DC Digital Communication PART1

Digital communication

H V KUMARASWAMY

Course: Digital Communication (EC61)

Course instructors:

1. Mr. H. V.KumaraSwamy, RVCE,Bangalore

2. Mr. P.Nagaraju, RVCE, Bangalore

3. Ms. M.N.Suma, BMSCE, Bangalore

Digital Communication

TEXT BOOK:

Digital Communications

Author: Simon Haykin

Pub: John Wiley Student Edition, 2003

Reference Books

1. “Digital and Analog Communication Systems” – K. Sam Shanmugam, John Wiley, 1996.

2. “An Introduction to Analog and Digital Communication”- Simon Haykin, John Wiley, 2003.

Digital Communication- Topics

• Chapter 1: Introduction

• Chapter 2: Sampling Process

• Chapter 3: Waveform Coding Techniques

• Chapter 4: Base-band shaping

Digital Communication- Topics

• Chapter 5: Digital Modulation Techniques

• Chapter 6: Detection and Estimation

• Chapter 7: Spread Spectrum Modulation.

Communication System

The purpose of a Communication System is to transport an information bearing signal from a source to a user destination via a communication channel.

MODEL OF A COMMUNICATION SYSTEM

Basic Blocks

1. Transmitter

2. Channel

3. Receiver

Communication

Types of Communication:

1. Analog Communication

2. Digital Communication

DCS - Block diagram

Digital Communication- Blocks

• Information Source

• Source Encoder and Decoder

• Channel Encoder and Decoder

• Modulator and Demodulator

• Channel

Block diagram with additional blocks

Additional Blocks

• Encryptor

• Decryptor

• Multiplexer

• Demultiplexer.

Digital Communication- Advantages

• Less Distortion, Low noise & interference.

• Regenerative Repeaters can be used.

• Digital Circuits are more reliable.

• Hardware implementation is more flexible.

Digital Communication- Advantages

• Secrecy of information.

• Low probability of error due to error detection and error correction.

• Multiplexing- ( TDM )

• Signal Jamming is avoided.

Digital Communication- Disadvantages

• Large Bandwidth

• Synchronization

Channels for Digital Communication

Channel Characteristics:

• Bandwidth

• Power

• Linear or Non-linear

• External interference

Types of Channels

1. Telephone Channels

2. Coaxial Cables

3. Optical fibers

4. Microwave radio

5. Satellite Channel

1. Telephone Channels

• Provides voice grade Communication.

• Good for data communication over long distances.

• Frequency range: 300Hz – 3400Hz.

• High SNR – about 30dB.

1. Telephone Channels contd..

• Flat amplitude response for voice signals.

• For data & image transmissions EQUALIZERS are used.

• Transmission rate = 16.8kb/s

2. Coaxial Cable

• Single-wire conductor inside an outer Conductor with dielectric between them.

• Wide Bandwidth

• Low external Interference.

2. Coaxial Cable contd..

• Closely spaced Repeaters are required.

• Transmission rate = 274 Mb/s.

3.Optical fibers

• Communication is by light rays.

• Fiber consists of Inner core and an outer core called CLADDING.

• Refractive Index of Cladding is less.

3.Optical fibers

• Larger Bandwidth.

• Immune to cross talk and EMI.

• More secure.

• Low cost.

• Date rate = Terra bits/sec.

4. Microwave radio

• Transmitter & Receiver With antennas.

• Works on Line-of-sight principle.

• Point to Multipoint communication.

• Reliable & High Speed of Transmission.

4. Microwave Radio

• Operating Frequency - (1 – 30)GHz

• System Performance degrades due to meteorological variations.

5. Satellite Channel.

• Repeater in the sky.

• Placed in geo-stationary orbit.

• Long distance transmission.

• High Bandwidth.

5. Satellite Channel

• Operates in microwave frequency.

