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We have seen advantages of digital modulation over analogue modulation, and we also looked at
the optical carrier frequencies. We now look at the basic concepts of digital modulation
relevant for optical communication systems.
the direction of polarization along ê
ω௖
(= 2πf௖
, where fc is the carrier frequency

where λ is the wavelength in metre

.

 Amplitude shift keying :
the bit, the scheme is known as ASK or OOK.
‘off’ depending on whether the bit is ‘1’ or ‘0’ respectively.

Lecture 5

Digital communication for Optical communication

We have seen advantages of digital modulation over analogue modulation, and we also looked at
We now look at the basic concepts of digital modulation
communication systems. An electric field with amplitude
̂, propagating along the +z direction with an angular
the carrier frequency in Hertz), having a propagation constant β

where λ is the wavelength in metre), and specific phase φ , can be represented as,

Eሬ⃗(t) = êE଴e

௝(ఠ೎௧ିఉ௭ାథ)

Amplitude shift keying: If the amplitude of the electric field is modulated depending on
the bit, the scheme is known as ASK or OOK. It is the same switching the source ‘on’ or
‘off’ depending on whether the bit is ‘1’ or ‘0’ respectively.
Digital communication for Optical communication

We have seen advantages of digital modulation over analogue modulation, and we also looked at
We now look at the basic concepts of digital modulation that are
amplitude E0 and its
angular frequency
propagation constant β (
ଶగ

,

can be represented as

If the amplitude of the electric field is modulated depending on
It is the same switching the source ‘on’ or

 Frequency shift keying: If the carrier frequency (colour of the light) is changed depending
on the bit, the scheme is called FSK.
This example represents what ASK and FSK mean. Consider the baseband signal is the
bit-sequence ‘1101’, which is to be transmitted. The carrier frequency is several Terahertz
(corresponding to optical communication). Tb is the duration of one bit or the bit slot.
Please note that this representation is not to scale. The carrier and the baseband time
scales are not to scale with respect to each other. In the case of ASK, the amplitude is high
(ON) when the bit in the digital signal is ‘1’ and low (OFF) when the digital signal is ‘0’.
In the case of FSK, ‘1’ represents a high frequency, and ‘0’ represents a low frequency. It
requires a way to switch between high frequency and low frequency, or for instance, blue
colour for high frequency and green colour for low frequency. As the bit to be transmitted
changes, the colour of the source changes as well.
 Phase shift keying: The third way of digital modulation is changing the phaseφ of the
carrier as a function of the input bit. For instance, consider the bit sequence‘1 0 1 1’. Let
us say, we represent bit ‘1’ as phase 0, and a bit ‘0’ as phase π. This choice of phase is not
strict, it is something understood and agreed upon by the transmitter and the receiver. It is
preferable to choose the phases that are far apart (difference of π), so that they are easily
distinguishable. The phases corresponding to ‘1’ and ‘0’ can also be chosen as గ

and ଷగ

.
At the end of the bit slots, where there is a change in the bit from ‘1’ to ‘0’ or vice-versa,
the phase of the carrier wave also changes correspondingly. In case of similar consecutive
bits, there is no phase change. The envelope of the wave remains constant in case of
either bit. This is how the PSK format is visualized.
Traditionally, until almost 15 years ago, OOK was the only scheme that was used in optical
communication. In fact, instead of switching amplitude, the OOK scheme was based on the
switching of intensity (I), which is related to the electric field amplitude as I = |E଴
|

. This was
implemented by switching the source (LED or laser) on and off according to the bit at the rate at
which it is to be transmitted. This is why all the traditional books on optical communication deal
only with intensity modulation.
FSK is not generally used in optical communication systems, the reason being, it is very difficult
to switch the frequency of a laser source. It is possible, but it is much more complicated than
switching amplitudes or switching phases. We will later learn the methods for intensity
modulation and phase modulation. We will not deal with FSK, since it is not very easy to
implement.
Constellation representation: Consider the case of OOK data. The conventional representation
of the baseband signal, s(t) is

bit = 1; s(t) = E଴
bit = 0; s(t) = 0

A constellation is the representation of the baseband signal
argand plane. In this representation, the real (x-axis is called the Q (quadrature). Thus, in the case of OOK, the bit ‘1’ is represented as complex
number 1 + j0, which is on the real axis, and the bit ‘0’ is represented as
the origin. These two states marked on the complex plane constitute the constellation.
concerned only with the amplitude of the carrier wave and not the phase, the constellation points
lie on the real axis, without any image

