Multiplexing

7/21/2019 Multiplexing

http://slidepdf.com/reader/full/multiplexing-56d97afc0a88a 1/21

UCCN2043 – Lecture Notes (Prepared by Lee HengYew)

Page 1 of 21

7.0 Multiplexing

In a communication system, the costliest element is the transmission medium. To make the

best use of the medium, we have to ensure that the bandwidth of the channel is utilized to its

fullest capacity.

Multiplexing is the technique used to combine a number of channels and send them over the

medium to make the best use of the transmission medium. We will discuss the various

multiplexing techniques in this lesson.

7.1 Multiplexing and De-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 fiber 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 two ‘degrees of freedom’, i.e. bandwidth

(frequency) and time.




Page 2 of 21

Use of multiplexing technique is possible if the capacity of the channel is higher than the data

rates of the individual data sources. Consider the example of a communication system in

which there are three data sources.

As shown in Figure 7.1, the signals from these three sources can be combined together

(multiplexed) and sent through a single transmission channel. At the receiving end, thesignals are separated (de-multiplexed).

Figure 7.1: Multiplexing and de-multiplexing.

•

At the transmitting end, equipment known as a multiplexer (abbreviated to MUX) is

required.

• At the receiving end, equipment known as a de-multiplexer (abbreviated to DEMUX) is

required.

Conceptually, multiplexing is a very simple operation that facilitates good utilization of the

channel bandwidth.

The group of multiplexing technologies may be divided into several types, all of which have

significant variations:

• Frequency Division Multiplexing (FDM)

• Time Division Multiplexing (TDM)

• Wavelength Division Multiplexing (WDM)

• Code Division Multiplexing (CDM)

• Discrete Multitone (DMT) (combination of FDM and QAM modulation)

• Space Division Multiplexing (SDM)




Page 3 of 21

7.2 Frequency Division Multiplexing (FDM)

Frequency-division multiplexing (FDM) is derived from amplitude modulation (AM)

techniques and is inherently an analog technology. The transmission medium is ‘divided’ into

several communication channels where each communication channel is assigned with acarrier frequency f c.

FDM achieves the combining of several digital signals into one medium by sending signals in

several distinct frequency ranges (bands) ‘centered’ around f c over that medium.

Each signal occupies its own specific band of frequencies all the time, i.e. the messages share

the channel bandwidth.

One of FDM's most common applications is cable television. Only one cable reaches acustomer's home but the service provider can send multiple television channels or signals

simultaneously over that cable to all subscribers. Receivers must tune to the appropriate

frequency (channel) to access the desired signal.

FDM is widely used in radio and television systems (e.g. broadcast radio and TV) and was

widely used in multichannel telephony. However, it is prone to noise problems, and has been

overtaken by Time Division Multiplexing which is better suited for digital data.

The multichannel telephone system illustrates some important aspects and is considered

below. For speech, a bandwidth of ≈ 3 kHz is satisfactory. The physical line, e.g. a co-axialcable will have a bandwidth compared to speech as shown below.




Page 4 of 21

From AM, we have noted:

where

Carrier frequency = f c

DSB-SC – Double Sideband Suppressed Carrier

In order to use bandwidth more effectively, Single Sideband (SSB) is used i.e.

m(t )

cos( )ω ct

carrier

f c

freq

SSB

Filter SSBSC

Note – the Upper Sideband (USB) has been selected.

We have also noted that the message signal m(t ) is usually band limited, i.e.

m(t )

cos( )ω ct

SSB

Filter SSBSC

BandLimiting

Filter

Speech

300Hz – 3400Hz

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.




Page 5 of 21

10kHz300Hz 3400Hz 300Hz 3400Hz

f f f

Speech m(t ) Convention

For telephony, the physical line is divided (notionally) into 4 kHz bands or channels, i.e. the

channel spacing is 4 kHz. Thus we now have:

f

Bandlimited

Speech

Guard Bands

4kHz

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.

Consider now a single channel SSB system.

m(t )BLF

SSB

Filter

f c

DSBSC SSBSC

300Hz 3400Hz




Page 6 of 21

The spectra will be

m(t )

DSBSC

freq

freq

freq

f c

f c

Consider now a system with 3 channels

f

f

f

ΣΣΣΣ

BLF

BLF

BLF

SSB

Filter

SSBFilter

SSB

Filter

f c1

f c2

f c3

f 1

f 2

f 3

FDM

Signal

M (t )

Bandlimited

m1(t )

m2(t )

m3(t )

FDM Transmitter

or Encoder

Each carrier frequency, f c1, f c2 and f c3 are separated by the channel spacing frequency, in this

case 4 kHz, i.e

• f c2 = f c1 + 4 kHz,

• f c3 = f c2 + 4 kHz.