• Uplink frequency is more than down link frequency

Topics in this session:– Geometric interpretation of signal– Response of bank of correlators to

noisy input– Detection of known signals in

noise

Geometric interpretation of signal

Using N orthonormal basis functions we can represent M signals as

MiTttStSN

jjiji ,.....,2,10)()(

1

Coefficients are given by

Nj

MidtttSS j

T

iij

,.....,2,1

,.....,2,1)()(0

Mi

S

S

S

S

iN

i

i

i ,.....,2,1

.

.

.2

1

Visualizing signal vectors as a set of M points in an N dimensional Euclidean space, which is also called signal space

The squared-length of any vector si is given by inner product

N

jijiii SSSS

1

22),(

The vector si is called signal vector

Two vectors are orthogonal if their inner product is zero

The energy of the signal is given by

dttSET

ii )(0

2

T N

kkik

N

jjiji dttStSE

0 11

)]([)]([

T

kj

N

jik

N

kiji dtttSSE

01 1

)()(

T

kj

N

jik

N

kiji dtttSSE

01 1

)()(

N

jiji SE

1

2

dttStS

SSSS

k

T

i

N

jkjijki

2

0

1

22

)]()([

)(

ki SS Is a Euclidean distance between vectors

Response of bank of correlators

to noisy input

Mi

TttWtStX i

.,......3,2,1

0)()()(

Received Signal X(t) is given by

NjWS

dtttXX

jij

T

o

jj

,........2,1

)()(

W(t) is AWGN with Zero Mean and PSD N0/2

Output of each correlator

T

jiij dtttSS0

)()(

First Component

Second Component

T

o

jj dtttWW )()(

N

jjj tXtXtX

1

)()()('

N

i ij j jj=1

N

j jj=1

X'(t) =S (t)+W(t)- (S + W )φ (t)

= W(t)- W φ (t)

= W'(t)

N

j jj=1

N

j jj=1

X(t) = X φ (t)+X'(t)

= X φ (t)+W'(t)

Mean and variance

ij

jij

jji

jjx

S

WES

WSE

XEm

][

][

][

][

])[(

][

2

2

2

j

ijj

jjx

WE

SXE

XVar

T T2

x j j j

0 0

T T

j j

0 0

σ = E W(t)φ (t)dt W(u)φ (u)du

= E φ (t)φ (u)W(t)W(u) dtdu

T T2

x j j j

0 0

T T

j j w

0 0

σ = φ (t)φ (u)E[ W(t)W(u) ] dtdu

= φ (t)φ (u)R (t,u)dtdu

),( utRw = autocrrelation function

)(2

),( 0 utN

utRw

T

j

T T

jjjx

dttN

dudtututN

0

20

0 0

02

)(2

)()()(2

jallforN

jx2

02

kj

dtutN

dudtututN

dudtutRut

duuuWdtttWE

WWE

SXSiXE

mXmXEXXCov

kj

T

T T

kj

T T

wkj

T T

kj

kj

ikkjj

kxkjxjkj

0

)()(2

)()()(2

),()()(

)()()()(

][

)])([(

)])([(][

0

0

0 0

0

0 0

0 0

Detection of known signals in

noise

Mi

TttwtStx i

.....,,.........3,2,1

0)()()(

MiwSx i ,,.........3,2,1

Detection of known signals in noise


H V KUMARASWAMY

Assistant Professor

Dept of Telecommunication & P G Studies

R V College of Engineering

Bangalore-59

Topics to be coveredI Digital Carrier Modulation Schemes• Optimum receiver for Binary Modulation

Schemes• Binary ASK, PSK, FSK.

• Comparison of digital modulation schemes, • M-ary signaling schemes • Synchronization methods

Topics to be covered (cont.)

II Detection and Estimation

Gram-Schmidt Orthogonalization procedure.

Geometric interpretation of signals. Response of bank of correlators to noisy

input. Detection of known signals in noise.

Topics to be covered (cont.)

Probability of error.

Correlation receiver.

Matched filter receiver.

Detection of signals with unknown phase in noise.

