multiple xing gfgfgfgf

MultiplexingMultiplexing

• 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.

1


CHANNELBL

BH freq

BH

BL

Time t

Frequency

Multiplexing is a technique which allows kusers to occupy the

channel for the duration in time that the channel is available.

Now consider a signal v t Amp ts ( ) cos( ) The signal is characterised by amplitude, frequency, phase and time. 2


• 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.

3


These two basic methods are illustrated below.

M1M2 M3

M4M5

time

freq

BL

BH

B

time

freq

M1M2

M3M4

M5

t

BL

BH

M1

M2

M3

M4

M5

BL

BH

B M1 M2 M3 M4 M5

ttFDM TDM

t

BL

BH

4

• 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in radio and television systems (e.g. broadcast radio and TV) and was widely used in multichannel telephony (now being superseded by digital techniques and TDM).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

Frequency Division Multiplexing FDMFrequency Division Multiplexing FDM

5


3 k H z

G H z

f r e q

F r o m A M w e h a v e n o t e d :

m ( t )

c o s ( ) c t

D S B S C

c a r r i e r

f c

f r e q

f r e q

B

m ( t )

D S B S C

6

In order to use bandwidth more effectively, SSB is used i.e.

m(t)

cos( )ct

carrier

fc

freq

SSBFilter

SSBSC

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

m(t)

cos( )ct

SSBFilter

SSBSCBandLimitingFilter

Speech

300Hz –3400Hz


7


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.

10kHz300Hz 3400Hz 300Hz 3400Hz

f f f

Speech m(t) Convention

8


For telephony, the physical line is divided (notionally) into 4kHz bands or channels, i.e. the channel spacing is 4kHz. Thus we now have:

f

BandlimitedSpeech

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.

9


Consider now a single channel SSB system. m(t)BLF

SSBFilter

fc

DSBSC SSBSC

300Hz 3400Hz

m(t)

DSBSC

freq

freq

freq

fc

fc

The spectra will be

10


Consider now a system with 3 channels

f

f

f

BLF

BLF

BLF

SSBFilter

SSBFilter

SSBFilter

fc1

fc2

fc3

f1

f2

f3

FDMSignal

M(t)

Bandlimited

m1(t)

m2(t)

m3(t)

FDM Transmitteror Encoder 11


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:

fc1 fc2 fc3

4kHz 4kHz 4kHz

freq

M(t)

Shaded areas are toshow guard bands.

f1 f2 f3

12


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:

SSBFilter

SSBFilter

SSBFilter

LPF

LPF

LPF

M(t)FDMSignal

f1

f2

f3

fc1

fc2

fc3

m1(t)

m2(t)

m3(t)

BandLimited

Back tobaseband

13


• 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.

14


For ‘designs’ around say 60kHz, QkHz

kHz

60

4= 15 which is reasonable.

However, for designs to have a centre frequency at around say 10Mhz,

QkHz

kHz

10 000

4

,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.

15

Basic 12 Channel GroupBasic 12 Channel Group

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 4kHz channels basic group.

16

Basic 12 Channel GroupBasic 12 Channel Group

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

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

f1 = 12kHz

f1 = 16kHz

f12 = 56kHz

Increase in 4kHz steps

FDM OUT12 – 60kHz

12.3 15.4kHz

16.3 19.4kHz

56.3 59.4kHz

CH1m1(t)

CH2m2(t)

CH12m12(t)

SSB Filter

17

Super GroupSuper Group

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

BASICGROUP12 – 60kHz

12Inputs

SSBFILTER

420kHz


12Inputs

SSBFILTER

468kHz


12Inputs

SSBFILTER

516kHz


12Inputs

SSBFILTER

564kHz


12Inputs

SSBFILTER

612kHz

18

Super GroupSuper 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 QkHz

kHz

612

4812 - which is reasonable

Hence, a total of 17 designs are required for 60 channels. In a similar way, super groupsmay be multiplexed to form a master group, and master groups to form super master groups…

19

Time Division Multiplexing TDMTime 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:

TransmissionLine

Tx RxSW1 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)

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). 20


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.

t

t

t

t

V1

V2

V3

SW1‘Sample’

Position 1 2 3 1 2 3

m1(t)

m2(t)

m3(t)

0

0

0

21


t

1 2 3 1 2 3 1

t

Time slot

ChannelTimeSlots

V1

V2

V3

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

22


• 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.