Page 7 of 21

The spectrum of the FDM signal, m(t ) will be:

f c1 f c2 f c3

4kHz 4kHz 4kHz

freq

M (t )

Shaded areas are to

show guard bands.

f 1 f 2 f 3

Note that:

• The baseband signals m1(t ), m2(t ), m3(t ) have been multiplexed into adjacent channels,

the channel spacing is 4 kHz.

•

The SSB filters are set to select the USB, tuned to f 1, f 2 and f 3 respectively.

A receiver FDM decoder is illustrated below:

SSB

Filter

SSB

Filter

SSBFilter

LPF

LPF

LPF

M (t )

FDM

Signal

f 1

f 2

f 3

f c1

f c2

f c3

m1(t )

m2(t )

m3(t )

Band

Limited

Back to

baseband

The SSB filters are the same as in the encoder, i.e. each one centered on f 1, f 2 and f 3 to select

the appropriate sideband and reject the others.

These are then followed by a synchronous demodulator, where each fed with a synchronous

local oscillator (LO), f c1, f c2 and f c3 respectively.




Page 8 of 21

For the 3 channel system (Transmitter and Receiver) shown, there is:

• 1 design for the BLF (used 3 times)

• 3 designs for the SSB filters (each used twice)

• 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 × 4 kHz = 14.4 MHz. Therefore there

are 3600 different SSB filter designs. Not only this, but the designs must range from kHz to

MHz.

Consider also the ‘Q’ of the filter, where Q is defined as Q =centre frequency

bandwidth.

For ‘designs’ around say 60 kHz, QkHz

kHz =

60

4= 15 which is reasonable. However, for designs

to have a centre frequency at around say 10 MHz, Q kHz kHz

= 10 0004, 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, super-groups, master-groups and super-master groups.

Channel Grouping

The diagram below illustrates the FDM principle for 12 channels (similar to 3 channels) to a

form a basic group.

m1(t )

m2(t )

m3(t )

m12(t )

Multiplexer

12kHz 60kHz

freq

i.e. 12 telephone channels are multiplexed in the frequency band 12kHz → 60 kHz in 4 kHz

channels ≡ basic group. A design for a basic 12 channel group is shown below:




Page 9 of 21

300Hz 3400kHz

4kHz

300Hz 3400kHz

4kHz

300Hz 3400kHz

4kHz

Band Limiting Filters

DSBSC

8.6 → 15.4kHz

12.6 → 19.4kHz

52.6 → 59.4kHz

f 1 = 12kHz

f 1 = 16kHz

f 12 = 56kHz

Increase in 4kHz steps

Σ

FDM OUT12 – 60kHz

12.3 → 15.4kHz

16.3 → 19.4kHz

56.3 → 59.4kHz

CH1

m1(t )

CH2

m2(t )

CH12

m12(t )

SSB Filter

These basic groups may now be multiplexed to form a super group.

BASICGROUP

12 – 60kHz

12

Inputs

SSB

FILTER

420kHz

BASIC

GROUP

12 – 60kHz

12

Inputs

SSB

FILTER

468kHz

BASIC

GROUP

12 – 60kHz

12

Inputs

SSB

FILTER

516kHz

BASIC

GROUP

12 – 60kHz12

Inputs

SSB

FILTER

564kHz

BASIC

GROUP

12 – 60kHz12

Inputs

SSB

FILTER

612kHz

ΣΣΣΣ

5 basic groups multiplexed to form a super group, i.e. 60 channels in one super group.




Page 10 of 21

Note – the channel spacing in the super group in the above is 48 kHz, i.e. each carrier

frequency is separated by 48 kHz. 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 Q

kHz

kHz = ≈

612

48 12 - which is reasonable. Hence, atotal 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…

7.3 Time Division Multiplexing (TDM)

TDM is a digital technology derived from sampling techniques. It is widely used in digital

communications. In TDM, messages occupy all the channel bandwidth but for short time

intervals of time, i.e. the messages share the channel time.

In comparison with FDM,

• FDM – messages occupy narrow bandwidth – all the time.

• TDM – messages occupy wide bandwidth – for short intervals of time.

TDM involves sequencing groups of a few bits or bytes from each individual input stream,

one after the other, and in such a way that they can be associated with the appropriate

receiver. If done sufficiently and quickly, the receiving devices will not detect that some of

the circuit time was used to serve another logical communication path.