Maximum likelihood estimation

Topics in this session: Detection & Estimation

1 Model of digital communication system

2 Gram-schmidt orthogonalization procedure

Fundamental Issues in digital communications

1.Detection

2.Estimation

Detection theory deals with the design and evaluation of decision – making processor that observes the received signal and guesses which particular symbol was transmitted according to some set of rules.

Estimation Theory deals with the design and evaluation of a processor that uses information in the received signal to extract estimates of physical parameters or waveforms of interest.

The results of detection and estimation are always subject to errors

Model of digital communication system

Message source

Vectortransmitter

modulatorWaveformchannel

detectorVector

receiver

noise

Receiver

{mi} {Si} {Si(t)}

X(t)

X

Transmitter

Model (cont..)Consider a source that emits one symbol every T

seconds, with the symbols belonging to an alphabet of M symbols which we denote

m1, m2, . . . . . . mM.

We assume that all M symbols of the alphabet are equally likely. Then

iallforM

emittedmPp ii

1

)(

Mi

S

S

S

S

iN

i

i

i ,.....,2,1

.

.

.2

1

The output of the message source is presented to a vector transmitter producing vector of real number

Where the dimension N ≤ M.

The modulator then constructs a distinct signal si(t) of duration T seconds. The signal si(t) is necessarily of finite energy

Channel: Channel is linear, with a bandwidth that is

large enough to accommodate the transmission of the modulator output si(t) without distortion.

The transmitted signal si(t) is perturbed by an additive, zero-mean, stationary, white, Gaussian noise process.

GRAM – SCHMIDT ORTHOGONALIZATION

PROCEDURE:In case of Gram-Schmidt Orthogonalization procedure,

any set of ‘m’ energy signals {Si(t)} can be represented by a linear combination of ‘N’ orthonormal basis functions where N≤m. That is we may represent the given set of real valued energy signals S1(t), S2(t). . . . . . . Sm(t) each of duration T seconds in the form

)(........)()()( 12121111 tStStStS NN

)(........)()()( 22221212 tStStStS NN

)(........)()()( 2211 tStStStS NmNmmm

mi

TttStS

N

jjiji ......3,2,1

0)()(

1

nj

mittStS

T

jiij ......3,2,1

.....3,2,1)()()(

0

The co-efficient Sij may be viewed as the jth

element of the N – dimensional Vector Si

iN

i

i

i

S

S

S

S

'

'

'

'2

1

i = 1,2,3 . . . . . . m

Let )(4)(3 211 ttS

)(2)( 212 ttS

4

31S

2

12SVector

)(2

2)( 11 tEtfCos

T

EtS bc

b

b

)(22

)2(2

)( 12 tEtfCosT

EtfCos

T

EtS bc

b

bc

b

b

for Symbol ‘1’

for Symbol ‘0’

PSK

)(2

2)( 11 tEtfCos

T

EtS bc

b

b

0)(2 tS

for Symbol ‘1’

for Symbol ‘0’

ASK

)(2

2)( 111 tEtfCos

T

EtS b

b

b

)()2(2

)( 222 tEtfCosT

EtS b

b

b

for Symbol ‘1’

for Symbol ‘0’

FSK


H V KUMARASWAMY

Topics in this session:– Optimum transmitter &

receiver

– Correlative receiver

– Matched filter

Optimum transmitter & receiver

Probability of error depends on signal to noise ratio

As the SNR increases the probability of error decreases

An optimum transmitter and receiver is one which maximize the SNR and minimize the probability of error.

Correlative receiver

ObservationVector x

Receiver consists of a bank of M product-integrator or correlators

Φ1(t) ,Φ2(t) …….ΦM(t) orthonormal function

The bank of correlator operate on the received signal x(t) to produce observation vector x

Implemented in the form of maximum

likelihood detector

Operates on observation vector x to produce an estimate of the transmitted symbol

Inner products {(x,sk)} k= 1, 2 ..M

The largest in the resulting set of numbers is selected

The optimum receiver is commonly referred as a correlation receiver

MATCHED FILTER

dthxty jj )()()(

)()( tTt jj h

dtTxty jj )()()(

dxTy jj )()()(

T

jj dxTy0

)()()(

00)( tth j

Yj(t) = xj where xj is the j th correlator output

The impulse response of the matched filter is time-reversed and delayed version of the input signal