23


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

BLF S/Hm1(t)

fs1

‘PAM’

1

BLF S/Hm2(t)

fs2

‘PAM’

2

BLF S/Hm3(t)

fs3

‘PAM’

3

MultiplexingAnalogue

ToDigital

Convertor

Serial output

Binary digitaldata d(t)

Band limitingFilter 0 B Hz

Sample and HoldSample rate fsfs 2B Hz

Multiplexing ADCConverts each inputin turn to an n bit code.

Again for simplicity, each message input is assumed to be a DC level. 24


25


26


• 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.

27

School of Electrical, Electronics andComputer Engineering

University of Newcastle-upon-Tyne

Baseband digital Modulation Baseband digital Modulation

Prof. Rolando CarrascoProf. Rolando Carrasco

Lecture Notes University of Newcastle-upon-Tyne

2005

Baseband digital informationBaseband digital information

Bit-rate, Baud-rate and Bit-rate, Baud-rate and BandwidthBandwidth

BB1

denotes the duration of the 1 bitHence Bit rate =

bits per second

All the forms of the base band signalling shown transfer data at the same bit rate.

E 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 = E1

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

Non Return to Zero (NRZ)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 E 2

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.

Non Return to Zero (NRZ) Non Return to Zero (NRZ) (Cont’d)(Cont’d)

The data sequence 1010…… could then be completely recovered

Hence the minimum channel bandwidth

RateBaudSinceRateBaud

TB

EE

1

22

11min

Return to Zero (RZ)Return to Zero (RZ)

Considering RZ signals, the max frequency occurs when continuous 1’s are transmitted.

This produces a square wave with periodic time E 2

2min

RateBaudfB U

If the sequence was continuous 0’s, the signal would be –V continuously, hence

''DCfL

.

Bi-PhaseBi-Phase

Maximum frequency occurs when continuous 1’s or 0’s transmitted.

E1

2min

RateBaudfB U

This is similar to RZ with Baud Rate = = 2 x Bit rate

The minimum frequency occurs when the sequence is 10101010…….e.g.

B E

2min

RateBaudfB L

In this case =

Baud Rate = Bit rate

Digital Modulation and Digital Modulation and NoiseNoise

The performance of Digital Data Systems is dependent on the bit error rate, BER, i.e. probability of a bit being in error.

NasNbitsTotal

EErrorsofNoP

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

Prob. of Error or BER,


Amplitude Shift Keying ASK


Frequency Shift Keying FSK


Phase Shift Keying PSK

System Block diagram for System Block diagram for AnalysisAnalysis

DEMODULATOR – DETECTOR – DECISION DEMODULATOR – DETECTOR – DECISION

For ASK and PSK

Demodulator-Detector-DecisionDemodulator-Detector-Decision

FOR FSK

DemodulatorDemodulator

Demodulator Cont’d)Demodulator Cont’d)

TRCdesignHence

dtVRC

V INout

1

Detector-DecisionDetector-Decision

1V 0V - is the voltage difference between a ‘1’ and ‘0’.

)22

( 21 VVVREF

Detector-Decision (Cont’d)Detector-Decision (Cont’d)

ND is the noise at the Detector input.