For constructing the constellation diagram of such a signal, consider an incoming data stream.
We find out the bit duration (inverse of bit rate), and then
each bit slot. We mark the amplitudes received in all such bit slots on the complex plane. It is
possible that the received amplitude values are slightly deviating from the ideal values, due to
non-idealities in the channel, such as noise
corresponds to a voltage of 5 V, and due to noise in the channel, the received signal maybe 4.8
V or 5.2 V. In such a case, there is a
spread in the constellation. It is important to un

is the representation of the baseband signal s(t) as a complex number in the
In this representation, the real (x-) axis is called I (in-phase) and the imaginary (y
Thus, in the case of OOK, the bit ‘1’ is represented as complex

, which is on the real axis, and the bit ‘0’ is represented as 0 + j0
These two states marked on the complex plane constitute the constellation.
concerned only with the amplitude of the carrier wave and not the phase, the constellation points
lie on the real axis, without any imaginary part.

For constructing the constellation diagram of such a signal, consider an incoming data stream.
We find out the bit duration (inverse of bit rate), and then measure the amplitude of the signal in
We mark the amplitudes received in all such bit slots on the complex plane. It is
possible that the received amplitude values are slightly deviating from the ideal values, due to

, such as noise. For example, in digital logic,

corresponds to a voltage of 5 V, and due to noise in the channel, the received signal maybe 4.8
V or 5.2 V. In such a case, there is a distribution around the ideal points, which results in a
It is important to understand the concept of constellation because all
as a complex number in the
and the imaginary (y-)
Thus, in case of OOK, the bit ‘1’ is represented as complex
0, which is at the
These two states marked on the complex plane constitute the constellation. Since OOK is
concerned only with the amplitude of the carrier wave and not the phase, the constellation points

For constructing the constellation diagram of such a signal, consider an incoming data stream.
the amplitude of the signal in
We mark the amplitudes received in all such bit slots on the complex plane. It is
possible that the received amplitude values are slightly deviating from the ideal values, due to
For example, in digital logic, a level high
corresponds to a voltage of 5 V, and due to noise in the channel, the received signal may be 4.8
around the ideal points, which results in a
derstand the concept of constellation because all

the impairments in the fiber, in the receiver, will be analyzed in terms of how the constellation is
In case of BPSK, the bits are represented by two-phase levels separated by a phase difference of
π, which can be chosen as (0, π), (గ

,
ଷగ

), or (గ

,
ହగ

). Consider the first example, where the bit ‘0’
is represented by phase 0 and bit ‘1’ is represented by phase π, keeping the amplitude constant.
The corresponding complex number representation for these bits (assuming E଴ = 1) are given as

