Transcript No Slide Title

Modulation Formats
General
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 over
which optical communications operate ranging from , say, 1 to 2 μm. This wavelength
range corresponds to a frequency range 1.5x102 to 3x102 THertz. Remember,
1 THerz=1x1012 Hertz. The bandwidth of the information sources currently available to
us 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 subject
of intensive study since the inception of electronic communications back in the 1920s.
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 Formats
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
1.
f(a
) is defined
2.
lim
x a
3.
lim
x a
f(x
f(x
) exists
)  f(a
)
(2) Digital modulation; a signal is defined as digital if its parameters are allowed to
take values that belong to a discrete set of values. A typical digital signal is
Digital signal definition S Dig
 0

 1
 0

for 0  t  1
for 1  t  2
for 2  t  3
Modulation Formats
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.
M1
Information
domain
M2
Carrier
domain
IM2
Channel
IM1
Carrier
domain
Information
domain
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.
Modulation Formats
General
One → Many
Receiver
Transmitter
Input
alphabet
“1” ●
“0” ●
“1” ●
Signal processing
and channel
“0” ●
One → Many
Receiver decision
space
The concept of one – to - many mapping in communications.
Modulation is a vast subject and by virtue of necessity we limit ourselves to digital
modulation as applied to optical communication systems.
Modulation Formats
General
The electric field of a e - m wave is given by

e(t, ω ,P,k,r, θ)
 E P exp  j [( k  r )  ωc t  θ]

where E is the peak electric field amplitude, P is the polarisation matrix, k is the wave
vector, r is the position vector, wc is the carrier angular frequency, t is the time, and θ
is 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.
I   S(z, t ) 
1
n
Re( E  H ) 
E(z, t )
2
2Z 0
2

P
(watts/uni t area)
A
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
Modulation Formats
The complete equation for an e – m wave can be substantially simplified if we limit
ourselves to modulation formats for high capacity transmission. Then,
e(t, ω ,θ)
 E0 exp  j ([ β z )  ωc t  θ]
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 that
there are three parameters that can be used to impart information on the optical
carrier.
[1]
Amplitude, E0; the format that modulates the amplitude of the optical carrier is
called “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 in
optical 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.
Modulation Formats
1
0
≈
Amplitude
General
Tb
time
Envelope
1
0
≈
Amplitude
Carrier
Baseband signal
ASK signal
time
The ASK format with a binary NRZ baseband signal.
[2]
Frequency, ω; when the baseband signal modulates the frequency of the
optical carrier the process is called “frequency nodulation”. For digital baseband
signals 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 distinguish
the two frequencies and make the correct decisions.
Modulation Formats
1
0
≈
Amplitude
General
A typical FSK modulated signal is shown in the diagram below.
Tb
time
Constant envelope
1
0
≈
Amplitude
f0 carrier
Baseband signal
f1 carrier
FSK signal
time
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.
Modulation Formats
1
0
≈
Amplitude
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 binary
baseband signal is illustrated below.
Phase 0
Phase π
Tb
time
Constant envelope
1
0
≈
Amplitude
Baseband signal
PSK signal
time
The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 and
the phase of “0” been shifted by π.
General
Modulation Formats
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 now
corresponds to
n  log 2M bits
As a result the M-ary signalling has been reduced to
BMary 
Bb
Bauds/s
log 2 M
With M = 2 the baud rate equals the bit rate, Bb.
Modulation Formats
The constellation concept
Until now the symbols of “1” and “0” for binary transmission have been defined as level
of, 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 representation
on the right is called for reason that will become apparent very soon, the
“constellation”
Complex plane
“1” (1, angle )V
Imaginary
axis
0+ j 0
Real axis
●
●
1+ j 0
“0” (0, angle 0)V
(a) Conventional representation.
(b) The “constellation” representation
Modulation Formats
The constellation concept
Perhaps, 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 and
it 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 assume
that 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 be
directly represented in the constellation diagram.
Imaginary
v2 ●
Voltage
Symbol
1+ j 0
00
●
0+j
01
●
Real
-1+ j 0
10
10
0 -j
11
Imaginary
v1
●
v3
●
v4
● 01
00
●
Real
● 11
Modulation Formats
The constellation concept
The constellation diagram in the previous slide showed very clearly the position of the
symbols 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, the
defined amplitude and phase of each symbol. This is the transmitted
constellation.
Amplitude –
Random variable
Amplitude
●
Phase
φ
10
●
●
11
●
●
φ
●
●
00
●
00
01
01
Phase –
Random variable
11
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.
Modulation Formats
The spectral efficiency concept
Intuitively one expects that the available channel bandwidth is efficiently used to
transport information. This is achieved by using an efficient modulation format subject
to 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 called
M-ary signalling. When n = 1, that is, one symbol is used to represents the
elements 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, also
known 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 Formats
The 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 Formats
The Hartley – Shannon Law
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 be
stated as
 S
log10 1  
 N
C  B
log10 2
 S
 3.32 B  log10 1   bit/s
 N
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
S
 10 SNR /10
N
The information rate, R, must satisfy the equation
dB
R
 S
 S
R  B log 2 1   bit/s and
 log 2 1  
B
 N
 N
is the spectralefficiency
Modulation Formats
The Hartley – Shannon Law
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
 Eb R 
E b 2R/B  1
R
 log 2 1 
  bit/s/Hz 

