Multiplexing

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Multiplexing

• Multiplexing is the name given to techniques,
  which allow more
• than one message to be transferred via the same
  
• communication channel. The channel in this
  context could be a
• transmission line, e.g. a twisted pair or
  co-axial cable, a radio
• system or a fibre optic system etc.

• A channel will offer a specified bandwidth,
  which is available for
• a time t, where t may ? ?. Thus, with reference
  to the channel
• there are 2 degrees of freedom, i.e.
  bandwidth or frequency
• and time.

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Multiplexing
Now consider a signal
The signal is characterised by amplitude,
frequency, phase and time.
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Multiplexing

• Various multiplexing methods are possible in
  terms of the channel bandwidth and time,
• and the signal, in particular the frequency,
  phase or time. The two basic methods are

1. Frequency Division Multiplexing FDM

FDM is derived from AM techniques in which the
signals occupy the same physical line but in
different frequency bands. Each signal occupies
its own specific band of frequencies all the
time, i.e. the messages share the channel
bandwidth.
2) Time Division Multiplexing TDM
TDM is derived from sampling techniques in which
messages occupy all the channel bandwidth but
for short time intervals of time, i.e. the
messages share the channel time.

• FDM messages occupy narrow bandwidth all the
  time.
• TDM messages occupy wide bandwidth for short
  intervals of time.

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Multiplexing
These two basic methods are illustrated below.
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Frequency Division Multiplexing FDM

• FDM is widely used in radio and television
  systems (e.g. broadcast radio and TV) and was
  widely used in multichannel telephony (now being
  superseded by digital techniques and TDM).
• The multichannel telephone system illustrates
  some important aspects and is considered below.
  For speech, a bandwidth of ? 3kHz is
  satisfactory.
• The physical line, e.g. a co-axial cable will
  have a bandwidth compared to speech as shown next

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Frequency Division Multiplexing FDM
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Frequency Division Multiplexing FDM
In order to use bandwidth more effectively, SSB
is used i.e.
We have also noted that the message signal m(t)
is usually band limited, i.e.
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Frequency Division Multiplexing FDM
The Band Limiting Filter (BLF) is usually a band
pass filter with a pass band 300Hz to 3400Hz for
speech. This is to allow guard bands between
adjacent channels.
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Frequency Division Multiplexing FDM
For telephony, the physical line is divided
(notionally) into 4kHz bands or channels, i.e.
the channel spacing is 4kHz. Thus we now have
Note, the BLF does not have an ideal cut-off
the guard bands allow for filter roll off in
order to reduce adjacent channel crosstalk.
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Frequency Division Multiplexing FDM
Consider now a single channel SSB system.
The spectra will be
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Frequency Division Multiplexing FDM
Consider now a system with 3 channels
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Frequency Division Multiplexing FDM
Each carrier frequency, fc1, fc2 and fc3 are
separated by the channel spacing frequency, in
this case 4 kHz, i.e. fc2 fc1 4kHz, fc3 fc2
4kHz.
The spectrum of the FDM signal, M(t) will be
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Frequency Division Multiplexing FDM
Note that the baseband signals m1(t), m2(t),
m3(t) have been multiplexed into adjacent
channels, the channel spacing is 4kHz. Note also
that the SSB filters are set to select the USB,
tuned to f1, f2 and f3 respectively.
A receiver FDM decoder is illustrated below
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Frequency Division Multiplexing FDM

• The SSB filters are the same as in the encoder,
  i.e. each one centred on f1, f2 and f3 to select
  the appropriate sideband and reject the others.
  These are then followed by a synchronous
  demodulator, each fed with a synchronous LO, fc1,
  fc2 and fc3 respectively.
• For the 3 channel system shown there is 1 design
  for the BLF (used 3 times), 3 designs for the SSB
  filters (each used twice) and 1 design for the
  LPF (used 3 times).
• A co-axial cable could accommodate several
  thousand 4 kHz channels, for example 3600
  channels is typical. The bandwidth used is thus
  3600 x 4kHz 14.4Mhz. Potentially therefore
  there are 3600 different SSB filter designs. Not
  only this, but the designs must range from kHz to
  MHz.

