2in

π

Q

π

Iin

π

Q

π

Iinout

V)(tv

πcos

V

)(tvπcos

tanjexpV

)(tvπcos

V)(tv

πcose

V

)(tvπcosj

V)(tv

πcose

)2π

(exp(jV

)(tvπcos

V)(tv

πcose)(te

and expanding

Now, if VI and VQ take one of the values {0,π} then the phase shift induced on the input signal ein takes one of the four values as shown in the table below.


vI(t) vQ(t) cos (πvI(t) /Vπ) j cos (πvQ(t) /Vπ) tan -1 (cos(π vQ (t)/Vπ)/ cos (π vI(t)/Vπ)

0 0 1 1 π/4

0 Vπ 1 -1 -π/4

Vπ 0 -1 1 3π/4

Vπ Vπ -1 -1 5π/4

The constellation diagram corresponding to this format is shown on the right:“0”→ voltage level 0and “1” → voltage level Vπ.

I - axis

Q - axis(I,Q) = (0,0)(I,Q) = (1,0)

(I,Q) = (1,1) (I,Q) = (0,1)

π/4

-π/4

3π/4

5π/4

It should be clear now that QPSK can be combined with differential encoding forDQPSK. The figure below summarises a measured constellation for 40 Gbit/s DQPSKwithout dispersion.


The constellation diagram for a 40 Gbit/s DQPSK format without dispersion.

Comparison of spectrum of NRZ and DQPSK at 10 Gbit/s data rate.

The DQPSK format operates at 20 Gbauds but single each channel operates as half the bit rate the impact of chromatic dispersion and polarisation mode dispersion Is limited compared to the full bit rate systems. This can be extended by using dual polarisation QPDK. The modulator for such a format is shown below.


The approach appears to be wasteful in terms of hardware but in transmitting at the data rate of 40 Gbit/s but at the symbol rate of 10 Gsymbolsthe effects of dispersion are suppressed.

Frequency shift keying ( FSK) has been used extensively in radio communications but its use in fibre communications has been limited to research only. The reason forthat is simple; there is no optical source that can be frequency modulated in excess of 10 Gbit/s and maintain capabilities for long haul transmission. The obvious candidate is the semiconductor laser and a lot of effort was directed towards frequency modulated lasers but the rapid increase in speed helped to consolidate the LiNbO3

technology as the key technology for high speed long haul systems. So, all the recent effort has been directed towards that technology.In FSK the information is embedded in the carrier by shifting the carrier frequency, ω0 itself;

Modulation FormatsFSK signalling format

)( 00c φ)tΔω)ω((j(expERe)te(

For a binary digital signal ω0 takes the values [ω0 – Δω] or [ω0 + Δω] depending on a “0” or “1” bit been transmitted. The frequency 2Δf separates in the frequency space the symbols “0” and “1”. The total bandwidth of the modulated carrier is givenapproximately by

2Bf2ΔFSK BW

where B the bandwidth of the information. Two classes of FSK are distinguished:[1] Wideband FSK; Δf >>B and the bandwidth approaches Δf ;[2] Narrowband FSK; Δf << B and the bandwidth approaches 2B.One of the difficulties in directly modulating the leasers, say DFBs, is the impact of FSK modulation on the amplitude modulation imparted on the field. In a relatively recent , 2004, Alcatel Lucent experiment the penalty due to the intensity modulation was set at 1 dB. That constrain limited the drive to 600 mV at 50 ohms leading to a peak-to-peak current of 12 mA. With an FM efficiency of 400 MHz/mA the peak-to-peak frequency swing is 4.8GHz and this is approximately 50% of the bit rate that was 10Gbit/s. The eye pattern below shows the intensity fluctuations at the output ofthe laser.


The eye at the output of the laser- amplitude modulation.

The eye at the output of the FSK-AM detector; a MZ interferometer with 11GHz FSR.


Tuneable lasers can offer an alternative approach to FSK modulation. Consider thestate of the art sampled grating Bragg grating laser (SGDBR) illustrated below.

The section of the laser that controls the phase can be modulated by a binary sequence giving rise to FSK modulation. However, since lasers of that class were designed for wide tuneability their performance does not addresses the requirements for data FSK transmission. The FSK capabilities of one such laser were assessed and some results are quoted in the next slide.

Output frequency vs. phase section current at 192.2 THz.


Time averaged spectrum of FSK modulation at 192.2 THz ; Δf= + /- 5GHz.