B
N0
R/B
 N0 B 
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 receiver
has a sensitivity of - 20 dBm for 10-9 BER with detector responsivity R = 1.
Modulation Formats
The Hartley – Shannon Law
10
Spectral efficiency (bit/s/Hz)
R > C - Out of bounds area
R=C
1
10 GBit/s example:
BER=10-9
R < C – Accessible area
R < C – Accessible area
0.1
-2
0
2
4
6
8
10
12
14
16
18
20
Eb/N0 (dB)
Graph of the maximum achievable spectral efficiency [Bit/s/Hz ]as function of Eb/N0 (dB).
Modulation Formats
The Hartley – Shannon Law
Step 1
We convert the power (-20 dBm) into the average optical power; thus
Poptaver 1103 1020/10  1.0 105
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
Popt - pk  2  Popt aver  2 10-5 W
and
Step 3

I max  2 10-5 A
E b  Popt pk  Tb  2 105 1001012  2 1015 Joules
The value of N0-rms will be found from the BER. For a BER of 10-9 the
ratio of peak optical power to rms noise is defined by the Q which is 12
for 10-9 BER.
I
Q  max
N0rms
 N0rms
Pmax 2  10 5


 1.66  10 6
Q
12
W
Modulation Formats
The Hartley – Shannon Law
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
1.6610 6
16
N0 

1
.
66

10
W /Hz
10  109
Step 5
The value of Eb/N0 is now
Eb
2  10 15

 12.0
16
N0 1.66  10
Step 6

Eb 
   10log10 12  10.8  11 dB
 N0  dB
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.
R 10  10 9

 0.5 bits/s/Hz
B 20  10 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.
The Hartley – Shannon Law
Modulation Formats
There are two key features of spectral efficiency:
[1]
[2]
Fundamental feature; higher signal-to-noise ratio is required for higher order
modulation.
Practical feature; the implementation penalties are higher for higher
constellations and symbol rates.
Modulation Formats
Intensity modulation
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 intensity
modulation of semiconductor lasers.
Output pulses
Modulating signal
Imod
Ibias
Laser
P1
Laser output
Constant current
source: Modulator
Constant current
source: Bias
Ithr
P0
Ibias
The diagram on the right shows the electronic
and optical waveforms.
I
Isignal
Input pulses
Intensity modulation
Modulation Formats
In addition to a simple transmitter an intensity modulated optical carrier offers the use
of a very simple receiver for detection. All it requires is a p-i-n or apd detector followed
by a low noise electronic amplifier. This combination of intensity modulated carrier and
a 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 possible
the introduction of optical fibre communications at an early date which required the
minimum 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 Gbits
because 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.
Intensity modulation
Modulation Formats
Measured spectrum of a directly modulated laser under 622 MBit/s
NRZ modulation with 0.7 mW between ‘1’ and ‘0’ level.
Intensity modulation
Modulation Formats
Chirped spectrum; black.
Theoretically expected spectrum; gray.
Spectra calculated for the directly modulated laser under 622 MBit/s NRZ modulation.
Intensity modulation
Modulation Formats
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 devices
modulate 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.
Modulation Formats
Technology - Modulators
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 is
shown below. The choice of a travelling wave modulator is dictated by bandwidth
requirements.
v1(t)
Waveguide
Ein / 2
Ein
Eout
kEin / 2
Electrical
Contacts
v2(t)
The equation of the operation of an amplitude modulator also known as Mach-Zehnder
(MZ) is given by,
E out 
E in
exp(j φ(t1
2
)  k exp(j φ 2(t
) 
E in
exp((j
2
π v(t
1
)/
Vπ   kexp(j π v 2(t
)/
Vπ ))
Technology - Modulators
Modulation Formats
With k = 1 the normalised output is written
 π

  exp(j π(v (t)
e out  cos 
(v (t)

v
(t))
 v 2(t))/
Vπ 
1
2
1















2Vπ


phase
modulation
(chirp(


ampitude modulation
and with v1(t) = - v2(t) the phase term is removed and
e out
 π
 cos 
v(t1
V
 π

2 π

)  Pout  Pin cos 
v(t1
V

 π

)

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 point
is 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.
Modulation Formats
Technology - Modulators
M - Z Modulator output
Power
●
0
●
Vπ
●
2Vπ
π
3Vπ
●
Drive voltage
4Vπ
Quadrature point
Field
The field and power output vs. drive voltage of a M - Z modulator.
One word of caution regarding the biasing point. Because of the material the bias point
drifts 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.
Technology - Modulators
Modulation Formats
Left ; the basic modulator.
Right ; the modulator with driver,
terminating load and monitoring
photodiode.
The architecture of a Mach – Zehnder modulator; from Photline
Modulation Formats
Technology - Modulators
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 frequency
stabilised laser with a co-packaged external modulator is shown below.
Frequency stabilised
DFB laser
Laser package
Device fibre tail
Optical
isolator
TE element
Transmission fibre
Power to TE
Temperature
External modulator
Laser TE
Controller
High quality
optical connector
Electronic
amplifier
Bias current
Constant current
bias source
Power monitor
Data
Modulation Formats
ASK signalling format
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.
A
Tp
-Tb/2
Tb/2
time
Tb
For a NRZ pulse the MZ is biased at quadrature and the input signal swings the
modulator drive voltage between zero and Vπ.
Modulation Formats
ASK signalling format
M -- Z power transmission
1
0.8
Signal drive
0.6
●
●
●
●
0.4
Bias
0.2
Phase π
Phase 0
0
2.6
0
V3.6
π / 2
4.6
Vπ
5.6
6.6
2V
7.6
π
8.6
9.63Vπ 10.6
4V
12.6
11.6
π
Drive voltage
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.
Modulation Formats
ASK signalling format
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 a
random 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 power
spectral density, (PSD), is given by the two sided function,
Sbaseb (f
2
2
 sin( π f Tb )
A
A2
)
Tb 
δ(f )
 
