ELEX 4340 : Data Communications
2013 Fall Session
Modulation
is lecture describes modulation, the technique used to transmit data signals over band-limited channels. Aer this lecture
you should be able to: explain the purpose of modulation; list some advantages of digital modulation; write expressions
for the time-domain signal, draw diagrams of the modulator, and draw constellation diagrams for: OOK, ASK, 4- and
8-PSK, m-ary QAM modulation; determine the spectrum of a modulated signal from the spectrum of the modulating signal,
compute the frequencies of FSK, MSK and GMSK signals, and determine if constellations are Gray-coded.
have switched to digital modulation (cellular, TV,
Modulation
...). ere are many advantages to digital modulation
including better spectral efficiency (less spectrum
e purpose of modulation is to shi the spectrum
required) and better power efficiency (less transmit
of the baseband signal to a higher frequency so it can
power required) and the ability to transmit any type
pass through a bandpass channel.
of content (audio, video, data, etc). We will study only
For example, in AM broadcasting a baseband audio
digital modulation in this course.
signal is shied to a higher frequency for example, to
a carrier frequency of between about 0.6 to 1.6 MHz,
so it can be transmitted by an antenna and propagate
to radio receivers PSK and QAM Modulation
ere are dozens of different types of modulation.
We will only look at some of the simplest and most
common examples.
e simplest type of modulator simply multiplies a
sinusoidal carrier with the baseband signal.
Another example is a TV video signal that is
shied to a frequency of several hundred MHz for
transmission over a co-ax cable. Different channels
are shied to different frequencies. is also allows
multiple TV signals to be carried on the same cable
without interfering with each other (FDMA).
e circuit or function that generates the modu-
lated signal is called a modulator. e corresponding
e modulated signal is
reverse operation at the receiver is called demodula-
tor. Oen both functions are included in one piece
of equipment called a “modem” (for MOdulator- s(t) = m(t) cos(ωc t)
DEModulator)
where the carrier is cos(ωc t) where ωc = 2πfc is
the frequency of the carrier signal and m(t) is the
Analog vs Digital Modulation modulating signal.
If the baseband signal has values 0 and 1 then
Analog modulation modulates the carrier with an ana-
the modulation is called on-off-keying (OOK) or
log baseband signal. e receiver recovers the analog
Amplitude Shi Keying (ASK). is is used only for
signal. Examples are AM and FM audio broadcasting.
the very simplest applications (e.g. remote controls).
Digital modulation modulates the carrier with a
digital baseband signal. e receiver recovers the Exercise 1: Draw the waveform of an OOK (ASK) signal. Show
digital data (bits). Almost all communication systems the periods of the carrier and the modulating signal.
lec13.tex 1
a phasor diagram showing the carrier magnitude and
QAM
phase of each for each possible modulation value.
If the baseband signal has values ±1 then the modula-
tion inverts the polarity of the signal. is is equivalent
to shiing the phase of the signal by 180 degrees since:
cos(θ + π) = − cos(θ)
For this reason this type of modulation is usually
called BPSK (Binary Phase Shi Keying).
Exercise 2: Label the other three points in the constellation
diagram with the equation of the signal that corresponds to
that point.
Instead of just changing the phase of the carrier, we
can change the amplitudes of the I and Q components.
For example if we multiply the I and Q components
by +/-1 or +/-3 (total of 4 levels) we can transmit 16
different possible waveforms (4 different I amplitudes
We can also vary the phase of the signal by other and 4 different Q amplitudes). is allows us to
amounts. For example, we can use phase shis of 0, transmit 4 bits per symbol. is is called 16-QAM.
90, 180 and 270 degrees to transmit 4 different phases. is is the constellation:
e transmitter can encode 2 bits if there are four
possible phases. is type of modulation is called
QPSK (Quadrature PSK).
is type of modulator can be implemented as two
signals modulating two carriers that are orthogonal
(90 degree phase difference). One is called the
in-phase (I) component and the other is called the
quadrature (Q) component.
where each point is labelled with the bits that are
transmitted if that symbol (a carrier with the given I
and Q amplitudes) is transmitted.
e equation for the modulated signal is:
M -ary Modulation
s(t) = ±1 cos(ωc t) + ±1 sin(ωc t)
It is common to view the modulating signal as a In general if we can transmit M distinct signals (sym-
complex value modulating (multiplying) a single car- bols) we can can encode log2 (M ) bits. is is called
rier. For the case of QPSK this complex modulating M -ary modulation. For example 64 − QAM can
signal has values ej0 , ejπ/2 , ejπ , ej3π/2 . encode 6 bits per symbol using a 64-point (8 × 8) con-
We can draw the possible I and Q amplitudes on a stellation. e following diagram shows the 64-QAM
2-D plane. is is called a constellation diagram. It is constellation used for the 802.11 WLAN standard:
2
Demodulation of QAM
By multiplying the received signal by I and Q carriers
and low-pass filtering we can recover the transmitted
I and Q components.
e constellation points can also be arranged in a
circle. is corresponds to changing only the phase
of the signal while leaving the amplitude fixed. We e receiver has to recover the phase of the carrier
can, for example have 8 phases (called 8-PSK) and to accurately set the I and Q phases. is can be done,
transmit 3 bits per symbol. for example, by transmitting a preamble that has a
Exercise 3: Draw the constellation for 8-PSK.
known phase.
Spectra of Modulated Signals FSK, MSK, GMSK
Multiplying the the baseband signal by a carrier shis We can also vary the frequency of the signal. is
the spectrum of the modulating signal from zero (DC) type of modulation is called Frequency Shi Keying
to the carrier frequency. Instead of being centered (FSK). It cannot be represented on a phasor diagram
at zero the spectrum of the modulating signal is now because the carrier phase is constantly changing (it
centered around the carrier frequency. would be an arc on a circle).
e bandwidth of the modulated signal is double Typically there are only two frequencies. e
the baseband bandwidth because the negative portion frequency deviation is the difference between the two
of the spectrum is also shied to the carrier frequency. frequencies. e bandwidth of the FSK signal in-
However we can transmit twice as much data: the creases with increasing frequency deviation and also
real and imaginary components can be modulated with increasing frequency of the modulating signal.
independently. A variant of FSK where the frequency shi is equal
to half of the bit rate is called minimum shi keying
(MSK). For example, if the symbol rate was 1kHz the
ISI two frequencies would differ by 500Hz. is makes
the two signals orthogonal and simplifies the design
e Nyquist criteria for no-ISI are the same for
of the receiver.
modulated signals as for baseband channels, but apply
A variant of MSK where the modulating signal is
to the I and Q channels separately.
filtered by a filter with a Gaussian impulse response
Exercise 4: If the I and Q modulating signals have symbol is called GMSK (Gaussian MSK). e advantage of
rates of 2 MHz, what is the minimum bandwidth of the I and Q GMSK is that it has a low sidelobe levels so it is oen
channels so that there is no ISI? What would be the bandwidth used for channelized RF systems such as GSM (2G cel-
of the modulated (RF) signal? What are the spectral efficiencies lular) and DECT (European digital cordless phone).
(symbols/second/Hz) of the baseband and of the modulated
signals?
3
Gray Coding
Constellations are usually gray coded. is means
that the bits corresponding to adjacent points in
the constellation differ by only one bit. Since errors
between adjacent points are the most likely, gray
coding minimizes the bit error rate. e 16-QAM and
64-QAM constellations shown above are gray-coded.
Exercise 5: Assign gray-coded values to the 8-PSK constella-
tion.
