QAM
Quadrature Amplitude
Modulation
QAM: Quadrature Amplitude Modulation combines
amplitude & phase changes to give additional capacity & is
widely used for data communications.
Quadrature Amplitude Modulation, QAM utilizes both
amplitude and phase components to provide a form of
modulation that is able to provide high levels of spectrum
usage efficiency.
QAM, quadrature amplitude modulation has been used for some
analogue transmissions including AM stereo transmissions, but it is
for data applications where it has come into its own. It is able to
provide a highly effective form of modulation for data and as such
it is used in everything from cellular phones to Wi-Fi and almost
every other form of high speed data communications system.
What is QAM, quadrature amplitude modulation?
Quadrature Amplitude Modulation, QAM is a signal in which two carriers
shifted in phase by 90 degrees (i.e. sine and cosine) are modulated and
combined. As a result of their 90° phase difference they are in quadrature
and this gives rise to the name. Often one signal is called the In-phase or
“I” signal, and the other is the quadrature or “Q” signal.
The resultant overall signal consisting of the combination of both I and Q
carriers contains of both amplitude and phase variations. In view of the fact
that both amplitude and phase variations are present it may also be
considered as a mixture of amplitude and phase modulation.
A motivation for the use of quadrature amplitude modulation comes from
the fact that a straight amplitude modulated signal, i.e. double sideband
even with a suppressed carrier occupies twice the bandwidth of the
modulating signal. This is very wasteful of the available frequency
spectrum. QAM restores the balance by placing two independent double
sideband suppressed carrier signals in the same spectrum as one ordinary
double sideband suppressed carrier signal.
Analogue and digital QAM
Quadrature amplitude modulation, QAM may exist in what may be termed
either analogue or digital formats. The analogue versions of QAM are
typically used to allow multiple analogue signals to be carried on a single
carrier. For example it is used in PAL and NTSC television systems, where
the different channels provided by QAM enable it to carry the components
of chroma or colour information. In radio applications a system known as C-
QUAM is used for AM stereo radio. Here the different channels enable the
two channels required for stereo to be carried on the single carrier.
Digital formats of QAM are often referred to as "Quantized QAM" and they
are being increasingly used for data communications often within radio
communications systems. Radio communications systems ranging from
cellular technology as in the case of LTE through wireless systems including
WiMAX, and Wi-Fi 802.11 use a variety of forms of QAM, and the use of QAM
will only increase within the field of radio communications.
Digital / Quantized QAM basics
Quadrature amplitude modulation, QAM, when used for digital
transmission for radio communications applications is able to
carry higher data rates than ordinary amplitude modulated
schemes and phase modulated schemes.
Basic signals exhibit only two positions which allow the transfer
of either a 0 or 1. Using QAM there are many different points
that can be used, each having defined values of phase and
amplitude. This is known as a constellation diagram. The
different positions are assigned different values, and in this way
a single signal is able to transfer data at a much higher rate.
As shown above, the constellation points are typically arranged in a
square grid with equal horizontal and vertical spacing. Although data is
binary the most common forms of QAM, although not all, are where
there constellation can form a square with the number of points equal
to a power of 2 i.e. 4, 16, 64 . . . . , i.e. 16QAM, 64QAM, etc.
By using higher order modulation formats, i.e. more points on
the constellation, it is possible to transmit more bits per symbol.
However the points are closer together and they are therefore
more susceptible to noise and data errors.
The advantage of moving to the higher order formats is that
there are more points within the constellation and therefore it is
possible to transmit more bits per symbol. The downside is that
the constellation points are closer together and therefore the
link is more susceptible to noise. As a result, higher order
versions of QAM are only used when there is a sufficiently high
signal to noise ratio.
To provide an example of how QAM operates, the constellation diagram below shows the
values associated with the different states for a 16QAM signal. From this it can be seen
that a continuous bit stream may be grouped into fours and represented as a sequence.
Normally the lowest order QAM encountered is 16QAM. The reason
for this being the lowest order normally encountered is that 2QAM is
the same as binary phase-shift keying, BPSK, and 4QAM is the same
as quadrature phase-shift keying, QPSK.