For causal system

MAXIMIZATION OF OUTPUT SNR

Tttwttx 0)()()(

)()()( 0 tntty

h(t) = impulse response = input signalW(t) =white noise

)(t

Impulse Response h(t)

SampleAt t = T

Outputφ(t) Known Signal

White Noise w(t)

+

MATCHED FILTER

)]([

)()(

2

2

00 tnE

TSNR

dfftjffHt )2exp()()()(0

2

2

0 )2exp()()()(

dffTjffHT

20 )(2

)( fHN

fS N

dffHN

dffStnE N

20

2

)(2

)()]([

dffH

N

dffTjffH

SNR20

2

0

)(2

)2exp()()(

)(

dffdffHdffTjffH22

2

)()()2exp()()(

Schwarz’s inequality

dffN

SNR2

00 )(

2)(

dffdtt22

)()(

dffN

SNR2

0max,0 )(

2)(

Rayleigh’s energy theorem

)2exp()(*)( fTjffH opt

)()(* ff

dftTfjfthopt )](2exp[)(*)(

)(

)](2exp[)()(

tT

dftTfjfthopt


H V KUMARASWAMY

Topics in this session:– Matched filter (cont..)

– Properties of Matched filter

– Problems

Impulse Response h(t)

SampleAt t = T

OutputΦ(t) Known Signal

White Noise w(t)

+

MATCHED FILTER

Φ(t) = input signalh(t) = impulse responseW(t) =white noise

00)( tth j

The impulse response of the matched filter is time-reversed and delayed version of the input signal

)()( tTt h

For causal system

•Matched filter properties

PROPERTY 1

The spectrum of the output signal of a matched filter with the matched signal as input is, except for a time delay factor, proportional to the energy spectral density of the input signal.

)2exp()(

)2exp()()(*

)()()(

2

0

fTjf

fTjff

ffHf opt

PROPERTY 2

The output signal of a Matched Filter is proportional to a shifted version of the AutoCorrelation Function of the input signal to which the filter is matched.

)()(0 TtRt

ERT )0()(0

At time t = T

PROPERTY 3

The output Signal to Noise Ratio of a Matched filter depends only on the ratio of the signal energy to the power spectral density of the white noise at the filter input.

)]([

)()(

2

2

00 tnE

TSNR

dfftjffHt )2exp()()()(0 2

2

0 )2exp()()()(

dffTjffHT

20 )(2

)( fHN

fS N

SNR at the output of matched filter is

dffHN

dffStnE N

202 )(2

)()]([

dffH

N

dffTjffH

SNR20

2

0

)(2

)2exp()()(

)(

dffdffHdffTjffH22

2

)()()2exp()()(

Schwarz’s inequality

dffN

SNR2

00 )(

2)(

dffdtt22

)()(

0

2

0max,0

2

)(2

)(

N

E

dffN

SNR

Rayleigh’s energy theorem

PROPERTY 4

The Matched Filtering operation may be separated into two matching conditions; namely spectral phase matching that produces the desired output peak at time T, and the spectral amplitude matching that gives this peak value its optimum signal to noise density ratio.

In polar form

)(exp)()( fjff

fTjfjfHfH 2)(exp)()(

dfTtfjffH

dfftjffHt

)](2exp[)()(

)2exp()()()('0

Spectral phase matched

dffHfTt

)()()()( '0

'0

)()( ffH

At time t = T, output is maximum

For spectral amplitude matching


H V KUMARASWAMY

Topics in this session:– Digital modulation techniques

– Digital modulation formats

– Coherent binary modulation techniques

– Coherent binary PSK [BPSK]

SHIFT KEYING METHODS Amplitude shift keying [ASK] Frequency shift keying [FSK] Phase shift keying [PSK]

Digital modulation techniques

Digital modulation formats

ASK

PSK

FSK

Hierarchy of digital modulation technique

TYPES OF DIGITAL

MODULATION SYSTEM

1.COHERENT

2.NON- COHERENT

BPSK

TRANSMITTER

BPSK

RECEIVER

If x1 > 0, the receiver decides in favour of symbol 1.