4
(
π
f
T
)
4




b 

Determinis ting spectrum
with f : - ,  
Continuous spectrum
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 one
of detrimental features of NRZ format because the power Is not used for information
transmission.
Modulation Formats
ASK signalling format
0.6
A2
δ(f )
2
0.5
PSD
0.4
A 2  sin( π f )
Tb 

2
 ( πf ) 
0.3
2
A  Tb  1
0.2
Pr(1
)  Pr(0
0.1
)
1
2
0
0
0.5
1
1.5
2
2.5
f
3
The PSD of the random unipolar signal for a NRZ rectangular pulse stream.
Modulation Formats
ASK signalling format
When the baseband signal modulates the carrier the combined signal can be
represented as
s c(t
)  E0 a(t
)exp(j
ωc t )
The two - sided PSD of the modulated carrier is now given by
E 02
E 02
2
2
δ(f  fc )  δ(f  fc )
S carrier(f ) 
Tb sinc (f  fc )  sinc (f  fc ) 
8
8
E 02 
k
2 k

sinc
(
)
δ
(f

) with k  0

8Tb k 
Tb
Tb


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 in
general.
Modulation Formats
ASK signalling format
2
0
E
4
Scarrier(f)
Deterministic signal
E 02
Tb
4
Bandwidth ≈ 2Bbase
fc = optical carrier
Stochastic signal
fc
f
90%
of power
95%
of power
The PSD of a binary ASK signal in the optical domain.
Modulation Formats
ASK signalling format
The modulation spectrum of a Mach – Zehnder modulator at 2.5 Gbit/s.
Modulation Formats
ASK signalling format
It is very instructive to construct the state and constellation diagram for the binary ASK
signalling format.
imaginary
“1 to 0”
“0”
●
●
“0 to 1”
State “0”
“1”
threshold
State diagram
“0”
“1”
“0”
0.5
0.5
“1”
0.5
0.5
●
●
State “1”
E0
Symbol “0”
real
Symbol “1”
Transition probabilities
State diagram and transition probabilities for Constellation diagram for binary ASK signalling.
binary ASK signalling.
Modulation Formats
ASK signalling format
DC impulse
Spectral nulls.
The PSD of a binary NRZ ASK signal for
10 Gbit/s data without filtering.
Modulation Formats
ASK signalling format
10 Gbit/s.
40 Gbit/s.
The spectral of NRZ modulation at 10 and 40 Gbit/s.
Modulation Formats
ASK signalling format
The key features of ASK signalling is that there is a DC term whose energy is not used
and 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 the
signalling interval ( Tb). Three typical RZ formats are shown below.
A
A
Tp
A
Tp
Tp
Tb
Tp= 50% Tb
time
Tb
Tp= 67% Tb
time
Tb
Tp= 33% Tb
time
Modulation Formats
ASK signalling format
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 an
issue 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 narrow
pulses 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 next
slide. 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 the
generation of RZ pulses with arbitrary duty cycle is much easier.
ASK signalling format
Modulation Formats
NRZ data
Clock or sinusoid
Data MZ
CW light
Pulse carver MZ
NRZ
Optical RZ
format
The concept of pulse carver modulator.
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.
Modulation Formats
ASK signalling format
RZ67 is created by driving the pulse carver with a 2Vπ voltage (peak to peak) sinusoid
at 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.
imaginary
Tb / D
”0”
State ”0”
“1”
E0
real
State ”1”
RZ67 D = 1.5
RZ50 D = 2
RZ33 D = 3
Symbol “0”
The state diagram and the constellation for RZ formats.
Symbol “1”
Modulation Formats
ASK signalling format
1.2
RZ33 signal drive
●
1
RZ50 signal
drive
M - Z power output
0.8
RZ67 signal drive
0.6
●
Bias
0.4
Bias
0.2
Phase 0
Bias
Phase π
●
0
00
1
V
π/2
2
Vπ
3
4
5
2Vπ
6
7
8
9
10
3Vπ
4Vπ
M - Z voltage
The bias and drive requirements for generation of RZ pulses using the carver concept.
Modulation Formats
ASK signalling format
The pulses of various RZ formats.
The two sided PSD of RZ33 and RZ50 format is given by
2
S carrier(f

E 02  sin( π f Tb /2) 

)
1

B
δ(f

kB
)

b 
b 


16B b  π f Tb /2  
k  

2
S carrier(f

E 02  sin( π f Tb /2) 
2k  1

)
B b )

