CSN200 Introduction to Telecommunications, Winter 2000
Lecture-18 Analog Transmission and Modulation
Analog Transmission of Digital Data (Broadband Transmission):
There are many occasions when data need to be transmitted over a voice communication network.
Many people use a computer to connect to their Internet Service Provider via the telephone lines to
transmit and receive data, check their email, surf the Web, etc.
Telephone networks were originally built for human speech, not for computer data and is unsuitable for
digital communication in its raw form.

The transmission impairments and the bandwidth limitation makes digital signalling (have a wide
spectrum) unsuitable for transmission over the local loop (designed for analog transmission).
Transmission Impairments:
Transmission lines suffer from three major problems:
Attenuation - is the loss of energy as the signal propagates outward. The amount of energy lost
depends on the frequency. Each Fourier component is attenuated by a different amount.
Delay distortion - It is caused by the fact that different Fourier components travel at different speeds.
For digital data, fast components from one bit may catch up and overtake slow
components from the bit ahead, mixing the two bits and increasing the probability of
incorrect reception.
Noise
- unwanted energy from the sources other than the transmitter. Thermal noise, cross talk,
impulsive noise.
Problems of using Voice Channels for Digital Transmission
A digital signal is comprised of a number of signals. Specifically, the signal is represented as follows,
signal = f + f3 + f5 +f7 +f9 +f11 +f13 ....f(infinity)
This means a digital signal has a base frequency, plus another at three times
the base frequency, plus another at five times the base frequency etc. f3 is
called the third harmonic, f5 the fifth harmonic and so on.
The third harmonic is one third of the amplitude of the base frequency (also
called the fundamental frequency), the fifth harmonic is one fifth the
amplitude of the fundamental and so on.
In order to send a digital signal across a voice channel, the bandwidth of the
channel must allow the fundamental plus third and fifth harmonic to
pass without affecting them too much.
As can be seen, this is what such a signal looks like, and is the minimum
required to be correctly detected as a digital signal by the receiver.
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Lecture-18 Analog Transmission and Modulation
Lets consider sending a 2400bps binary digital signal down a voice channel rated with a bandwidth of
3.1KHz. The base frequency of the digital signal is 1200Hz (it is always half the bit rate), so the
fundamental frequency will pass through the channel relatively unaltered. The third harmonic is
3600Hz, which will suffer attenuation and arrive severely altered (if at all). The fifth harmonic
has no chance of passing the channel.
In this case it can be seen that only the base frequency will arrive at the
end of the channel. This means the receiver will not be able to
reconstruct the digital signal properly, as it will require f3 and f5 for
proper reconstruction.
This results in errors in the detection process by the receiver.
The Public Switched Telephone Network has, for a long time, provided users with dial up telephone
connections on demand. Each connection has supported analogue speech in the voice range of 300Hz to
3400Hz. The signals provided by computers are digital, and are not designed to travel across the dial up
telephone connections.
In order for digital signals to be sent across a telephone connection, they must be converted to analogue
voice tones within the frequency range 300Hz to 3400Hz (this is done by a modem).

To get around the problems associated with the dc signalling or digital signalling, especially on
telephone lines, analog signalling is used. A continuous tone in the range 1000Hz to 2000Hz, called a
sine wave carrier is used. Its amplitude, frequency, or phase can be modulated (changed with the
information) to transmit information.
Frequency = Number of waves or Cycles per Sec
= 1/(Time Period in Sec)