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Frequency Division Multiplexing FDM
For designs around say 60kHz,
15 which is reasonable.
However, for designs to have a centre frequency
at around say 10Mhz,
gives a Q 2500 which is difficult to achieve.
To overcome these problems, a hierarchical system
for telephony used the FDM principle to form
groups, supergroups, master groups and
supermaster groups.
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Basic 12 Channel Group
The diagram below illustrates the FDM principle
for 12 channels (similar to 3 channels) to a
form a basic group.
i.e. 12 telephone channels are multiplexed in the
frequency band 12kHz ? 60 kHz in 4kHz channels ?
basic group.
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Basic 12 Channel Group
A design for a basic 12 channel group is shown
below
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Super Group
These basic groups may now be multiplexed to form
a super group.
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Super Group
5 basic groups multiplexed to form a super group,
i.e. 60 channels in one super group. Note the
channel spacing in the super group in the above
is 48kHz, i.e. each carrier frequency is
separated by 48kHz. There are 12 designs (low
frequency) for one basic group and 5 designs for
the super group.
The Q for the super group SSB filters is
- which is reasonable
Hence, a total of 17 designs are required for 60
channels. In a similar way, super groups may be
multiplexed to form a master group, and master
groups to form super master groups
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Time Division Multiplexing TDM
TDM is widely used in digital communications, for
example in the form of pulse code modulation in
digital telephony (TDM/PCM). In TDM, each message
signal occupies the channel (e.g. a transmission
line) for a short period of time. The principle
is illustrated below
Switches SW1 and SW2 rotate in synchronism, and
in effect sample each message input in a
sequence m1(t), m2(t), m3(t), m4(t), m5(t),
m1(t), m2(t),
The sampled value (usually in digital form) is
transmitted and recovered at the far end to
produce output m1(t)m5(t).
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Time Division Multiplexing TDM
For ease of illustration consider such a system
with 3 messages, m1(t), m2(t) and m3(t), each a
different DC level as shown below.
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Time Division Multiplexing TDM
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Time Division Multiplexing TDM

• In this illustration the samples are shown as
  levels, i.e. V1, V2 or V3. Normally, these
  voltages would be converted to a binary code
  before transmission as discussed below.
• Note that the channel is divided into time slots
  and in this example, 3 messages are time-division
  multiplexed on to the channel. The sampling
  process requires that the message signals are a
  sampled at a rate fs ? 2B, where fs is the sample
  rate, samples per second, and B is the maximum
  frequency in the message signal, m(t) (i.e.
  Sampling Theorem applies). This sampling process
  effectively produces a pulse train, which
  requires a bandwidth much greater than B.
• Thus in TDM, the message signals occupy a wide
  bandwidth for short intervals of time. In the
  illustration above, the signals are shown as PAM
  (Pulse Amplitude Modulation) signals. In practice
  these are normally converted to digital signals
  before time division multiplexing.

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Time Division Multiplexing TDM
A schematic diagram to illustrate the principle
for 3 message signals is shown below.
Again for simplicity, each message input is
assumed to be a DC level.
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Time Division Multiplexing TDM
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Time Division Multiplexing TDM
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Time Division Multiplexing TDM

• Each sample value is converted to an n bit code
  by the ADC. Each n bit code fits into
• the time slot for that particular message. In
  practice, the sample pulses for each
• message input could be the same. The
  multiplexing ADC could pick each input
• (i.e. a S/H signal) in turn for conversion.

• For an N channel system, i.e. N message signals,
  sampled at a rate fs samples per
• second, with each sample converted to an n bit
  binary code, and assuming no
• additional bits for synchronisation are
  required (in practice further bits are required)
  it is
• easy to see that the output bit rate for the
  digital data sequence d(t) is

Output bit rate Nnfs bits/second.
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• School of Electrical, Electronics and
• Computer Engineering
• University of Newcastle-upon-Tyne
• Baseband digital Modulation
• Prof. Rolando Carrasco
• Lecture Notes
• University of Newcastle-upon-Tyne
• 2005