If x1 < 0, the receiver decides in favour of symbol 0.

BPSK DECISION

tfCosT

EtS c

b

b 22

)(1

tfCosT

EtfCos

T

EtS c

b

bc

b

b 22

)2(2

)(2

Where Eb= Average energy transmitted per bit

210 bb

b

EEE

Representation of BPSK

bcb

TttfCosT

t 022

)(1

In BPSK system

)()( 11 tEtS b

)()( 12 tEtS b

b

T

EdtttSSb

)()( 1

0

111

b

T

EdtttSSb

)()( 1

0

221

BPSK CO-EFFECIENTS


H V KUMARASWAMY


– Design goals

– Coherent binary modulation techniques

– Coherent binary PSK [BPSK]

– Coherent binary FSK [BFSK]

DESIGN GOALS Maximum data rate Minimum probability of symbol error Minimum transmitted power Minimum channel bandwidth Maximum resistance to interfering signals Minimum circuit complexity

Digital modulation techniques

Digital modulation formats

ASK

PSK

FSK

BPSK

TRANSMITTER

BPSK

RECEIVER

If x1 > 0, the receiver decides in favour of symbol 1.

If x1 < 0, the receiver decides in favour of symbol 0.

BPSK DECISION

tfCosT

EtS c

b

b 22

)(1

tfCosT

EtfCos

T

EtS c

b

bc

b

b 22

)2(2

)(2

Where Eb= Average energy transmitted per bit

210 bb

b

EEE

Representation of BPSK

bcb

TttfCosT

t 022

)(1

Probability of Error Calculation

In BPSK system

)()( 11 tEtS b

)()( 12 tEtS b

b

T

EdtttSSb

)()( 1

0

111

b

T

EdtttSSb

)()( 1

0

221

The observation vector x1 is related to the

received signal x(t) by

dtttxxT

0

11 )()(

The error is of two types1) Pe(0/1) i.e. transmitted as ‘1’ but received as ‘0’ 2) Pe(1/0) i.e. transmitted as ‘0’ but received as ‘0’

1

02

21

2 2

)(exp

2

1)0/1( dx

xPe

Error of 1st kind is given by

μ = mean value = for the transmission of symbol ‘0’

= Variance = for additive white Gaussian noise.Threshold Value λ = 0. [Indicates lower limit in integration]

bE

2 20N

Probability of Error Calculation [Contd..]

1

0 0

21

0

0

)(exp

1)0/1( dx

N

Ex

NPP bee

0

1

N

ExZ b

dzZPPNE

ee

b

)/(

20

0

)(exp1

)0/1(

02

1)0/1(

N

EerfcP b

e

02

1)1/0(

N

EerfcP b

e

similarly

The total probability of error

assuming probability of 1’s and 0’s are equal.

)1()1/0()0()0/1( eeeee PPPPP

)]1/0()0/1([2

1eee PPP

02

1

N

EerfcP b

e

Coherent Binary FSK

tfCosT

EtS

b

b11 2

2)(

tfCosT

EtS

b

b22 2

2)(

for symbol 1

for symbol 0

tfCosT

tb

11 22

)(

Basic orthogonal functions

OtherwiseZeroandTtfortfCosT

t bb

022

)( 22

01

bES

bES

02

coefficients

M = 2 N = 2

Transmitter

Receiver

The correlator outputs are the subtracted one from the other and resulting a random vector ‘l’ (l=x1-x2). The output ‘l’ is compared with

threshold of zero volts.

If l > 0, the receiver decides in favour of symbol 1.

l < 0, the receiver decides in favour of symbol 0.