In TDM, each message signal occupies the channel (e.g. a transmission line) for a short

period of time. The principle is illustrated as follow:

Transmission

Line

Tx Rx

SW1 SW2

1

2

3

4

5

1

2

3

4

5

m1(t )

m2(t )

m3(t )

m4(t )

m5(t )

m1(t )

m2(t )

m3(t )

m4(t )

m5(t )




Page 11 of 21

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 ). For ease of illustration consider such a system with 3 messages,

m1(t ), m2(t ) and m3(t ), each at different DC level as shown below.

t

t

t

t

V 1

V 2

V 3

SW1

‘Sample’

Position 1 2 3 1 2 3

m1(t )

m2(t )

m3(t )

0

0

0

t

1 2 3 1 2 3 1

t

Time slot

Channel

Time

Slots

V 1

V 2

V 3

m1(t ) m2(t ) m3(t ) m1(t ) m2(t ) m3(t ) m1(t )

In this illustration the samples are shown as levels, i.e. V 1, V 2 or V 3. 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.




Page 12 of 21

The sampling process requires that the message signals are sampled at a rate f s ≥ 2 B, where f s

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.

This process is illustrated below.

A schematic diagram to illustrate the principle for 3 message signals is shown below.

BLF S/Hm1(t )

f s1

‘PAM’

1

BLF S/Hm2(t )

f s2

‘PAM’

2

BLF S/Hm3(t )

f s3

‘PAM’

3

Multiplexing

Analogue

To

Digital

Convertor

Serial output

Binary digital

data d (t )

Band limiting

Filter 0 → B Hz

Sample and Hold

Sample rate f s f s ≥ 2 B Hz

Multiplexing ADC

Converts each input

in turn to an n bit code.

Again for simplicity, each message input is assumed to be a DC level. (see next page)

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 turnfor conversion.

For an N channel system, i.e. N message signals, sampled at a rate f s samples per second, with

each sample converted to an n bit binary code, and assuming no additional bits for

synchronization 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 = Nnf s bits/second.




Page 13 of 21

001 011 110 001 011 110

t

t

t

m1(t )

m2(t )

m3(t )

f s1

f s2

f s3

PAM 1S/H

PAM 2

S/H

PAM 3

S/H

Sample

pulses

V 1

V 2

V 3

m1(t ) m2(t ) m3(t ) m1(t ) m2(t ) m3(t )

d (t )

e.g. n = 3 bits

There are two types of Time-division multiplexing:

•

Synchronous Time-division Multiplexing (Sync TDM)• Statistical Time-division Multiplexing (Stat TDM)




Page 14 of 21

Synchronous Time Division Multiplexing

• Transmitters take turns to transmit in round-robin order.

• An extra bit is inserted at the beginning of each frame. The extra bit alternated betweenzero and one.

Used by the de-multiplexor to detect a synchronization error.

• The following figure illustrates the synchronous TDM system used by the telephone

system in which a framing bit precedes each round of slots.

Copyright © 2009 Pearson Prentice Hall, Inc.

•

In synchronous TDM, every possible sender has a reserved time slot, whether it needs it or

not. This may lead to underutilization of the transmission channel.

• The following figure Illustrates a synchronous TDM system leaving slots unfilled when a

source does not have a data item ready in time.





Page 15 of 21

Statistical Time Division Multiplexing

• Select items for transmission in round-robin order.

• But if a sender’s data is not ready, skip that sender and move to the next one.

• All slots will be filled as long as some sender has some data ready to send.

• But now each slot must also contain an identifier to indicate who the receiver is.

•

The following figure Illustrates how statistical TDM avoids unfilled slots and takes less

time to send data.


7.4 Wave Division Multiplexing (WDM) (http://www.rp-photonics.com/wavelength_division_multiplexing.html)

Wavelength division multiplexing is a technique where optical signals with different

wavelengths are combined, transmitted together, and separated again. It is mostly used for

optical fiber communications to transmit data in several (or even many) channels with

slightly different wavelengths.

Through WDM, the transmission capacities of fiber-optic links can be increased strongly, so

that most efficient use is made not only of the fibers themselves but also of the active

components such as fiber amplifiers.

The following figure illustrates the use of prism to combine and separate wavelengths of light

in WDM technologies




Page 16 of 21


Theoretically, the full data transmission capacity of a fiber could be exploited with a single

data channel of very high data rate, corresponding to a very large channel bandwidth.

However, given the enormous available bandwidth (tens of terahertz) of the low-losstransmission window of silica single-mode fibers, this would lead to a data rate which is far

higher than what can be handled by optoelectronic senders and receivers.