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Baseband digital information
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Bit-rate, Baud-rate and Bandwidth
denotes the duration of the 1 bit Hence Bit
rate
bits per second
All the forms of the base band signalling shown
transfer data at the same bit rate.
denotes the duration of the shortest
signalling element. Baud rate is defined as the
reciprocal of the duration of the shortest
signalling element.
Baud Rate
baud
In general Baud Rate ? Bit Rate
For NRZ Baud Rate Bit Rate
RZ Baud Rate 2 x Bit Rate
Bi-Phase Baud Rate 2 x Bit Rate
AMI Baud Rate Bit Rate
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Non Return to Zero (NRZ)
The highest frequency occurs when the data is
1010101010. i.e.
This sequence produces a square wave with
periodic time
Fourier series for a square wave,
If we pass this signal through a LPF then the
maximum bandwidth would be 1/T Hz, i.e. to just
allow the fundamental (1st harmonic) to pass.
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Non Return to Zero (NRZ) (Contd)
The data sequence 1010 could then be
completely recovered

Hence the minimum channel bandwidth
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Return to Zero (RZ)
Considering RZ signals, the max frequency occurs
when continuous 1s are transmitted.
.

This produces a square wave with periodic time
If the sequence was continuous 0s, the signal
would be V continuously, hence
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Bi-Phase
Maximum frequency occurs when continuous 1s or
0s transmitted.
This is similar to RZ with Baud Rate
2 x Bit rate


The minimum frequency occurs when the sequence is
10101010. e.g.
In this case

Baud Rate Bit rate
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Digital Modulation and Noise
The performance of Digital Data Systems is
dependent on the bit error rate, BER, i.e.
probability of a bit being in error.
Prob. of Error or BER,
Digital Modulation There are four basic ways of
sending digital data

• The BER (P) depends on several factors
• the modulation type, ASK FSK or PSK
• the demodulation method
• the noise in the system
• the signal to noise ratio

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Digital Modulation and Noise
Amplitude Shift Keying ASK
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Digital Modulation and Noise
Frequency Shift Keying FSK
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Digital Modulation and Noise
Phase Shift Keying PSK
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System Block diagram for Analysis
DEMODULATOR DETECTOR DECISION
For ASK and PSK
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Demodulator-Detector-Decision
FOR FSK
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Demodulator
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Demodulator Contd)

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Detector-Decision
- is the voltage difference between a 1
and 0.
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Detector-Decision (Contd)
ND is the noise at the Detector
input. Probability of Error,

Hence
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Probability density of binary signal
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Probability density function of noise
()
Using the change of variable
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This becomes
()
The incomplete integral cannot be evaluated
analytically but can be recast as a
complimentary error function, erfc(x), defined by
Equations () and () become
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It is clear from the symmetry of this problem
that Pe0 is identical to Pe1 and the probability
of error Pe, irrespective of whether a one or
zero was transmitted, can be rewritten in
terms of ?v v1 v0

• for unipolar signalling (0 and ?v)
• for polar signalling (symbol represented by
  voltage

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Detector-Decision (Contd)
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Detector-Decision (Contd)
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FM/ FSK Demodulation
One form of FM/FSK demodulator is shown below
In general VIN (t) will be
Where
is the input frequency (rad/sec)
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FM/ FSK Demodulation (Contd)
i.e
Thus there are two components
Component (1) is at frequency 2 fIN Hz and
component (2) is effectively a DC voltage if

is constant.
The cut-off frequency for the LPF is designed so
that component (1) is removed and component (2)
is passed to the output.
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FM/ FSK Demodulation (Contd)
The V/F characteristics and inputs are shown
below Analogue FM
Modulation Index
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FM/ FSK Demodulation (Contd)
The spectrum of the analogue FM signal depends on
and is given by
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Digital FSK
Normalized frequency Deviation ratio
The spectrum of FSK depends on h
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Digital FSK (Contd)
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FM/ FSK Demodulation (Contd)
Consider again the output from the demodulator
The delay
is set to
where
and
is the nominal carrier frequency
Hence

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FM/ FSK Demodulation (Contd)
The curve shows the demodulator F/V
characteristics which in this case is non linear.
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Practical realization of F/V process
The comparator is LIMITER which is a zero
crossing detector to give a digital input to
the first gate.
This is form of delay and multiply circuit
where the delay
is set by C and R with
CR
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Practical realization of F/V process (Contd)
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Practical realization of F/V process (Contd)
Consider now
?
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Practical realization of F/V process (Contd)
Plotting Vout versus
(Assuming A1)