Probability of Error Calculation

bb

TttfCosT

t 022

)( 11

bb

TttfCosT

t 022

)( 22

The transmitted signals S1(t) and S2(t) are given by

)()( 11 tEtS b

)()( 22 tEtS b

for symbol 1

for symbol 0

The observation vector x1 and x2

bT

dtttxx0

11 )()(

bT

dtttxx0

22 )()(

Assuming zero mean additive white Gaussian noise with input

PSD =N0/2 hence variance = N0/2

The new observation vector ‘l’ is the difference of two random variables x1 & x2.

l = x1 – x2

b

b

E

E

xE

xE

lE

0

11121

conditional mean of random variable ‘l’ for symbol 1 was transmitted

similarly for ‘0’ transmission

bEl

E

0

0

21 ][][][

N

xVarxVarlVar

dlN

El

NPP bee

0 0

2

0

0 2

)(exp

2

1)0/1(

02N

ElZ blet

0

2

20

22

1

)exp(1

0

N

Eerfc

dzzP

b

N

E

e

b

01 22

1

N

EerfcP b

e

similarly

The total probability of error = ][2

110 ee PP

022

1

N

EerfcP b

e


H V KUMARASWAMY


(Contd..)

– ASK [or Binary ASK]

– QPSK

BASK

Transmitter

BASK Receiver

bcb

TttfCosT

t 022

)(1

1)()( 11 SymbolfortEtS b

00)(2 SymbolfortS

022

1

N

EerfcP b

e

422

0

2

2

2

10 b

b

bbb

TATA

EEE

Probability of error

BPSK

TRANSMITTER

BPSK

RECEIVER

COHERENT QUADRIPHASE – SHIFT KEYING [QPSK]

Transmitter

QPSK Receiver

elsewhere

TtitfT

Ets c

i

0

04

)12(2cos2

)(

elsewhere

TttfiT

E

tfiT

E

ts c

c

i

0

0)2sin(4

)12(sin2

)2cos(4

)12(cos2

)(

114

72cos

2)(

014

52cos

2)(

00.4

32cos

2)(

104

2cos2

)(

4

3

2

1

dibitinputfortT

Et

dibitinputfortT

Et

dibitinputfortT

Et

dibitinputfortT

Et

fS

fS

fS

fS

c

c

c

c

Transmitted signals

E = the transmitted signal energy per symbol.T = Symbol duration.

Tttt

Tttt

fT

fT

cb

cb

02sin2

)(

02cos2

)(

2

1

Basic functions

4,3,2,1

412sin

412cos

i

iE

iE

Si

Message points

Signal vectors, Si1 & Si2

Signal Space Representation

4,3,2,1

0)()()(

i

Tttwtstx i

1

0

11

4)12(cos

)()(

wiE

dtttxxT

2

0

22

4)12(sin

)()(

wiE

dtttxxT


-The signal energy per bit 2

E

-The noise spectral density is

20N

N

N

Eerfc

EEE

erfcP

2 0

0

1

2

1

22

2

1

No

Eerfc

No

Eerfc

No

Eerfc

PPC

24

1

21

22

11

1

2

2

21

No

Eerfc

No

Eerfc

PP Ce

24

1

2

1

2

No

EerfcPe 2

No

Eerfc

b

eP 2or

In QPSK E = 2 Eb


H V KUMARASWAMY

Topics in this session:– Probability of error in QPSK

– Non coherent ASK, FSK

– DPSK


-The signal energy per bit 2

E

-The noise spectral density is

20N

N

N

Eerfc

EEE

erfcP

2 0

0

1

2

1

22

2

1

No

Eerfc

No

Eerfc

No

Eerfc

PPC

24

1

21

22

11

1

2

2

21

No

Eerfc

No

Eerfc

PP Ce

24

1

2

1

2

No

EerfcPe 2

No

Eerfc

b

eP 2or

In QPSK E = 2 Eb

BASK

Transmitter

BASK Receiver

Non coherent ASK

Transmitter

Coherent FSK

Coherent FSK

Receiver

Non coherent FSK

BPSK

TRANSMITTER

Coherent BPSK

RECEIVER

DPSK [Differential PSK]