 1  B b  δ(f 
16B b  π f Tb /2  
2
k  

The PSDs for RZ33, 50 and 67 from computer simulations are shown below.
Modulation Formats Conversion for Future Optical Networks:
Javier Cano Adalid MSc Thesis , TUD, 2009
ASK signalling format
For RZ67 the PSD is given by
Modulation Formats
ASK signalling format
Modulation Formats
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.
The sign of the carrier is changing at
every bit transition and they are complete
independent 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.
Modulation Formats Conversion for Future Optical Networks:
Javier Cano Adalid MSc Thesis , TUD, 2009
Modulation Formats
ASK signalling format
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.
Amplitude
levels
Tb
3
2
1
0
time
A typical 4-level ASK format.
With four levels of signalling the number of bits, n, transmitted by one symbol is
n  log 2M for M  4 n  log 2 4  2 bits/symbol
A typical encoding scheme for a 4 - level ASK is
Binary
Symbol
Binary
Symbol
00
0
10
2
01
1
11
3
Modulation Formats
ASK signalling format
Stream A
Power
combiner
Stream B
Z
(a) Multilevel signal generation.
A
B
Z
0
0
0
0
1
1
1
0
2
1
1
3
Q
11
D-FF 3
Q
V3
V3
10
V2
Z
01
Power
splitter
Q
D-FF 2
Q
V2
V1
00
thresholds
time
(a) Multilevel signal decoding.
Q
D-FF 1
Q
V1
The generation and decoding of multilevel signals.
A
B
ASK signalling format
Modulation Formats
Experimental eye diagrams for 4-ary ASK signalling; notice how the inner eye shapes
and the different optimum sampling times change with distance .
ASK signalling format
Modulation Formats
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
M  2n
Now, each pulse corresponds to
n  log 2M bits/symbol
and as a result the M – ary signalling rate has be reduced to
B symbol 
Bb
bauds/s
log 2M
On the face of it by reducing the signalling rate through M - ary transmission we have
reduced the requirements on the system parameters..
Modulation Formats
ASK signalling format
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 original
binary 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.
ASK signalling format
Modulation Formats
For a binary format the transmitted constellation and the constellation in the receiver
before decision are shown below with the effect of noise exaggerated. .
Detection threshold
2Popt
“0”
Symbol dynamic
range
Space of “0”
“1”
Space of “1”
“0”
“1”
Noise processes
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 transmitter
and receiver constellations are shown in the next slide.
Modulation Formats
ASK signalling format
Symbol dynamic range
for binary
“00”
“01”
“10”
Detection thresholds
“00”
“11”
“01”
“10”
“11”
Symbol dynamic range for 4-ary
Noise processes
Transmitted constellation
Constellation at the receiver decision point
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
M 1
PM 
log 2M
For example with M=4 the optical power required is 3.3 dB more than that for M = 2
( binary).
PSK signalling format
Modulation Formats
1
0
≈
Amplitude
The basic features of the “phase shift keying”, (PSK), format as shown below.
Phase 0
Phase π
Tb
time
Constant envelope
1
0
≈
Amplitude
Baseband signal
PSK signal
time
The PSK format with a binary NRZ baseband signal with the phase of “1” been 0 and
the 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.
PSK signalling format
Modulation Formats
Basic concept; waveguide 3 - 9 μm depth.
A travelling wave phase modulator:
from: Sumitomo Osaka Cement Co. Ltd.
Driving voltage V0;
N peaks of wave.
Driving voltage V1;
N+1 peaks of wave.
Actual device.
Modulation Formats
PSK signalling format
Electrical contacts
signal
ground
x
y
z
waveguide
X - cut
y
x
z
ground
waveguide
Z - cut
The electrode configuration for phase modulator.
PSK signalling format
Modulation Formats
The phase shift induced by the applied voltage is given by
πL 3
V
Δφ  
n e r33 Γ
λ
g
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
Vπ  λ g /(n
the phase shift can be written as
Δφ 
3
e
r33  L)
π V

2 Vπ
For fibre communication modulators Vπ ~ 4 - 5 V.
Modulation Formats
PSK signalling format
The transmitter for “Binary PSK” (BPSK) with coherent detection is very simple.
CW optical
source
Binary phase
modulator
Phase modulated light
Binary data
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;
Δφ  
πL 3
V
n e r33 Γ
λ
g
Δφ  π 
V
Vπ
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.
Modulation Formats
PSK signalling format
threshold
π
π
0
φ1
φ2
0
φ3
Perturbed constellation.
Ideal constellation.
The impact of a fluctuating phase of an optical carrier.
For the BPSK format the optical field is given by
e(t )  E0 exp(  j( ωc t  φ c(t ) ) )
where only the phase φc(t) is modulated by the data
φ c(t )  π αnp(t  nTb )
n
where the random variable αn= 0 or 1 depending on the data sequence. For αn= 0
e(t1 )  E0 exp(  j( ωc t ) )
Modulation Formats
PSK signalling format
and for αn= 1
e0(t )  E0 exp(  j( ωc t  π ) )  - E0 exp(  j( ωc t ) )  - e(t1 )
The state diagram of a BPSK format is shown below. Some key observations can
now be made.
Phase
0
Time
1
0
1
Intensity
Modulation Formats
PSK signalling format
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 continuous
envelope 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
Popt
A 2c