Probability of Error,

DNerf

221

2

1

Hence

0 v1v0 v

0-

P(v0)

vn

Probability density of binary signalProbability density of binary signal

v0v1

2

210

2

)(

02

1

2

1)(

vv

n evP

)(1 nvP

vn

n

vv

vve dveP

n2

20

10

2

)(

2

12

1

Using the change of variable2

0vvx n

Probability density function of noiseProbability density function of noise

(*)

DN2

22

1

01

21

vv

dxxe eP

dxezerfcz

x

22

)(

222

1 011

vverfcPe

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

n

vvvv

e

e

dveP

vverfP

zerfzerfc

n2

21

10

2

)(2

0

011

2

1

221

2

1

)(1)(

(**)

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

22

12

1

v

erfPe

for unipolar signalling (0 and v)

for polar signalling (symbol represented by voltage 2

v


PSKFSKASKOptimumFor

PRK

N

SerfPSK

N

SerfFSK

OOK

N

SerfASK

IN

INe

IN

INe

IN

INe

,,

12

1

21

2

1

41

2

1

dB/10in SNR10

ePePeP

SNR in wattASK FSK PSK

000.002415.848912

00.00080.012710.0010

0.00020.0060.03796.30968

0.00240.0230.07913.98116

0.01250.05650.13122.51194

0.03750.1040.18671.58492

0.07860.15870.23981.000

Linear gainSNR in dB

000.002415.848912

00.00080.012710.0010

0.00020.0060.03796.30968

0.00240.0230.07913.98116

0.01250.05650.13122.51194

0.03750.1040.18671.58492

0.07860.15870.23981.000

Linear gainSNR in dB

Probability of Symbol Error

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

0 2 4 6 8 10 12 14

SNR in dB

Pro

bab

ility

of

Sym

bo

l Err

or

ASK

FSK

PSK


FM/ FSK Demodulation

One form of FM/FSK demodulator is shown below

In general VIN (t) will be

tCosVtV INcIN )(

IN ININ f 2Where is the input frequency (rad/sec)

ttCosttCosV

V

BACosBACosCosBCosASince

tCosVtCosVV

tVtVV

ININININc

x

INcINcx

ININx

2

2

1

)(.

2

FM/ FSK Demodulation (Cont’d)

INININc

x

ININININININc

x

CostCosV

V

ttCosttCosV

V

22

22

2

)2(

2

)1(222

2

2

tCosV

and

tCosV

INc

INc

i.e

Thus there are two components

Component (1) is at frequency 2 fIN Hz and component (2) is effectively a ‘DC’ voltage if

IN 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.

tCosV

V INc

OUT 2

2


The V/F characteristics and inputs are shown belowAnalogue FM

ccDCc

mmDCout

mmDCIN

DCIN

INout

mc

fTVf

ftCosVVfei

tCosVVV

tmVV

fVf

cxmy

Vf

1,

..

)(

0

0

Modulation Index m

m

m

c

f

V

f

f


tnCosJVtVFM mcn

ncs

1

)()(

The spectrum of the analogue FM signal depends on and is given by

Digital FSK

ccDCc

DC

DC

DCIN

DCIN

DCIN

INout

fTVf

sforfVVf

sforfVVf

sforVVV

sforVVV

tmVV

fVf

cxmy

1,

'0

'1

'0

'1

)(

000

011

0

1

0

Normalized frequency Deviation ratio

0101 .. ffModulusei

R

ffh

b

The spectrum of FSK depends on h

Digital FSK (Cont’d)

FM/ FSK Demodulation (Cont’d)FM/ FSK Demodulation (Cont’d)

Consider again the output from the demodulator INc

OUT CosV

V2

2

4cT

cc f

T1

cfThe delay is set to where and is the nominal carrier frequency

c

INcOUT f

fCos

VV

4

2

2

2 Hence

c

INcOUT f

fCos

VV

22

2

FM/ FSK Demodulation (Cont’d)FM/ FSK Demodulation (Cont’d)

The curve shows the demodulator F/V characteristics which in this case is non linear.

Practical realization of F/V processPractical 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

Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)


INf cf

Consider now

≠


c

INOUT f

fAEV

4 Plotting Vout versus

INf (Assuming A=1)

multiple xing gfgfgfgf

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