= (1/T) Cycles per Sec or Hertz
Every sound wave has two parts, half above the zero point (positive), and half below (negative) and three
important characteristics.
 The height of the wave is called amplitude.
 The length of the sound wave is expressed as the number of waves per second or frequency,
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
Lecture-18 Analog Transmission and Modulation
expressed in Hertz (Hz).
The phase is the direction in which the wave begins.
Bandwidth refers to a range of frequencies.
Human hearing ranges from about 20 Hz to about 14,000 Hz (some up to 20,000 Hz). Human voice
ranges from 100 Hz to about 3,100 Hz.
The bandwidth of a voice signal is 3000 Hz (3 kHz).
The bandwidth of a voice grade telephone circuit is 0 to 4000 Hz or 4000 Hz (4 kHz).
Guardbands prevent data transmissions from interfering with other transmission when these circuits are
multiplexed using FDM.
It is important to note that the limit on bandwidth is imposed by the equipment used in the telephone
network.
The actual capacity of bandwidth of the wires in the local loop depends on what exact types of wires were
installed, and the number of kilometers in the local loop.
Actual bandwidth of local loops in North America varies from 300 kHz to 1.5 MHz depending on
distance. Longer the loop, lower the bandwidth.
Modulation:
Modulation is the technique that modifies the form of an electrical signal so the signal can carry
information on a communications media.
Types of Modulation:
 Analog Modulation (analog encoding of digital information)
 Digital Modulation (digital encoding of analog information)
Analog Modulation:
Modifies the form of an analog electrical signal so the signal can carry information.
The signal that does the carrying is the carrier wave. Modulation changes the shape of the carrier wave (a
sine wave) to transmit 0s and 1s.
There are three fundamental methods of analog modulation of an analog signal:
 Amplitude Modulation (AM)
 Frequency Modulation (FM)
 Phase Modulation(PM)
These three fundamental methods of analog modulation are called differently when the information is a
digital signal:
 Amplitude Shift Keying (ASK)
 Frequency Shift Keying (FSK)
 Phase Shift Keying (PSK)
All analog modulation techniques employ a carrier signal. A carrier signal is a single frequency that is
used to carry the intelligence (data).
For digital data, the intelligence is either a 1 or 0. When we modulate the carrier , we are changing its
characteristics to correspond to either a 1 or 0.
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Lecture-18 Analog Transmission and Modulation
 Amplitude Modulation (AM) varies the amplitude or height of the signal to carry the information.
(Fig 4-9)
 One amplitude level is used to represent a 1 and another for a 0.
 This is also called Amplitude Shift Keying or ASK.
 Not commonly used because it is too susceptible to noise, causing more errors in transmission.
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Lecture-18 Analog Transmission and Modulation
 Frequency Modulation (FM) varies the frequency of the signal to send data. (Fig 4-10)
 One frequency represents 1s and another frequency represents 0s.
 For example, a 1200 Hz tone may send a 0 bit while a 2400 Hz tone sends a 1 bit.
 This is also called Frequency Shift Keying or FSK.
 It is not as widely used now as Phase Modulation is more efficient.
 Phase Modulation (PM) varies the phase of the carrier signal to send data. (Fig 4-11)
 Phase refers to the relationship of one wave to another. One cycle of a sine wave has 360 so if
a sine wave has a phase of 180 every time a zero bit was sent and a phase of 0 every time a
one bit was sent, it would appear as in Fig. 5-10. A 180 phase shift of a signal is one half a
full cycle.
 One phase of the carrier sinewave is used to represent 1’s and another phase 0’s.
 PSK (Phase Shift Keying) (Fig 4-11)
 Uses 180 phase shift of the carrier every time there is a change from a 1 to a 0 or a 0 to
a 1.
 DPSK (Differential Phase Shift Keying)
 The phase of the carrier shifts 180 every time a 1 is transmitted.
Phase Modulation is a very common form of modulation used in high speed modems today.
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Lecture-18 Analog Transmission and Modulation
Modulator:
The circuit or device does the process of modulation is called the modulator.
Demodulation:
Demodulation is the process of converting back the modulated signal to its original information (in our
case the digital signal, 1s and 0s).
Demodulator:
The circuit or device does the process of demodulation is called the demodulator.
MODEMS:
Modem is an acronym for Modulator/demodulator, and takes digital electrical pulses from a computer,
terminal, or microcomputer and converts them into a continuous analog signal, for transmission over
an analog voice grade circuit.
It then re-converts the analog signal to its original digital format.
Most modems accept commands from a microcomputer keyboard.
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Lecture-18 Analog Transmission and Modulation
Bit Rate versus Baud Rate versus Symbol Rate:

Two different terms were used to describe the rate at which data is transmitted:
Bit Rate - Bits per second (bps) and
Baud Rate - Baud per second (Not known as bps, but confusion may happen).
Bit Rate:
The rate at which information bits are transmitted over a communication path. Normally
expressed in bits per second, (bps).
Baud Rate: Is a unit of signalling speed, indicating the number of signal events or signal changes per
second. A signal change occurs when the amplitude, frequency or phase of a carrier signal
changes.
In the early days of modems, signalling units (tokens) were called "baud" in honour of the
French inventor Emile Baudot who, in 1875, invented a 5 bit code for representing the
alphabet. Each 5 bits were a token communicating a letter of the alphabet or a control code.
If each signal event represents only one bit, then bits per second and baud are identical.
When each signal event represents more than one bit of information, then bps no longer equals baud.

The terms bit rate (the number of bits per second) and baud rate are used incorrectly much of the time.
They are not the same.
A bit is a unit of information, a baud is a unit of signaling speed, the number of times a signal on a
communications circuit changes.