2
A 2c
Eb 
Tb
2
Ac 
2Eb
Tb
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.
Modulation Formats
PSK signalling format
Euclidean distance d  2 E b
Phase
0
Time
0
1
d
1
 Eb
Eb
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.
Modulation Formats
PSK signalling format
1
+1
-1
1
1
1
1
time
-1
BPSK – NRZ format
e(t)
≈
+1
≈
e(t)
1
time
-1
-1
BPSK – RZ format
The power spectral density of the BPSK - NRZ format is
 sin π f T 

S base(f)  A 2c T 
 πf T 
2
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 is
known as “suppressed carrier signalling.”
Modulation Formats
PSK signalling format
Scarrier(f)
E 02
Tb
2
Bandwidth ≈ 2Bbase
fc = optical carrier
Stochastic signal
fc
f
90%
of power
95%
of power
The single sided PSD of a BPSK – NRZ format; bandwidth ~ 2Rb.
The PSD of a RZ-50% BPSK pulse is shown in the next slide together with the PSD
of BPSK with NRZ format.
Modulation Formats
PSK signalling format
A 2c T  sin π f T/2 


S base(f) 
2  π f T/2 
2
1
Scarrier(f)
0.8
BPSK - NRZ
BPSK - RZ 50%
0.6
0.4
0.2
0
-3
-2
-1
0
1
2
fT
The spectra of BPSK with NRZ and RZ - 50% pulses.
3
Modulation Formats
PSK signalling format
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 a
degree that depends on the filtering and the chirping. The absence of the carrier in
the 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;
Residual carrier constellation
Φ<π
Φ=π
0
Suppressed carrier constellation
Modulation Formats
PSK signalling format
The architecture of a RZ BPSK transmitter is similar to the one used in ASK.
NRZ data
CW light
Clock
Phase
modulator
Pulse carver MZ
NRZ
Optical RZ
format
Schematic of a RZ BPSK transmitter architecture.
The key assumption underlining the development of the concept of BPSK is that the
phase of the carrier evolves as a constant vs. time. This implies an optical oscillator of
zero linewidth and a great stability. In general these conditions cannot be met in
practice and a solution has emerged through signal processing.
Modulation Formats
PSK signalling format
The study of PSK signalling will be concluded with the study of the differentially
encoded PSK, (DPSK). With the PSK format the information is embedded in the
phase of the carrier so in order to retrieve the information a detection system sensitive
to the phase must be used. Such a system is refer to as “coherent” and the receiver is
very complex compared to the ASK receiver. One way to recover information
embedded in the phase of the carrier without a coherent receiver is to encode the
information before modulation “differentially”. To understand the process consider a
data 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.
Modulation Formats
PSK signalling format
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
y i  y i1  x i
where  indicates modulo 2 addition
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 the
decoding is simply,
~
x ~
y ~
y where ~
x indicates an estimated quanity
i
i1
i
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.
PSK signalling format
Modulation Formats
y i  y i1  x i
AND
xi
XOR
yi
xi
yi
yi - 1
Delay
Tb
Negative AND
y i  y i1x i  y i1x i
Differential encoder.
Delay
flip-flop
yi - 1
Logic circuit for differential encoder.
~
xi  ~
y i1  ~
yi
~
xi
~
y i-1
Delay
Tb
Differential decoder.
~
yi
I1
I2
Out
0
0
0
0
1
1
1
0
1
1
1
0
Modulo-2 addition - Exclusive OR
Sometimes the expressions y i  y i1  x i and ~x1  ~y i1  ~y i are found in the literature.
Modulation Formats
PSK signalling format
Consider
the following table as an example of differential encoding
.
K
-1
0
1
2
3
4
5
6
7
1
0
1
1
0
1
0
0
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
Xk
Yk
~
y
k
~
xk

Decoding with correct channel polarity.
where k-1 the reference digit, ~
y k and ~
x k 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).
Modulation Formats
PSK signalling format
k
-1
Xk
1
2
3
4
5
6
7
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
1
0
1
1
0
1
0
0
x*k
Sequence inverted
0
Reference digit
Decoding with inverted channel polarity.
If the PSK format is used to transmit a binary sequence without differential encoding
the format is known as “binary PSK” ( BPSK). When differential encoding is added
then it becomes “differential binary PSK” ( DBPSK).
Modulation Formats
PSK signalling format
It is now straightforward to translate this encoding scheme to PSK. The basic rule is
that 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
1
0
1
1
0
1
0
0
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
1
0
1
1
0
1
0
0
xk
yk
Decoded
1
1
Modulation Formats
PSK signalling format
The architecture of a DBPSK transmitter is shown below.
Phase
modulator
CW light
Pulse carver MZ
Optical RZ
format
NRZ
Data
Clock or RF
DBPSK encoder
Tb
Synchronisation
The constellation and state diagram is shown overleaf.
Modulation Formats
PSK signalling format
Phase
0
Time
1
1
0
Intensity
The constellation and state diagram of the DBPSK format.
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.
Modulation Formats
PSK signalling format
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. Polo
1 October 2009
SUNRISE TELECOM. com
Modulation Formats
PSK signalling format
Tb
A
B
DI transmission
1/Tb
A
B
Delay interferometer
Direct detection
receiver
Optical frequency
Direct detection receiver for the DBPSK format.
Modulation Formats
PSK signalling format
The transfer function of the MZM is given by
e out(v (t
), v 2(t ) )  cos( ( π /2Vπ (v
) (t
)  v (t ) ) exp(j π(v (t
)  v 2(t ) ) /2Vπ )
1
1
1