Also, various types of dispersion in the transmission fiber would have very detrimental

effects on such wide-bandwidth channels, so that the transmission distance would be strongly

restricted.

WDM solves these problems by keeping the transmission rates of each channel at reasonably

low levels (e.g. 10 Gbit/s) and achieving a high total data rate by combining several or many

channels.

Two different versions of WDM, defined by standards of the International

Telecommunication Union (ITU), are distinguished:

•

Coarse wavelength division multiplexing (CWDM, ITU standard G.694.2)

•

Dense wavelength division multiplexing (DWDM, ITU standard G.694.1)

Course Wave Division Multiplexing (CWDM)

• Uses a relatively small number of channels, e.g. four or eight, and a large channel spacing

of 20 nm.

• The nominal wavelengths range from 1310 nm to 1610 nm.

• The wavelength tolerance for the transmitters is fairly large, e.g. ±3 nm, so that un-stabilized DFB lasers can be used.

• The single-channel bit rate is usually between 1 and 3.125 Gbit/s.




Page 17 of 21

Dense Wave Division Multiplexing (DWDM)

•

Extended method for very large data capacities, as required e.g. in the Internet backbone.

• Uses a large number of channels (e.g. 40, 80, or 160), and a correspondingly small channel

spacing of 12.5, 25, 50 or 100 GHz.

• All optical channel frequencies refer to a reference frequency which has been fixed at

193.10 THz (1552.5 nm).

•

The transmitters have to meet tight wavelength tolerances. Typically, they are

temperature-stabilized DFB lasers.

•

The single-channel bit rate can be between 1 and 10 Gbit/s, and in the future also 40 Gbit/s.

7.5 Code Division Multiplexing (CDM)

CDM allows signals from a series of independent sources to be transmitted at the same time

over the same frequency band.

This is accomplished by using orthogonal Code division multiplexing codes to spread each

signal over a large, common frequency band. At the receiver, the appropriate orthogonal code

is then used again to recover the particular signal intended for a particular user.

The key principle of CDM is spread spectrum. Spread spectrum is a means of communication

with the following features:

1.

Each information-bearing signal is transmitted with a bandwidth in excess of the

minimum bandwidth necessary to send the information.

2. The bandwidth is increased by using a spreading code that is independent of the

information.

3. The receiver has advance knowledge of the spreading code and uses this knowledge to

recover the information from the received, spread-out signal.

Spread spectrum seems incredibly counterintuitive. We’ve spent quite some lecturing hours

studying ways to transmit information using a minimum of bandwidth. Why should we nowstudy ways to intentionally increase the amount of bandwidth required to transmit a signal?

If you understand CDM, you will see that spread spectrum is a good technique for providing

secure, reliable, private communication in an environment with multiple transmitters andreceivers. In fact, spread spectrum and CDM are currently being used in a number of

commercial cellular telephone systems and satellite communications.

Application of CDM (in this case CDMA) in cellular telephony

• Each mobile device is assigned unique 64-bit code (called Chip spreading code)

•

To send a binary 1, mobile device transmits the unique code

• To send a binary 0, mobile device transmits the inverse of code




Page 18 of 21

• At the receiver

• Gets summed signal

• Multiplies it by receiver code

• Adds up resulting values

•

Interprets as a binary 1 if sum is near +64

•

Interprets as a binary 0 if sum is near –64

CDM / CDMA Application Example

• For simplicity, assume 8-chip spreading codes

• 3 different mobiles use the following codes:

- Mobile A: 10111001

-

Mobile B: 01101110

- Mobile C: 11001101

•

Assume- Mobile A sends a 1

- Mobile B sends a 0

-

Mobile C sends a 1

• Signal code: 1-chip = +N volt; 0-chip = -N volt

• Three signals transmitted:

• Mobile A sends a 1, or 10111001, or +-+++--+

• Mobile B sends a 0, or 10010001, or +--+---+

•

Mobile C sends a 1, or 11001101, or++--++-+

• Summed signal received by base station: +3, -1, -1, +1, +1, -1, -3, +3

Base station decode for Mobile A:

Signal received: +3, -1, -1, +1, +1, -1, -3, +3

Mobile A’s code: +1, -1, +1, +1, +1, -1, -1, +1 (10111001)

Product result: +3, +1, -1, +1, +1, +1, +3, +3

Sum of Product results: +12

Decode rule: For result near +8, data is binary 1

Base station decode for Mobile B:Signal received: +3, -1, -1, +1, +1, -1, -3, +3

Mobile B’s code: -1, +1, +1, -1, +1, +1, +1, -1 (01101110)