To remove the confusion between the bps and baud, ITU-T now recommends the term baud rate be
replaced by the term Symbol rate (symbols per second).
The bit rate and the symbol rate (or baud rate) are the same only when one bit is sent on each symbol. If
we use QAM or TCM, the bit rate would be four to eight times the baud rate.
Multibit Encoding of Information:
Before high speed modems (above 2400 bps) were possible a technique had to be developed to encode
bits so the bit rate could be larger than the signalling rate or baud.

All high speed modems use multibit encoding techniques so more than one bit of information is sent
each time the carrier changes state.

If each change of the carrier signal sends more than one bit of information then
bps > baud
For example, if we have 4 possible amplitude levels for the carrier sine wave then each level can be used
to represent 2 bits of information, (Fig 4-12)
Sending Multiple Bits Simultaneously:
Each of the three modulation techniques can be refined to send more than one bit at a time. It is possible
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Lecture-18 Analog Transmission and Modulation
to send two bits on one wave by defining four different amplitudes.
Amplitude
1 volt
2 volts
3 volts
4 volts
Bit value
00
01
10
11
For 2 bits per baud, we need 22 or 4 unique states of the carrier.
If the carrier sinewave amplitude was changing 1000 times per second but each amplitude represented 2
bits of information, then
baud = 1000 Hz
bps = 2000 bps