2 



Amplitude modulation
Phase modulation
With v1(t) = - v2(t) the phase modulation is removed and
eout(v (t1 ), v 2(t ) )  cos( ( π /Vπ (v
) (t1 ) )
Popt  Poptcos2( ( π /Vπ (v
) (t1 ) )
For phase modulation the MZ is biased for zero output without signal and then driven
by 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.
Modulation Formats
Output power
PSK signalling format
Optical power
Vπ
2Vπ
Optical field
3Vπ
π
0
π π
time
4Vπ
Intensity dips
Drive voltage
Difference v1(t) - v2(t)
- v1(t)
time
2Vπ
Phase modulated
light
CW light
Vπ for zero
transmission
v1(t)
The operation of the MZ modulator as phase modulator.
Modulation Formats
PSK signalling format
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.
vI(t)
- vI(t)
Phase
modulator I
DQPSK modulator
CW light
Phase
modulator Q
VPM =-Vπ/2
Phase
modulator
- vQ(t)
vQ(t)
Modulation Formats
PSK signalling format
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 the
term “channel in quadrature”, (Q – channel ), the other channel is known as “ channel
in 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 of
each MZ is given by
 v(t ) 
e out(t
and expanding

)  e in cos  π
V
π 


 v(t ) 
 v (t
  cos  π Q
e out(t )  e in  cos  π I
Vπ 
Vπ




 v(t ) 
 v (t
  j cos  π Q
 e in  cos  π I
Vπ 
Vπ




 e in 


)
(exp(j

π 
)
2 
) 
 




 v (t

 cos  π Q


Vπ
v Q(t )  
v(tI ) 

2 
2 
1 
  cos  π
  exp j tan 
cos  π
Vπ 
Vπ  



 cos  π v(tI




Vπ



)   
 
 

)  


  
Modulation Formats
PSK signalling format
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
Q - axis
The constellation diagram corresponding to this
format is shown on the right:“0”→ voltage level 0
and “1” → voltage level Vπ.
(I,Q) = (1,0)
3π/4
(I,Q) = (0,0)
π/4
5π/4
I - axis
-π/4
(I,Q) = (1,1)
(I,Q) = (0,1)
PSK signalling format
Modulation Formats
It should be clear now that QPSK can be combined with differential encoding for
DQPSK. The figure below summarises a measured constellation for 40 Gbit/s DQPSK
without 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.
Modulation Formats
PSK signalling format
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 Gsymbols
the effects of dispersion are suppressed.
Modulation Formats
FSK signalling format
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 for
that 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;
e( t )  Re Ec exp( (j ( (ω0  Δω)
t )  φ0 )
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 given
approximately by
FSKBW  2Δ f  2B
FSK signalling format
Modulation Formats
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-topeak 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 of
the laser.
The eye at the output of the laseramplitude modulation.
The eye at the output of the FSK-AM detector;
a MZ interferometer with 11GHz FSR.
Modulation Formats
FSK signalling format
Tuneable lasers can offer an alternative approach to FSK modulation. Consider the
state 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.
Modulation Formats
FSK signalling format
-5 GHz
+5 GHz
12 GHz / ma
f0 = 92.2 THz
Output frequency vs. phase
section current at 192.2 THz.
Time averaged spectrum of FSK modulation
at 192.2 THz ; Δf= + /- 5GHz.
Modulation Formats
Single Sideband signalling format
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
and other signalling formats suppress it.
Residual carrier
Then, there is the upper and low sidebands
Upper sideband
but only one sideband existed in the original
Original baseband
baseband signal with a bandwidth of
signal
Lower sideband
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,
F(  ω )  F( ω )
The spectral of NRZ ASK modulation
at 40 Gbit/s.
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
.
Modulation Formats
F(ω)
Single Sideband signalling format
Fourier transform of a real function is
- ωm 0 ωm
ω
Hermitian. Only a single sideband
Upper sideband
Upper sideband
needs to be transmitted. To illustrate this
Lower sideband
Lower sideband
concept consider the details of the
diagram on the right. Let assume that the
- ωc
0
ωc
Double sideband SC
modulation signal is a real time function
given by x(t) and let us define the analytic
signal ( see appendix B)
x a(t)  x(t )  j xˆ(t )
The Fourier transform of the analytic
signal is
X a(f )  2X(f )
f 0
When xa(t) modulates the carrier exp(j2πf0t)
the frequency components are shifted by
+f0 and there are no negative frequencies.
- ωc
- ωc
- ωc
0
ωc
0
ωc
0
ωc
Upper sideband only
Lower sideband only
Reconstructed signal F(ω)
Modulation Formats
Single Sideband signalling format
Lower sideband
Carrier
rb=10Gbits
The output spectrum of a lower sideband transmitter;
P.M. Watts et al., ECOC 2005, Paper TU 4.2.4
The Hilbert transformer was implemented using a four tap FIR digital filer;
xˆ( n) 
2
2
2
x( n)  x( n  2)  x(n
3π
π
π
 4) 
2
x(n
3π
where x(n) is the input data sampled at twice the bit rate.
 6)
Modulation Formats
Single Sideband signalling format
Filter
Interference from
the lower band
Filter
Residual
carrier
SSB
ω0
ω
ω0
ω
Advantages:
[1]
The filter is realisable.
[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 radio
communications. A number of successive experiments has taken place where a fibre
Bragg filter is used as the optical filter because of its excellent performance.
Modulation Formats
The detection of modulated optical carriers
In order to detect the information embedded on the optical carrier the receiver must be
suitable equipped. In this part of the module the architectures of suitable receivers
will be discussed.
Before we embark on the stude of receiver architectures it is important to introduce the
classes 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 the
optical frequencies as it is common in radio and microwaves.
The detailed study of optical detection, that is the interaction between radiation and
matter, 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 detector
is 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 Formats
The detection of modulated optical carriers
Under the constraints imposed by the semi-classical approach the photocurrent of an
optical detector is given by
 Popt( t )
ip( t )  e n q