12 GHz / ma

+5 GHz-5 GHz

f0 = 92.2 THz

Up to now all the modulation formats studied generate a double sides spectrum. For example consider the ASK format for 40 Gbit/s. The residual carrier is a waste

Modulation FormatsSingle Sideband signalling format

The spectral of NRZ ASK modulation at 40 Gbit/s.

Residual carrierUpper sideband

Lower sideband

and other signalling formats suppress it. Then, there is the upper and low sidebands but only one sideband existed in the original baseband signal with a bandwidth of 40 GHz.( see figure on the left). The question now arises; is the lower sideband necessary? Mathematics; for any real value signal function f(t) there is ”conjugate symmetry” in the Fourier transform, that is,

Original baseband signal

)ω(F)ω(F

and all the information embedded in f(t) is contained in either the positive or the negative frequency components. The conjugate symmetry exists because the

Fourier transform of a real function is Hermitian. Only a single sideband needs to be transmitted. To illustrate this concept consider the details of thediagram on the right. Let assume that themodulation signal is a real time function given by x(t) and let us define the analyticsignal ( see appendix B)

Modulation Formats

ωωm0- ωm

ωc- ωc 0

- ωc ωc0

- ωc ωc0

- ωc ωc0

F(ω)

Upper sideband Upper sideband

Lower sideband Lower sideband

Double sideband SC

Upper sideband only

Lower sideband only

Reconstructed signal F(ω)

.

)(txj)(tx(t)xaˆ

The Fourier transform of the analytic signal is

0f)(f2X)(fXa

When xa(t) modulates the carrier exp(j2πf0t)the frequency components are shifted by +f0 and there are no negative frequencies.

Single Sideband signalling format

Single Sideband signalling formatModulation Formats

The output spectrum of a lower sideband transmitter;P.M. Watts et al., ECOC 2005, Paper TU 4.2.4

CarrierLower sideband

rb=10Gbits

The Hilbert transformer was implemented using a four tap FIR digital filer;

6)(nx3π2

4)(nxπ2

2)n(xπ2

n)(x3π2

n)(x ˆ

where x(n) is the input data sampled at twice the bit rate.

Single Sideband signalling formatModulation Formats

Advantages: [1] The filter is realisablerealisable.[2] The residual carrier makes possible the detection without a coherent receiver. [3] The interference from the lower sideband is manageable. [4] It is possible to use electronic dispersion compensation at the receiver because

the phase information is preserved.

This approach is also called vestigial sideband and used extensively in radiocommunications. A number of successive experiments has taken place where a fibreBragg filter is used as the optical filter because of its excellent performance.

ω0ω

Filter

ωω0

FilterResidual carrier

Interference from the lower band

SSB

In order to detect the information embedded on the optical carrier the receiver must besuitable equipped. In this part of the module the architectures of suitable receiverswill be discussed. Before we embark on the stude of receiver architectures it is important to introduce theclasses of detection and their ramifications. Since optical communications are carrier communications with the carrier frequency vastly larger than the information bandwidth the receivers cannot directly detect theoptical frequencies as it is common in radio and microwaves. The detailed study of optical detection, that is the interaction between radiation andmatter, belongs to quantum mechanics. However, in field optical communications the essentials of the interaction can be derived without recourse to quantum mechanics. This is achieved by assuming that the electric filed incident on the detectoris classically described but the response of physically realisable detectors is modelled using the same statistics that a quantum mechanical model would have provided. This“quantum mechanically correct” detector response is then mused as the fundamental observable quantity on which the decisions are based. These receivers are called “semi classical” and have the advantage of using well known detection techniques.

Modulation FormatsThe detection of modulated optical carriers

Under the constraints imposed by the semi-classical approach the photocurrent of an optical detector is given by


hf

)t(Pne)t(i opt

qp

where e; the electronic change, nq the ability of the device to concert photons into electrons known as the quantum efficiency and nq <1, Popt(t); the envelope of theoptical radiation, h the Planck constant and f the frequency of the radiation. Since hf Is the energy of one photon the ratio (Popt / hf) is the number of photons in Popt. The simplest possible receiver is based on this equation and the detection class is known as “direct detection” and the receiver as “direct detection receiver”.

The basic architecture of a direct detection receiver.

Optical envelope

Optical detector Low noise

amplifier

)t(ipElectronic

signal

time

time

hf

The direct detection is based on the assumption that information is embedded in the amplitude of the optical carrier, that is, ASK modulation. If the information isembedded in the phase of frequent of the carrier direct detection will not detect it and instead it will follow the envelope of the radiation. In general to detect information embedded in the phase or frequency a new class of detection must be used known as“ coherent detection”.