This technique could be further refined to send three bits at the same time by defining 8 different
amplitude levels or four bits by defining 16, etc. The same approach can be used for frequency and
phase modulation.
For 3 bits per baud we need 23 or 8 states.
For 4 bits per baud we need 24 or 16 states.
In general to transmit n bits per baud you require 2n states.
baud = bps / (# of bits/baud)
or
bps = baud * (# of bits/baud)
A 14,400 bps modem may use 2400 baud with 6 bits/baud encoding.
26 = 64 so there must be 64 unique states of the carrier for each of the 64 combinations of 6 bits to be
identified.
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Lecture-18 Analog Transmission and Modulation
It is not practical to use amplitude modulation with 64 different amplitude levels, or frequency modulation
with 64 different frequencies. As the number of different amplitudes, frequencies or phases
becomes larger, it becomes very difficult for a receiving modem to differentiate among them
correctly. Errors are made in interpreting the signal state.
In practice, the maximum number of bits that can be sent with any one of these techniques is about five
bits. The solution is to combine modulation techniques.
One popular technique is quadrature amplitude modulation (QAM) involves splitting the signal into
eight different phases, and two different amplitude for a total of 16 different possible values.
QAM: Quadrature Amplitude Modulation involves modulating the carrier with 8 different phases (3
bits) and two different amplitudes (1 bit) for 16 possible states of the carrier. So one signal
change can represent 4 bits (4 bits/baud). This is used in 9600 bps modems with a 2400 baud
rate.
The problem with high speed modulation techniques such as QAM is that they are more sensitive to
imperfections in the communications circuit.
Trellis coded modulation (TCM) is an enhancement of QAM that combines a noise reduction technique.
Various forms of TCM encode 6,7, 8 or 10 bits per baud.
At 8 bits/baud a modem using a 2400 baud signaling rate would transmit at 19,200 bps and
require 256 unique states of the carrier.
Capacity of a Voice Circuit:
The capacity of a voice circuit (the maximum data rate) is the fastest rate at which you can send your data
over the circuit.
The maximum symbol rate in any circuit depends upon the bandwidth available and the signal-to-noise
ratio.
Voice grade lines provide a bandwidth of 3000 (=3300 - 300) Hz and a signal-to-noise of 30dB.
Maximum Symbol (Baud) Rate:
The maximum symbol rate in any circuit depends upon the bandwidth available and the amount of noise
in the circuit.
 As a rule, the maximum baud rate is usually the same as the bandwidth.
The maximum baud rate in a dial-up voice circuit (with a bandwidth) is usually 3000 bauds.
Overtime, modem designers began to realize that the telephone network was getting better and that more
bandwidth was available. The baud rate has been extended to 3429 in newer v.34 and v.34+ modems.
(Uses a carrier of 1959 Hz, this implies that less than one cycle of the carrier is being used for each
signaling event. Needs a bandwidth from 244 [=1959-3429/2] Hz to 3674 [=1959 +3429/2] Hz.)
V.34+ uses a symbol rate of 3429 and the number of bit per symbol is 9.8 resulting a maximum data rate
of 33600 bps. Which is the maximum data rate limit according to shanon' theorem.
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Lecture-18 Analog Transmission and Modulation
Shanon's Theorem:
There is a limit to the amount of information that could be communicated over a band limited channel in
the presence of noise. This is known as the channel capacity (maximum number of bits per sec).
One of the most fundamental laws used in telecommunications is Shanon's law.
In 1948 Shanon proved that the maximum data rate of a noisy channel whose bandwidth is B Hz, and
whose signal-to-noise ratio is S/N, is given by
Channel Capacity = B log2 (1+S/N) bps
where: bps = bits per second
B = channel bandwidth
S/N = signal to noise power ratio
For a bandwidth of 3.1 kHz and a signal to noise ratio of 30 dB (a ratio of 1000/1),
the maximum data rate is 31 kbps.
Channel Capacity
= B log2 (1+S/N) bps
= 3100 log2 (1+1000) bps
= 3100 log2 (1001) bps
= 3100 log2(29.967) bps
= 3100 x 9.967 bps
= 30,898 bps
= 31 kbps
A telephone circuit has a signal-to-noise ratio of about 30dB and a newer bandwidth of about 3429 Hz.
A signal-to-noise ratio of 30 dB = a ratio of 1000 to 1. log2 (1+1000) is roughly equal to 10.
So, the bps = 3429 x 10 = 34290 = 33.6 kbps.
Todays Modems reached that limit of data rate on a old telephone line (it is not the wire itself, it includes
the circuitry at the local telephone offices).
Nyquist Theorem (Noiseless channel):
Max. data rate = 2 B log2 M bps
where B is the bandwidth, M is signal levels
Shannon Theorem (Random noise):
Max. data rate = B log2 ( 1 + S/N ) bps
where B is the bandwidth, S/N is the signal-to-noise ratio.
Signal-to-noise ratio (SNR):
SNR = 10 log10 S/N decibels(dB)
Nyquist Sampling Theorem:
If a signal f(t) is sampled at regular intervals of time and at a rate higher than twice the highest
significant signal frequency, then the samples contain all the information of the original signal.
The function f(t) may be reconstructed from these samples by the use of a low-pass filter.
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Lecture-18 Analog Transmission and Modulation
QAM (Quadrature Amplitude Modulation):
QAM operates by modulating a carrier sine wave signal in both amplitude and phase. Each unique
combination of amplitude and phase is known as a "symbol".
And when you talk of amplitude and phase, you immediately think of vectors. It turns out that modem
designers use the concept of vectors to visualize the symbols being transmitted. For example, the
figure below shows one representative symbol, a combination of amplitude and phase.
Figure: Graph of a single symbol, showing the amplitude and phase
As you try to represent a large number of symbols, however, the graph can get fairly busy. Additionally,
some symbols will have the same phase angle but different values of amplitude. These two
vectors will lay atop one another and it will be hard to see the one with the lesser amplitude.
Because of this, modem designers graph only the end points of the vectors, using a dot to
represent the end point location of the vector. When a large number of symbols are drawn on a
graph, the resulting figure is known as a "constellation" because it begins to look like a star map.
A simple constellation of only four symbols is shown in the figure below.
Transmitted Symbol
Received Symbol
01
00
Decision Region
10
Error Vector
11
Figure: A four point constellation showing the values assigned to each symbol and the receiver
decision region
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Lecture-18 Analog Transmission and Modulation
This figure also illustrates the decision region, another aspect of the transmission of a symbol from the
transmitter to the receiver. Although the transmitter sends the symbol accurately, the