Non-coherent PSK

Transmitter

Receiver

Input Binary Sequence {bK} 1 0 0 1 0 0 1 1

{b’K} 0 1 1 0 1 1 0 1

{dK-1} 1 1 0 1 1 0 1 1

{d’K-1} 0 0 1 0 0 1 0 0

{bKdK-1} 1 0 0 1 0 0 1 1

{b’Kd’K-1} 0 0 1 0 0 1 0 0

Differentially Encoded 1 sequence {dK}

1 0 1 1 0 1 1 1

Transmitted Phase 0 0 Π 0 0 Π 0 0 0

Received Sequence(Demodulated Sequence)

1 0 0 1 0 0 1 1

Input Binary Sequence {bK} 1 0 0 1 0 0 1 1

Differentially Encoded 1 sequence {dK}

1 0 1 1 0 1 1 1

Transmitted Phase 0 0 Π 0 0 Π 0 0 0

Received Sequence(Demodulated Sequence)

1 0 0 1 0 0 1 1


H V KUMARASWAMY

Topics to be covered in this session

I Minimum shift keying

II M-ary FSK

III M-ary PSK

Minimum shift keying

Proper utilization of phase during detection, for improving noise performance

Complexity increasesCPFSK (Continuous-phase frequency-shift keying)

.

0])0(2[2

1])0(2[2

)(

2

1

SymbolfortfCosT

E

SymbolfortfCosT

E

ts

b

b

b

b

θ(0) denotes the value of the phase at time t=0

])(2[2

)( ttfCosT

Ets c

b

b

An angle-modulated wave

θ(t) is the phase of s(t), continuous function of time.

)(2

121 fff c Carrier frequency

Phase bb

TttT

ht 0)0()(

)ff(Th 21b Deviation ratio

Measured with respect to bit rate 1/Tb

At time t=Tb

0

1)0()(

Symbolforh

SymbolforhTb

Phase Tree

Phase Trellis, for sequence 1101000

)2()]([2

)2()]([2

)( tfSintSinT

EtfCostCos

T

Ets c

b

bc

b

b

In terms of In phase and Quadrature Component

bb

TttT

t 02

)0()(

+ Sign corresponds to symbol 1

- Sign corresponds to symbol 0

h=1/2

bbbb

b

bb

b

b

b

TtTtT

CosT

E

tT

CosCosT

E

tCosT

Ets

2

2

2])0([

2

])([2

)(1

For the interval of bb TtT

Half cosine pulse

In phase components

+ Sign corresponds to θ(0) =0- Sign corresponds to θ(0) = п

bbb

b

bb

b

b

b

bQ

TttT

CosT

E

tT

CosTSinT

E

tSinT

Ets

202

2

2])([

2

])([2

)(

Quadrature components

+ Sign corresponds to θ(Tb) =п/2- Sign corresponds to θ(Tb) = -п/2

Half sine pulse

Four possibilities

bbcbb

TtTtfCostT

CosT

t

)2(

2

2)(1

bcbb

TttfSintT

SinT

t 20)2(2

2)(2

bTttststs 0)()()( 2211

Basic functions

bbb

T

T

TtTCosE

dtttssb

b

)0(

)()( 11

bbb

T

TtTSinE

dtttssb

b

20)(

)()(2

0

22

coefficients

Signal Space Characterization of MSK

bb

T

T

TtTws

dtttxxb

b

11

11 )()(

b

T

Ttws

dtttxxb

20

)()(

22

2

0

22

0

2

0 4

1

N

Eerfc

N

EerfcP bb

e

0N

EerfcP b

e

MSK receiver

Q-channel

Sketch the waveform of the MSK signal for the sequence for the 101101.Assume that the carrier frequencya) Is 1.25 times the bit rate. b) Equal to the bit

Solution (a) fc =(f1+f2)/2 =1.25/ Tb OR f1+f2=2.5/Tb

Also f1-f2=1/(2Tb)