hf


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 the
optical 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”.
hf
Optical time
envelope
Optical
detector
ip( t )
Low noise
amplifier
Electronic
signal
The basic architecture of a direct detection receiver.
time
Modulation Formats
The detection of modulated optical carriers
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 is
embedded 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 interfere
with 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 visible
interference pattern. These features are illustrated in the next slide.
Modulation Formats
The detection of modulated optical carriers
Incoherent waves of the same
frequency (monochromatic).
Coherent waves (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 length
can be defined;
Δx c 
c
Δt c
n
Modulation Formats
The detection of modulated optical carriers
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 time
and length. In practice, no wave is truly monochromatic (since this requires a
wave train of infinite duration), but in general, the coherence time of the source is
inversely proportional to its bandwidth.
The general description of, say, the electric component of an optical wave is
e( t )  E 0 cos( ω 0 t 

frequency
θ
(t ) )
random phase
where the instantaneous frequency is defined as
ω( t ) 
 θ(t )

(phase of wave) ω0 
t
t
The source bandwidth depends on the term ∂θ(t) /∂t.
Modulation Formats
The detection of modulated optical carriers
The basic architecture of a coherent receiver is shown below.
Beam combiner
Optical carrier with
information
Local oscillator wave
without information
Optical
detector
ip(t) ~ e signal( t ) eLO( t )
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.
Modulation Formats
The detection of modulated optical carriers
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
e S( t )  ES cos( ωS t  θ)
e LO( t )  ELO cos( ωLO t )
θ  θ( t )
and
Re
nq
hf
The photocurrent is derived as follows;
ip( t )  R e S( t )  e LO( t )  R E S cos( ω S t  θ)
 E LO cos( ωLO t )
2


2
 R E S2 cos2( ω S t  θ)
 E LO
cos2( ωLO t )  2E SE LO cos( ω S t  θ)
cos( ωLO t)
1
1 2
1
1

 R  E S2  E S cos( 2ω S t  θ)
 E LO
 E LO cos(2 ωLO t)  E SELO cos( ω S t  θ  ωLO t)
2
2
2
2

 R E SE LO cos( ω S t  θ  ωLO t)
The terms containing the frequencies 2ωS, 2ωLO and ωS+ωLO are too high to be
to detected so the expression of photocurrent is simplified to
Modulation Formats
The detection of modulated optical carriers
1 2
1

ip( t )  R  E S2  ELO
 2 E SELO cos( ω S t  ωLO t  θ )
2
2

Since the optical power contained in a signal is proportional to the square of the field
the last equation can be written as


ip( t )  R PS  PLO  2 PSPLO cos( ωS t  ωLOt  θ )
where Ps and PLO the signal and local oscillator power respectively. The third term
involves the expression PLPLO that indicates that the signal filed is multiplied by the
local 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.
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,
.
ip( t )  R PS  PLO  2 PSPLO cos( ωIF t  θ )


The key features of heterodyne detection are
Modulation Formats
The detection of modulated optical carriers
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.
Option II - ωS = ωLO; homodyne detection. Then,


ip( t )  R PS  PLO  2 PSPLO cos( θ )
Simplifying the two equations the signal photocurrent is given by
ip S( t )  2 R PSPLO cos( ωIF t  θ )


Heterodyne detection
and
ip S( t )  2 R PSPLO cosθ )

Homodyne detection
Modulation Formats
The detection of modulated optical carriers
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 the
bit 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,
Modulation Formats
The detection of modulated optical carriers
Phom  4PSPLO
Phet  2PSPLO
PDD  PS
Optical
detector
Signal optical
carrier
Directional
coupler
Decision
detector
Demodulator
ipS( t )
Baseband filter
Data
IF Amplifier
Local
oscillator
Automatic frequency
control
Temperature control
Receiver digital
controller
Power control
Heterodyne coherent optical receiver.
Modulation Formats
The detection of modulated optical carriers
Optical
detector
Signal optical
carrier
Directional
coupler
ipS( t )
Decision
detector
Baseband filter
Data
Local
oscillator
Automatic phase
control
Temperature control
Power control
Homodyne coherent optical receiver.
Receiver digital
controller
Modulation Formats
The detection of modulated optical carriers
In the diagrams of heterodyne and homodyne receivers a 3 - dB coupler was used to
combine the signal and local oscillator fields. Because only one output was used from
the 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 is
used. The operation relies on a fundamental properly of the coupler; the signal at one
output fibre suffers a π/2 phase shift with relation to the throughput fibre. The diagram
below shows the details of the configuration.
Detector A
Signal optical
carrier
vA
+
vB
-
Directional
coupler
Local
oscillator
Detector B
The input to the optical detectors are ;
e A( t)  ES sin( ωS t )  ELO cos( ωLO t )
and
eB(t)  ES cos( ωS t )  ELO sin( ωLO t )
Modulation Formats
The detection of modulated optical carriers
At the detector outputs the current will be
i A( t )  ESELO sin( ωS ωLO )t and iB( t )   ESELO sin( ωS  ωLO )t  i A( t )   i B( t )
Subtracting,
iout( t )  i A( t )  iB( t )  2 i A( t )
This last equation shows that twice the we current of four time the power is obtained in
comparison with the single optical detector or 6 dB improvement. Since the two
components of the photocurrent are subtracted the large dc term generated by the
local 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.
Modulation Formats
The detection of modulated optical carriers
The basic three modulation formats for coherent detection (ASK, FSK and PSK) can
be detected with a heterodyne receiver. The homodyne receiver can operate only with
ASK 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
 nq e
R PSPLO cosθ
2
ip S( t )   hf
0