bit = 1; s(t) = E଴e

௝గ = −1 + j0

bit = 0; s(t) = E଴e

௝଴ = 1 + j0

These points lie on the real axis of the complex plane at positions −1 and +1 respectively.
Comparing with the constellation for OOK, we see that the separation between the points is more
in case of BPSK, which means that BPSK signal is more resilient to noise compared to OOK
(assuming no other constraints for BPSK).
The envelope of a BPSK signal is constant since there is no change in amplitude in this case.
Thus a phase detector that is able to detect the 0 or π phase is required in order to construct the
constellation of a received BPSK signal. If the signal is corrupted due to noise (due to
transmitter, channel, receiver etc.), there would be an error in the detected phase, which would
appear as a change in the angle of the constellation point. Later on, when we discuss the impact
of noise and the signal-to-noise ratio, we will analyze it in reference to the change in the
constellation.
We have so far dealt with transmitting a single bit in one-bit duration (Tb), with OOK and BPSK
modulation formats. The question arises at this point: is it possible to transmit more than one bits
in one-bit duration? It is possible if we use more than two amplitude or phase levels to represent
the bits. A combination of more than one bits is encoded in these amplitude or phase levels,
known as symbols, and these symbols are transmitted instead of the bits. Hence, in addition to the bit
rate that we defined in bits/s, we also define the symbol rate or baud rate. There exists a unique
relation between bit rate and symbol rate, depending on the way the bits are encoded into
symbols.
Consider the example of the bit sequence ‘000110110101001000110010’ as shown. In the case of
OOK or BPSK, one bit is transmitted per bit slot. Instead, we now try to transmit more than one
bits in the one-bit slot by encoding two bits in one symbol. Thus, the bits ‘00’ are represented by
symbol A, ‘01’ by B, ‘10’ by C and ‘11’ by D. Depending on the bit sequence, the symbols A, B,
C and D are transmitted in each bit slot Tb, instead of transmitting each bit individually. Assume
T௕ = 50 ps. In the case of OOK and BPSK, each slot corresponds to one bit, thus the bit rate is

ହ଴ ௣௦
= 20 Gbps. The bit rate and the symbol rate are the same in this case. Now consider the
case of two bits per symbol, the same bit rate of 20 Gbps can be achieved with T௕ = 100

ps. Thus, with two bits per symbol, only half the symbol rate,
Gbaud is required to obtain the same bit rate. Alternately, encoding two bits per symbol while
maintaining the symbol duration
the bit rate of the previous case.

The same idea can be extended to encode more number of bits per symbol.
encoding three bits in one symbol (‘000’ as
Similarly, encoding four bits in one symbol (‘0000’ as
16 symbols. The advantage of this higher-order encoding is to achieve larger bit rates for the
same symbol rate. The reason behind attempting to increase the order of encoding is that the
symbol rate or the symbol duration is g

electronics. The current state-of-
which has still not been commercialized, and hence not available at low cost, except at specific

high-end labs. Thus, in order to cater to the current standards of 100 Gbps data rates, the only
way is to implement higher-order encoding schemes (
Gbaud) symbol rates. We can thus see that the bit rates in an optical co
not limited by the channel, but by the bandwidth of the electronics involved in the system.
Thus, with two bits per symbol, only half the symbol rate, ଵ
ଵ଴଴ ௣௦
= 10 Gsymbol
, is required to obtain the same bit rate. Alternately, encoding two bits per symbol while

as 50 ps, the bit rate obtained is ଶ
ହ଴ ௣௦
= 40 Gbps, which is twice

can be extended to encode more number of bits per symbol.

encoding three bits in one symbol (‘000’ as A, ‘001’ as B and so on) would result in 8 symbols.
Similarly, encoding four bits in one symbol (‘0000’ as A, ‘0001’ as B and so on) would result in
The advantage of this higher-order encoding is to achieve larger bit rates for the
The reason behind attempting to increase the order of encoding is that, the
symbol rate or the symbol duration is generally limited by the speed or the bandwidth
-the-art electronics can support up to symbol rates of 96 Gbaud,
which has still not been commercialized, and hence not available at low cost, except at specific
Thus, in order to cater to the current standards of 100 Gbps data rates, the only
the way is to implement higher-order encoding schemes (modulation formats) with lower (10 or 20
We can thus see that the bit rates in an optical communication system
not limited by the channel, but by the bandwidth of the electronics involved in the system.
Gsymbol/s or 10
, is required to obtain the same bit rate. Alternately, encoding two bits per symbol while
Gbps, which is twice

can be extended to encode more number of bits per symbol. For example,
and so on) would result in 8 symbols.
and so on) would result in
The advantage of this higher order encoding is to achieve larger bit rates for the
The reason behind attempting to increase the order of encoding is that, the
bandwidth, of the
art electronics can support up to symbol rates of 96 Gbaud,
which has still not been commercialized, and hence not available at low cost, except at specific
Thus, in order to cater to the current standards of 100 Gbps data rates, the only
) with lower (10 or 20
communication system