Coherence is a property of waves that measures the ability of the waves to interferewith each other. [1] Two waves that are coherent can be combined to produce an unmoving distribution

of constructive and destructive interference (a visible interference pattern) depending on the relative phase of the waves at their meeting point.

[2] Waves that are incoherent, when combined, produce rapidly moving areas of constructive and destructive interference and therefore do not produce a visibleinterference pattern. These features are illustrated in the next slide.



Coherent waves (monochromatic). Incoherent waves of the same frequency (monochromatic).

Incoherent waves with different frequencies (not monochromatic).

A wave can also be coherent with itself, a property known as temporal coherence. If a wave is combined with a delayed copy of itself (as in an interferometer), the duration of the delay over which it produces visible interference is known as the coherence time of the wave, Δtc. From this, a corresponding coherence lengthcan be defined;

cc Δtnc

Δx

The temporal coherence of a wave is related to the spectral bandwidth of the source. A truly monochromatic (single frequency) wave would have an infinite coherence timeand length. In practice, no wave is truly monochromatic (since this requires awave train of infinite duration), but in general, the coherence time of the source isinversely proportional to its bandwidth.

The general description of, say, the electric component of an optical wave is


))(tθtω(cosE)t(ephaserandomfrequency

00

where the instantaneous frequency is defined as

t)tθ(

ωwave)of(phaset

)t(ω 0

The source bandwidth depends on the term ∂θ(t) /∂t.

The basic architecture of a coherent receiver is shown below.


)t(e)t(e~(t)i LOsignalp

Optical carrier with information

Local oscillator wave without information

Beam combiner

Optical detector

The basic architecture of coherent detection.

The essential features of coherent detection can be easily understood by making by making two assumptions;[1] the polarisation of the incoming signal and that of the local oscillator are the

same;[2] the fields of the signal and local oscillator are of constant amplitude over the

surface of the detector.

Under these two assumptions the derivation of the photocurrent proceeds as follows. The optical detectors used in optical communications are linear in terms of optical power but quadratic in the field. Then, assuming that


t)ωθtcos( ωEER

t)ωθtcos( ωEEt)ω(2cosE21

E21

θ)t2ω(cosE21

E21

R

t)ω(cosθ)tω(cosE2E)tω(cosEθ)t( ωcosER

)tω(cosEθ)tω(cosER)t(e)t(eR)t(i

LOSLOS

LOSLOSLOLO2LOSS

2S

LOSLOSLO22

LOS22

S

2LOLOSSLOSp

fh

neRand)t(θθ)tω(cosE)t(eθ)tω(cosE)t(e q

LOLOLOSSS

The photocurrent is derived as follows;

The terms containing the frequencies 2ωS, 2ωLO and ωS+ωLO are too high to beto detected so the expression of photocurrent is simplified to


)θtωtω(cosEEE

21

E21

R)t(i LOSLOS2LO

2Sp 2

Since the optical power contained in a signal is proportional to the square of the field the last equation can be written as

)θtωtω(cosPP2PPR)t(i LOSLOSLOSp

where Ps and PLO the signal and local oscillator power respectively. The third terminvolves the expression that indicates that the signal filed is multiplied by thelocal oscillator field and it is also known as the coherent gain. It is this cross product that accounts for the superior performance in receiver sensitivity in coherent detection.

LOLPP

The last equation makes possible two options for detection;Option I – ωS ≠ ωLO; heterodyne detection. Defining |ωS – ωLO|= ωIF where IF stands

for intermediate frequency. Then, . )θt( ωcosPP2PPR)t(i IFLOSLOSp

The key features of heterodyne detection are:[1] The receiver sensitivity is shot-noise limited; increase in unrepeated

transmission distance. [2] The phase information embedded in the carrier can be restored; improved

receiver sensitivity and use of multi-level modulation format[3] The heterodyne receiver can achieve linear detection; electronic post –

processing in the receiver. [4] The receiver bandwidth exceeds substantially the information bandwidth.