transmission channel can modify the symbol in ways that cause the symbol received by the
receiver to be different than the one transmitted. For example, suppose a noise transient occurs
during the transmission of the symbol. This may cause the amplitude to be larger or smaller than
what was transmitted, which makes the constellation point move compared to what was
transmitted. This difference is called the "error vector". However, as long as the received
constellation point is within the decision region, it will be interpreted as the correct symbol and
the proper bits will be communicated.
As the modem uses more and more symbol points, the decision region shrinks, leading to a higher error
rate in the presence of noise. Thus, a modem designer can’t just keep increasing the number of
symbols to gain a higher data rate – at some point you can no longer communicate data at an
acceptable error rate.
To a large degree, this is why your V.34 modem doesn’t connect at 33.6 Kbps very often. To
communicate at 33.6 Kbps with V.34, the modem has to use a very large number of symbol
points (1,664 symbols, 10.7 bits per symbol). Since the transmit power is limited, the overall size
of the constellation can only be so large. This means that the symbol points must be very close
together, making it very difficult for the receiver to accurately distinguish which symbol was
sent. To operate, therefore, the modem must "downrate" to a constellation which uses a smaller
number of symbol points. In reality, there are other types of channel impairments, such as
available bandwidth, which also limit operation at these higher rates, but noise, both Gaussian
and quantization, plays a large part.
Phase Reference Signal
Quadrature Amplitude Modulation produces 8 signal states from a combination of 4 angles and 2
amplitude levels.
Similarly the number of signal states can be increased to 16 signal states from a combination of 4 angles
and 4 amplitude levels. And so on upto a practical limit imposed by noise and detection errors.
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Lecture-18 Analog Transmission and Modulation
TCM (Trellis coded modulation):
TCM is an enhancement of QAM that combines a noise reduction technique.
Trellis Coded Modulation (TCM) encoding is a forward, error-correcting technique that allows a modem
to more readily recover data corrupted by noise and other transmission impairments on the
telephone line. Trellis encoding allows error detection and correction without retransmission of
the data. This is different to and separate from the error-control methods of the V.42 LAPM and
MNP protocols. Trellis encoding is available when the modem is operating in the ITU-T V.32 or
V.32bis mode and connected to another V.32 or V.32bis modem. In the case of V.32bis, TCM is
unconditionally active at 7200 bps and above and cannot be disabled. In the case of V.32, TCM
can be activated only at 9600 bps. The factory default is for TCM to be enabled. It can be
disabled with the AT&U1 command.
LAPM – Link Access Protocol for Modems. A type of error control used by modems. It is
included in the V.42 and V.42bis protocol.
This trellis coding technique developed about the time of V.32, generally credited to Gottfried
Ungerboeck at IBM’s Zurich Research Laboratory.
Trellis codes explanation: If you look back at the above figure, you’ll see how the decision region
surrounds the transmitted symbol point. As more and more points are defined, the decision
region shrinks until a small amount of noise can move the symbol point into another symbol’s
decision region, causing an incorrect decode by the receiver.
Suppose, however, that you had a way to subset the constellation points, removing half or more of the
points to maximize the decision region around each remaining point. This would allow the
receiver to more accurately decode which symbol point was sent, in the presence of noise.
This is essentially what’s done with trellis (frame or lattice) codes. A number of constellations are
created, each with the maximum sized decision region around each symbol.
In trellis code, the constellation is divided into 2, 4, 8, ... subsets with size Total Points/2, Total Points/4,
Total Points/8, etc. That results in larger distances between signal points in the new subset
constellations.
The following figure illustrates the partitioning of constellation corresponds to 16-QAM. The distances
between signal points increases from successive partitioning of the original constellation.
To send n bits/symbol with quadrature modulation, we start with a constellation of 2n+1 signal points.
Two incoming bits per symbol enter a 2/3 convolutional encoder; the resulting three codded bits
per symbol determine the selection of a particular subset. The remaining uncoded data bits
determine which particular point from the selected subset is to be signaled.
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Lecture-18 Analog Transmission and Modulation
Since each symbol point represents a unique string of bits, and if the receiver knew what constellation was
being used, it could do a better job of decoding what symbol had actually been sent. The
problem, of course, is to tell the receiver what subset constellation to use.
[ This is accomplished in an "after the fact" manner in the receiver by allowing only certain transitions
from one state to another. Suppose that we create four different subset constellations. For each
starting state, we then establish valid transitions to only two other states and use an extra bit per
symbol to force legal transitions, only, through a convolutional encoder. The receiver decodes
the symbols as it normally would, assuming only a single constellation. The receiver then does a
"traceback" and examines the sequence of state transitions. If an invalid state transition occurred,
the receiver then goes back and examines the error vectors for the symbols, computing the
distance from the actually received symbol point to valid symbol points (Viterbi decoding). The
closest valid symbol point, which also creates a legal sequence of state transitions, is selected.
Nothing is free, however. To accomplish this bit of magic, an extra bit per symbol (for two dimensional
codes) or every two symbols (for four dimensional codes) is required. Sending an extra bit per
symbol requires that we double the number of symbols and we lose 3 dB of signal to noise ratio
(SNR) performance by doing this. The trellis code, however, provides about 6 dB of coding gain
so we achieve about 3 dB better SNR performance. ]
Ref:
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Text Book:
Chapter-4, Fitzgerald
Communication System -by Simon Haykin
Rockwell:
www.nb.rockwell.com/K56flex/whitepapers/k56whitepaper.html
Netexpress:
http://www.netexpress.net/techsupp/flex.html
v90:
http://www.v90.com/
AT Commands: http://www.internetpro.net/~phred/files/refman.html
Brian Brown:
http://www.cit.ac.nz/smac/dc100www/dc_006.htm#analogue
Chen:
http://www.tec.hkr.se\chen\courses\index.html
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