Additionally 8QAM is not widely used. This is because error-rate
performance of 8QAM is almost the same as that of 16QAM - it is
only about 0.5 dB better and the data rate is only three-quarters
that of 16QAM. This arises from the rectangular, rather than square
shape of the constellation.
QAM advantages and disadvantages
Although QAM appears to increase the efficiency of transmission for radio
communications systems by utilizing both amplitude and phase
variations, it has a number of drawbacks. The first is that it is more
susceptible to noise because the states are closer together so that a
lower level of noise is needed to move the signal to a different decision
point. Receivers for use with phase or frequency modulation are both
able to use limiting amplifiers that are able to remove any amplitude
noise and thereby improve the noise reliance. This is not the case with
QAM.
The second limitation is also associated with the amplitude component of
the signal. When a phase or frequency modulated signal is amplified in a
radio transmitter, there is no need to use linear amplifiers, whereas
when using QAM that contains an amplitude component, linearity must
be maintained. Unfortunately linear amplifiers are less efficient and
consume more power, and this makes them less attractive for mobile
applications.
QAM vs PSK & other modes
When deciding on a form of modulation it is worth comparing AM vs
PSK and other modes looking at what they each have to offer.
As there are advantages and disadvantages of using QAM it is
necessary to compare QAM with other modes before making a
decision about the optimum mode. Some radio communications
systems dynamically change the modulation scheme dependent
upon the link conditions and requirements - signal level, noise, data
rate required, etc.
SUMMARY OF TYPES OF MODULATION WITH DATA CAPACITIES
MODULATIO BITS PER -- ERROR MARGIN -- COMPLEXITY
N SYMBOL
OOK 1 1/2 0.5 Low
BPSK 1 1 1 Medium
QPSK 2 1 / √2 0.71 Medium
16 QAM 4 √2 / 6 0.23 High
64QAM 6 √2 / 14 0.1 High
QAM Theory and Formulas
the basic theory and relevant formulas or equations behind QAM quadrature
amplitude modulation give additional insight into its operation.
QAM theory basics
Quadrature amplitude theory states that both amplitude and phase change
within a QAM signal.
The basic way in which a QAM signal can be generated is to generate two
signals that are 90° out of phase with each other and then sum them. This will
generate a signal that is the sum of both waves, which has a certain amplitude
resulting from the sum of both signals and a phase which again is dependent
upon the sum of the signals.
If the amplitude of one of the signals is adjusted then this affects both the
phase and amplitude of the overall signal, the phase tending towards that of
the signal with the higher amplitude content.
As there are two RF signals that can be modulated, these are referred to as the
I - In-phase and Q - Quadrature signals.
The I and Q signals can be represented by the equations below:
I=Acos(Ψ) and Q=Asin(Ψ)
It can be seen that the I and Q components are represented as
cosine and sine. This is because the two signals are 90° out of phase
with one another.
Using the two equations it is possible to express the signal as:.
cos(α+β)=cos(α)cos(β)−sin(α)sin(β)
Using the expression A cos(2πft + Ψ) for the carrier signal.
Acos(2πft+Ψ)=Icos(2πft)−Qsin(2πft)
QAM Formats: 8-QAM, 16-QAM, 32-QAM, 64-QAM, 128-QAM, 256-QAM
Quadrature amplitude modulation can be used with a variety of
different formats: 8QAM, 16QAM, 64QAM, 128QAM, 256QAM, but there
are performance differences and trade-offs
QAM, quadrature amplitude modulation provides some significant
benefits for data transmission. As 16QAM transitions to 64QAM, 64QAM
to 256 QAM and so forth, higher data rates can be achieved, but at the
cost of the noise margin.
Many data transmission systems migrate between the different orders
of QAM, 16QAM, 32QAM, etc., dependent upon the link conditions. If
there is a good margin, higher orders of QAM can be used to gain a
faster data rate, but if the link deteriorates, lower orders are used to
preserve the noise margin and ensure that a low bit error rate is
preserved.
As the QAM order increases, so the distance between the different
points on the constellation diagram decreases and there is a higher
possibility of data errors being introduced. To utilise the high order
QAM formats, the link must have a very good Eb/No otherwise data
errors will be present. When the Eb/No deteriorates, then other the
power level must be increased, or the QAM order reduced if the bit
error rate is to be preserved.