)θ(cosPP2PPR)t(i LOSLOSp

Option II - ωS = ωLO; homodyne detection. Then,

Simplifying the two equations the signal photocurrent is given by

detectionHomodyne

LOSSp

detectionHeterodyne

IFLOSSp )θcosPPR2)t(iand)θt( ωcosPPR2)t(i

The key features of heterodyne detection are:

The key features of heterodyne detection are:[1] The receiver sensitivity is shot-noise limited; Increase in unrepeated

transmission distance.[2] The phase information embedded in the carrier can be restored; improved

receiver sensitivity and use of multi-level modulation format.[3] The heterodyne receiver can achieve linear detection; electronic post –

processing in the receiver.[4] The homodyne receiver is a baseband receiver; relative ease in increasing

thebit rate.


The architecture of the heterodyne and homodyne receiver are shown in the next slides. The function of the digital controller entails more that is shown in the diagrams.Especial important is the concept of channel acquisition which is initiated and controlled by the receiver controller. The details depend on the application. The last equation makes possible the comparison of the mean signal power for homodyne,heterodyne and direct detection. That is,

Heterodyne coherent optical receiver.


Optical detector

IF Amplifier

Demodulator Baseband filter

Decision detector

Automatic frequency control

Local oscillator

Directional coupler

Temperature control

Data

Signal optical carrier

Power control

Receiver digital controller

)t(ipS

SDDLOShetLOShom PPP2PPP4PP


Optical detector

Baseband filter

Decision detector

Automatic phase control

Local oscillator

Directional coupler

Temperature control

Data


Power control

Receiver digital controller

)t(ipS

Homodyne coherent optical receiver.

In the diagrams of heterodyne and homodyne receivers a 3 - dB coupler was used tocombine the signal and local oscillator fields. Because only one output was used fromthe coupler half of the power of the signal and half of the power of the local oscillator are wasted. This loss can be in principle eradiated if a balanced optical receiver isused. The operation relies on a fundamental properly of the coupler; the signal at oneoutput fibre suffers a π/2 phase shift with relation to the throughput fibre. The diagrambelow shows the details of the configuration.


Local oscillator

Directional coupler


Detector A

Detector B

+

-

vA

vB

The input to the optical detectors are ;

)tω(sinE)tω(cosE(t)eand)tω(cosE)tω(sinEt)(e LOLOSSBLOLOSSA

At the detector outputs the current will be


)t(i)t(it)ωω(sinEE)t(iandt)ωω(sinEE)t(i BALOSLOSBLOSLOSA

Subtracting,)t(i2)t(i)t(i)t(i ABAout

This last equation shows that twice the we current of four time the power is obtained incomparison with the single optical detector or 6 dB improvement. Since the two components of the photocurrent are subtracted the large dc term generated by thelocal oscillator is cancelled and also any excess noise generated by the local oscillator. However, close matching of the two detectors is required if good excess noise cancellation is to be obtained.

The basic three modulation formats for coherent detection (ASK, FSK and PSK) canbe detected with a heterodyne receiver. The homodyne receiver can operate only withASK and PSK. We will now discuss some of the details for both receiver classes. [1] Homodyne Detection. In this case the photocurrent directly delivers the

information baseband. In order to detect ASK or PSK signals the local oscillator(laser) must somehow be synchronised with the transmitter oscillator (laser).The signal photocurrent output for ASK homodyne detection is

Modulation Formats

Since the transmitter and receiver are independent there will be a phase difference between the two waves therefore the angle θ is in reality θ – φwhere φ is the arbitrary transmitter wave angle. In order to recover thesymbol “1” the angle difference should be zero.

"0"for 0

"1"forθcosPPRhf

en2

)t(i LOSq

Sp

The detection of modulated optical carriers

The impact of phase error in ASK is illustrated in the constellation diagram below.


The impact of phase tracking error for ASK format.

Ideal position of the symbol “1” (θ - φ) = 0.

Position of the symbol “1” (θ - φ) ≠ 0.

Penalty due to phase tracking error

There are three possible approaches to carrier tracking for ASK; injection locking, selective amplification and optical phase locked loop. Injection locking requires high power level at the input exceeding substantial the receiver sensitivity of most homodyne systems. The selective amplification of the carrier without amplification of the signal sidebands is possible before the photodetector and the amplified carrier then acts as the local oscillator.

The last is the optical phase locked loop, (OPLL). Various variants of the OPPL theme

have been Investigated and the most important are:[1] The balanced loop.[2] The decision driven loop.[3] The Costas loop. As expected all three variants are strongly sensitive to the phase noise as to require anarrow linewidth laser in order to operate at the quantum limit of sensitivity. From theviewpoint of phase noise the best performance is obtained by the decision driven phase locked loop.