Product result: -3, -1, -1, -1, +1, -1, -3, -3

Sum of Product results: -12

Decode rule: For result near -8, data is binary 0

Base station decode for Mobile C:

Signal received: +3, -1, -1, +1, +1, -1, -3, +3

Mobile C’s code: +1, +1, -1, -1, +1, +1, -1, +1 (11001101)

Product result: +3, -1, +1, -1, +1, -1, +3, +3

Sum of Product results: +8Decode rule: For result near +8, data is binary 1




Page 19 of 21

7.6 Discrete Multitone (DMT)

DMT is a form of multicarrier modulation that encodes bits in the frequency domain. It is

now used in certain wireless communication systems (802.11) and Digital Subscriber Line

(DSL) technologies.

Through the use of DMT, DSL technology enables very high speed connections from

individual computers to switching stations over a standard copper telephone line.

• DMT places the data onto 247 separate sub-channels, each 4 KHz wide. This is like

having 247 different dial-up lines connected to a computer all at the same time!

On top of that DSL allows a subscriber to be able to receive phone calls over the same line at

the same time, without risk of disconnection or data loss.

The existing local loop*1 can handle up to 1.1 MHz bandwidth

•

The first 4 KHz bandwidth is used for regular telephone voice service

•

Rest of the bandwidth is divided into 256 channels each occupying a bandwidth of

4.312 KHz

Each sub-channel can carry up to 60 Kbps data rate. (4 KHz × 15 bits/Signal Change) = 60

Kbps

Allocation of the 1.1 MHz bandwidth (refer to Figure 7.6 below)

• Channel 0 is used for voice

• Channel 1 to 5 are not used to allow a gap between voice and Data

• Channels 6 to 30 (25 channels) are used for up stream transmission and control. One

for Control and 24 for data. Thus upstream data rate is: 24 × 4 KHz × 15 bits/ Signal

change = 1.44 Mbps• Channel 31 to 255 (225 channels) are used for downstream transmission, one for

control and 224 for data. Thus the downstream data rate is : 224 × 4 KHz × 15 bits/

Signal change = 13.4 Mbps

Voice Upstream Downstream

Ch 0 Ch 6 to 30 Ch 31 to 255

0 4 26 108 138 1104 KHz

Figure 7.6

Note that these are theoretical maximum bandwidth. The actual practical data rate is usually

lower and depends on:

• The S/N Ratio of the link

• The distance between the customer location and the Central Office*2 (CO)

Note: 1.Central Office (CO) is the physical building where the local telephone switching

equipment is located. All telephone lines in a town lead to the CO.

Note: 2. the pair of wires (twisted pair) connecting a telephone subscriber to a CO.




Page 20 of 21

The actual data rates are as follows:

• Upstream: 64 Kbps to 1.5 Mbps

• Downstream: 500 Kbps to 9 Mbps

Being an adaptive technology, the ADSL modems, when turned ON, check the quality of lineand automatically adjust the data rate.

• The noise level of each sub-channel is monitored; if a sub-channel with a particular

frequency becomes too noisy, data will be reallocated from the noisy sub-channel to

others with less noise.

•

As the frequency response of the channel changes with time, the ADSL system

constantly shifts data from one sub-channel to another, searching for the frequency

distribution that allows for an optimal data rate.

7.7 Space Division Multiplexing

In wired communication, space-division multiplexing simply implies different point-to-point

wires for different channels.

•

One example is an analogue stereo audio cable, with one pair of wires for the left

channel and another for the right channel.

However, wired space-division multiplexing is typically not considered as multiplexing.

In wireless communication, space-division multiplexing is achieved by multiple antennaelements forming a phased array antenna. Examples are:

• Multiple-input and multiple-output (MIMO) multiplexing

• Single-input and multiple-output (SIMO) multiplexing

• Multiple-input and single-output (MISO) multiplexing

For example, a IEEE 802.11n wireless router with N antennas makes it possible to

communicate with N multiplexed channels, each with a peak bit rate of 54 Mbit/s, thus

increasing the total peak bit rate with a factor N .

Different antennas would give different multi-path propagation (echo) signatures, making it

possible for digital signal processing techniques to separate different signals from each other.These techniques may also be utilized for space diversity (improved robustness to fading) or

beam-forming (improved selectivity) rather than multiplexing.




Page 21 of 21

7.8 Comparison of Different Multiplexing Techniques

Documents

Multiplexing