for "1"
for "0"
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 – φ
where φ is the arbitrary transmitter wave angle. In order to recover the
symbol “1” the angle difference should be zero.
Modulation Formats
The detection of modulated optical carriers
The impact of phase error in ASK is illustrated in the constellation diagram below.
Position of the
symbol “1” (θ - φ) ≠ 0.
Penalty due to phase
tracking error
Ideal position of the
symbol “1” (θ - φ) = 0.
The impact of phase tracking error for ASK format.
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.
Modulation Formats
The detection of modulated optical carriers
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 a
narrow linewidth laser in order to operate at the quantum limit of sensitivity. From the
viewpoint of phase noise the best performance is obtained by the decision driven
phase locked loop.
Modulation Formats
The detection of modulated optical carriers
Clock
recovery
I - arm
Polarisation
controller
Optical
carrier
signal
90o
optical hybrid
Lowpass filter
Lowpass filter
Local
oscillator
Q - arm
Polarisation
controller
Loop filter
Local oscillator
tunable laser
Decision Driven Optical Phase Locked Loop.
Data
x
Modulation Formats
The detection of modulated optical carriers
With PSK signalling the signal photocurrent output is
 nqe
R PSPLO cosθ for "1"
2
ip S( t )   hf
- 2 n q e R P P cosθ for "0"
S LO

hf
where cos θ represent the phase error in tracking. The techniques suitable for ASK
homodyne are also suitably for PSK homodyne and again the phase error is
translated 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. If
the 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 signal
has an in-built reference that can be for synchronous detection. The basic principle is
shown in the next slide.
Modulation Formats
The detection of modulated optical carriers
Tb
A
DPSK formatted
signal
Data
B
Delay interferometer
Direct detection
receiver
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 with
the 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 error
which can be used to drive the PLL. This approach is also known as balanced OPLL.
Modulation Formats
The detection of modulated optical carriers
It should be understood that this approach will lead to a performance penalty at the
receiver. A block diagram of the residual carrier approach is shown below.
Optical
detector
Optical PSK signal
with residual carrier
Data
Directional
coupler
Local
oscillator
Baseband filter
Optical phase
locked loop
Optical
detector
OPPL
Loop filter
Homodyne coherent optical receiver with optical phased lock loop
using the residual carrier approach.
Modulation Formats
The detection of modulated optical carriers
[2] Heterodyne detection: When heterodyne detection is used there is a
bewildering range of options with respect o the second electronic detection.
This is because all the techniques developed for radio communications can
now 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 nonlinear
element 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.
Modulation Formats
The detection of modulated optical carriers
Bandpass filter
Square law
device

Loop filter
Voltage
controlled
oscillator
Input
Frequency
divide by 2
90o
phase
shift

Output
filter
Output
The squaring loop technique for carrier recovery.
Another approach to the recovery of the carrier is to reduce the depth of modulation
so 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.
Modulation Formats
The detection of modulated optical carriers

Data detection arm
IF signal
Data
Carrier recovery arm
Frequency
doubler
Bandpass
filter
Frequency
divider
Carrier recovery synchronous demodulator.
The DPSK can be detected without a synchronous receiver following the DPSK signal
with an optical interferometer but now the interferometer is placed in the lf section of
the receiver, see below.
Phase detector
Heterodyne
DPSK
signal
Double
balanced
mixer
Delay T

Lowpass
filter
Data
Demodulation of DPSK signal with
an electrical interferometer.
Modulation Formats
The detection of modulated optical carriers
The synchronous demodulation techniques can be used for ASK and FSK heterodyne
receivers. Because of the complexity of synchronous demodulation non-synchronous
techniques can be used for ASK and FSK. The performance is not as good as
with synchronous demodulation but the simplicity is very appealing. Typical
configurations are shown in the next slide.
Lowpass
filter
Bandpass
filter
IF input
IF
amplifier
Decision
detector
Envelope
detector
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.
Modulation Formats
The detection of modulated optical carriers
Channel for f1
Envelope
detector
IF input
IF
amplifier
Bandpass
filter f1
Lowpass
filter
Bandpass
filter f2
Lowpass
filter
Envelope
detector
Channel for f2
A dual channel non-synchronous FSK demodulator.
+
-
Output