Clock recovery

x

Local oscillator tunable laser

Polarisation controller

Polarisation controller

Optical carrier signal 90o optical hybrid

Local oscillator

Lowpass filter

Lowpass filter

Loop filter

I - arm

Q - arm

Data

Decision Driven Optical Phase Locked Loop.

With PSK signalling the signal photocurrent output is


"0"forθcosPPR

hf

en2-

"1"forθcosPPRhf

en2

)t(i

LOSq

LOSq

Sp

where cos θ represent the phase error in tracking. The techniques suitable for ASKhomodyne are also suitably for PSK homodyne and again the phase error istranslated into performance penalty in the same way as for ASK. It is not always necessary use a complete coherent receiver for the demodulation of PSK signals. Ifthe transmitted PSK signal uses the DPSK format the detection can be very simple.Since the phase off the current DPSK pulse depends on the previous phase the signalhas an in-built reference that can be for synchronous detection. The basic principle isshown in the next slide.


Tb

Delay interferometer

A

B

Direct detection receiver

DPSK formatted signal

Data

A key feature of this approach is that a direct detection receiver can be used but the transmission advantages of the format are used in the design of the transmission system. Since PSK is a suppressed carrier format another option is to transmit a residual carrier by using incomplete phase modulation. The pilot carrier together withthe signal are combined in a 3 dB directional coupler and detected by a balanced receiver. The output signal from the difference amplifier is a function of the phase errorwhich can be used to drive the PLL. This approach is also known as balanced OPLL.

It should be understood that this approach will lead to a performance penalty at thereceiver. A block diagram of the residual carrier approach is shown below.


Baseband filter

OPPL Loop filter

Directional coupler

Optical detector

Local oscillator

Optical PSK signal with residual carrier

Optical detectorOptical phase

locked loop

Data

Homodyne coherent optical receiver with optical phased lock loop using the residual carrier approach.

[2] Heterodyne detection: When heterodyne detection is used there is abewildering range of options with respect o the second electronic detection. This is because all the techniques developed for radio communications cannow be used in optical communications. Starting with PSK it is important to notice that the PSK spectrum contains no energy at the carrier frequency. It is therefore necessary to introduce a nonlinearelement within the phase recovery subsystem to ensure carrier recovery. First, by squaring the PSK signal a signal at twice the original frequency is produced that can be filtered and used for phase estimation. The figure below illustrates the squaring loop technique.



Bandpass filter Square lawdevice

Loop filter

Voltage controlled oscillator

Frequency divide by 2

90o

phase shift

Outputfilter

Input

Output

Bandpass filter Square lawdevice

Loop filter

Voltage controlled oscillator

Frequency divide by 2

90o

phase shift

Outputfilter

Input

Output

The squaring loop technique for carrier recovery.

Another approach to the recovery of the carrier is to reduce the depth of modulationso that a small competent of the carrier is transmitted. However, to detect the residual carrier satisfactory a substantial amount of signal power may be sacrificed leading to performance penalties. A variation on the residual carrier technique is to recover the carrier at the IF stage, see below.


IF signal

Frequency doubler

Bandpass filter

Frequency divider

DataCarrier recovery arm

Data detection arm

Carrier recovery synchronous demodulator.

The DPSK can be detected without a synchronous receiver following the DPSK signalwith an optical interferometer but now the interferometer is placed in the lf section of the receiver, see below.

Lowpass filter

Delay T

Heterodyne DPSK signal

Data Double balanced

mixer

Phase detector

Demodulation of DPSK signal with

an electrical interferometer.

Modulation FormatsThe detection of modulated optical carriersThe synchronous demodulation techniques can be used for ASK and FSK heterodynereceivers. Because of the complexity of synchronous demodulation non-synchronoustechniques can be used for ASK and FSK. The performance is not as good aswith synchronous demodulation but the simplicity is very appealing. Typical configurations are shown in the next slide.

IF amplifier

Envelope detector

Bandpass filter

Lowpass filter

Decision detector

IF input Data

Non-synchronous ASK single envelope demodulator.

The ASK non-synchronous receiver can also operate as a FSK receiver is the bandpass filter following the IF amplifier is tuned at one of the frequencies corresponding to a binary FSK. A two channel non –synchronous FSK receiver is shown below.


IF amplifier

Envelope detector

Envelope detector

+

-

IF input

Channel for f1

Bandpass filter f1

Bandpass filter f2

Lowpass filter

Lowpass filter Output

Channel for f2

A dual channel non-synchronous FSK demodulator.

modulation formats. optical communication systems are carrier systems. this implies that a wave of a...

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