Solving f1=1.5/Tb f2=1/Tb

(b) fc=1/Tb f1+f2=2/Tb f1-f2=1/(2Tb)\

Solving f1=1.25/Tb f2=0.75/Tb


H V KUMARASWAMY

Topics in this session:

M-ary Modulation Technique

M-ary PSK and FSK

Problems

Bandwidth calculation

1....,..........,.........2,1,02

22

)(

Mi

M

itfCos

T

Ets ci

TttfCosT

t c 022

)(1

TttfSinT

t c 022

)(2

M - ary PSK

Orthogonal Functions

Signal Constellation for octaphase – shift - keying

M=8

Receiver for Coherent M-ary PSK

The decision making process in the phase discriminator is based on the noisy inputs

1..........1,02

1..........1,02

MiwM

iSinEx

MiwM

iCosEx

QQ

II

M - ary QAM

Block Diagram of M –ary QAM System - Transmitter

Block Diagram of M –ary QAM System - Receiver

Signalling Constellation M=16

M-ary QPSK M-ary QAM

Serial to Parallel

D / A VCOBinary Data M-ary FSK

M-ary FSK

Problems

A bandpass data transmission scheme uses a PSK signalling scheme with

bcbc T

TttACostS 10

,0,)(2

mSecTTttACostS bbc 2.0,0,)(1

The Carrier Amplitude at the receiver input is 1mV and the PSD of the Additive white gaussian Noise at the input is 10-11 Watts/Hz. Assume that an ideal correlation receiver is used. Calculate average bit error rate of the receiver.

3

3

11

323

0

2

0

110

107.0

1044.12

1)236.2(

2

1

52

1

)102(*2

10*2.0*)10(

2

1

22

1

2

1

/102

1

12.0

erfc

erfcerfc

N

TAerfc

N

EerfcP

HzWattN

mVA

RmSecT

bbe

c

bb

Using erfc function

3

0

2

107.000069.0)2.3(

10

Q

QN

TAQP b

e

Using Q function

Bandwidth calculation

1 ASK BW=2rb

2 PSK BW=2rb

3 FSK BW>2rb


H V KUMARASWAMY

Topics in this session:

Synchronization Carrier synchronizationSymbol synchronizationApplications

1 Voice-grade modem2 Digital radio3 Digital communication by satellite

Synchronization

1 carrier recovery or Carrier Synchronization

2 Clock recovery or Symbol Synchronization

3 Word Synchronization

•Carrier Synchronization

Mth power loop

Square loop ( M = 2 )

Costas loop

Mth power loop

Costas loop

•Symbol Synchronization

1 Transmitting clock along with the data-bearing signal

[ multiplexed form ]

- waste of clock power

2 Use a noncoherent detector to extract clock

3 Clock is extracted from the demodulated base band signal

•Matched filter

•Early-late gate synchronizer

•Applications

1 Voice-grade ModemsVoice frequency range- 300-3400 Hz

A/DMod

Dem

Mod

Dem D/A

Modem Modem

Telephone channelvoice voice

FSK modem operating at 1200bps, commonly used frequencies 1300Hz & 2100Hz

16 QAM

Phase jitter in M-ary PSK & DPSK

DPSK limited to 4800bps

M-ary QAM

•Digital radio

- Information originating from a source is transmitted to its destination by means of digital modulation techniques over an appropriate number of microwave radio links.

- LOS [ Line Of Sight ] propagation.- 64kbps PCM is used- M-ary QAM [ M=64, M=256 ]- Multipath fading- Diversity Techniques

LOS [ Line Of Sight ] propagation

Reflected wave

Building

Digital Communication by Satellite

-TDMA-Transmission are organized into frames-A frame contain N bursts-Preamble , Post amble, guar time



M-ary PSK

Coherent MSK

QPSK for BW saving

-Power efficiency is increased by using TWT near saturation

-Independent simultaneous provisions for carrier and clock recovery, overhead recovery time is minimized

Documents

DC Digital Communication PART1