Accordingly there is a balance to be made between the data rate
and QAM modulation order, power and the acceptable bit error
rate. Whilst further error correction can be introduced to mitigate
any deterioration in link quality, this will also decrease the data
throughput.
QAM formats and applications
QAM is in many radio communications and data delivery
applications. However some specific variants of QAM are used in
some specific applications and standards.
There is a balance between data throughput and signal to noise
ratio required. As the order of the QAM signal is increased, i.e.
progressing from 16QAM to 64QAM, etc. the data throughput
achievable under ideal conditions increases. However the downside
is that a better signal to noise ratio is required to achieve this.
Constellation diagrams for QAM
The constellation diagrams show the different positions for the
states within different forms of QAM, quadrature amplitude
modulation. As the order of the modulation increases, so does the
number of points on the QAM constellation diagram.
The diagrams below show constellation diagrams for a variety of
formats of modulation:
QAM bits per symbol
The advantage of using QAM is that it is a higher order form of modulation and as a result it is able to
carry more bits of information per symbol. By selecting a higher order format of QAM, the data rate of a
link can be increased.
The table below gives a summary of the bit rates of different forms of QAM and PSK.
QAM FORMATS & BIT RATES COMPARISON
MODULATION BITS PER SYMBOL SYMBOL RATE
BPSK 1 1 x bit rate
QPSK 2 1/2 bit rate
8PSK 3 1/3 bit rate
16QAM 4 1/4 bit rate
32QAM 5 1/5 bit rate
64QAM 6 1/6 bit rate
QAM noise margin
QAM FORMATS & NOISE PERFORMANCE
MODULATION ηB EB / NO FOR
6
BER = 1 IN 10
16QAM 2 10.5
64QAM 3 18.5
256QAM 4 24
1024QAM 5 28
QAM Modulator & Demodulator
The modulation and demodulation of quadrature amplitude
modulation, QAM utilises circuits that are able to accommodate
both I and Q components.
In any system that uses quadrature amplitude modulation, QAM,
there will be modulators and demodulators.
These QAM modulators and demodulators are required to provide
the capability to modulate both the in-phase and quadrature
components of the modulating signal onto the carrier.
QAM modulator basics
The QAM modulator essentially follows the idea that can be seen
from the basic QAM theory where there are two carrier signals with
a phase shift of 90° between them. These are then amplitude
modulated with the two data streams known as the I or In-phase
and the Q or quadrature data streams. These are generated in the
baseband processing area.
The two resultant signals are summed
and then processed as required in the RF
signal chain, typically converting them in
frequency to the required final frequency
and amplifying them as required.
It is worth noting that as the amplitude of
the signal varies any RF amplifiers must
be linear to preserve the integrity of the
signal. Any non-linearities will alter the
relative levels of the signals and alter the
phase difference, thereby distorting he
signal and introducing the possibility of
data errors.
QAM demodulator basics
The QAM demodulator is
very much the reverse of
the QAM modulator.
The signals enter the
system, they are split and
each side is applied to a
mixer. One half has the
in-phase local oscillator
applied and the other
half has the quadrature
oscillator signal applied.
The basic modulator assumes that the two quadrature signals
remain exactly in quadrature.
A further requirement is to derive a local oscillator signal for the
demodulation that is exactly on the required frequency for the
signal. Any frequency offset will be a change in the phase of the
local oscillator signal with respect to the two double sideband
suppressed carrier constituents of the overall signal.
Systems include circuitry for carrier recovery that often utilises a
phase locked loop - some even have an inner and outer loop.
Recovering the phase of the carrier is important otherwise the bit
error rate for the data will be compromised.
References:
https://www.electronics-notes.com/articles/radio/modulation/quadrature-amplitude-
modulation-what-is-qam-basics.php
https://www.electronics-notes.com/articles/radio/modulation/quadrature-amplitude-
modulation-qam-theory-formulas-equations.php
https://www.electronics-notes.com/articles/radio/modulation/quadrature-amplitude-
modulation-types-8qam-16qam-32qam-64qam-128qam-256qam.php
https://www.electronics-notes.com/articles/radio/modulation/quadrature-amplitude-
modulation-qam-modulator-demodulator.php
