COMM702: Modulation II

Lecture 4

- Coherent and non-coherent binary pass-band data

transmission

Binary Digital Modulation

Sinusoidal Carrier

ASK

FSK

Digital Message

PSK

band transmission-Parameters of Digital Pass

(1) Probability of Error:

The goal is to obtain optimum receiver so as to minimize the

average probability of error.

(2) Power Spectra:

It is important in:

- Occupancy of B.W

- Cochannel interference in multiplexed systems

(3) Bandwidth (Spectral) efficiency:

The objective of efficient modulation is to maximize the bandwidth

efficiency defined by:

Where is the bit rate in [bits/sec] and B is the signal bandwidth in Hz.

][bits/s/HzB

Rb

bR

Detection of Digital Communications

Non-Coherent - The receiver is equipped

with an envelope detector

-The envelope detector

demodulates the incoming

signal without need

to a phase.

-It is simpler than the

coherent detection but its

performance is lower than

the coherent detector.

Coherent

-The receiver generates a

carrier signal with the

same phase and frequency

as the transmitted one.

-It is complex but has better

performance than

non-coherent detection.

Binary Amplitude Shift Keying Time Domain Representation:

A binary amplitude shift keying signal (BASK) can be defined as:

Where m(t) is rectangular pulses and is the carrier frequency.

cf

)(tm

)(ts

tftmT

Ets c

b

2cos)(2

)(

Time Domain Representation of BASK

Next figure shows OOK

OOKOn-off keying (OOK)

OOK

b

Power spectral density of OOK • The PSD of OOK signal is given by:

Where is the PSD of which is a random unipolar binary

waveform with amplitude 0 and 1. The PSD of m(t) is:

Then, from (1) and (2), the PSD of OOK signal is:

)( fSm)(tm

)2()(sin

)(4

1)(

22

2

b

bm

Tf

TfffS

Reference: Page 394

Digital & analog

Communication

Systems, K. Sam.

)1()]()([2

)( cmcm

b

s ffSffST

EfS

22

2

22

2

)(

))((sin

)(

))((sin)]()([

8)(

cb

cb

cb

cbcc

b

SffT

ffT

ffT

ffTffff

T

EfS

Power spectral density of BASK

16

2A

bT

E

8

22

2

)(

))((sin

8 cb

cb

b ffT

ffT

T

E

SK BandwidthA

• Null-to-null bandwidth:

Where is the bit rate [bits/sec].

is the bit duration [sec]

bRWB 2.

bR

bb

TR

1

bT

Generation of BASK

)(ts)(tmE

tftmT

Ets c

b

2cos)(2

)(

tfT

t c

b

2cos2

)(1

Coherent Detection of BASK

S(t)

T

T

T

tfT

t c

b

2cos2

)(1

1x0

threshold

Coherent Detection of BASK-Threshold determination

1 0

0,

]4

4sin[

4cos12

12

2cos2

2cos2

)()(

1)(

,0intervalthein1isbitdtransmittetheAssume

1

0

0 0

11

xzeroisbitdtransmittetheWhen

E

f

TfT

T

E

dttfT

E

dttfT

tfT

Edtttsx

tmthen

Tt

c

bcb

b

c

T

b

c

b

c

T T

b

b

b

b b

E

2

E

b

bcT

nnRfSince

0

Coherent Detection of ASK-Non

• Since the information is conveyed in the amplitude or the envelope of

the modulated signal, then an envelope detector can be used to extract it.

• Advantages of non-coherent detection:

- No need for carrier synchronization

- Simple implementation.

• Disadvantages of non-coherent detection:

- Its performance is lower than the coherent one in presence of noise.

Envelope

Detector

Decision

Block

)(ˆ tm

Calculate the threshold in H.W:

this case

tftmT

Ets c

b

2cos)(2

)( )(2

tmT

E

b

Performance of digital modulations in presence of noise

• The additive noise to the signal is assumed to be stationary Gaussian random process (signal) with zero mean and variance No/2.

• The performance of a digital communication system is described by the probability of bit error and the probability of symbol error as a function of the received Eb/No ratio.

• For binary modulation systems, symbol and bit error probability are the same.

• The method to obtain the probability of error of coherent digital modulations is as follows:

We express the digital signal as a linear combination of orthonormal

waveforms and then we draw the signal vectors (or constellation diagram) as a function of these orthonormal waveforms and then calculate the distance between the vector points as described before.

Probability of Error of Coherent OOK

Then s(t) can be expressed as:

If the transmitted bit is 0, then S(t)=0

• The distance between So and S1 is:

• Then the probability of error of coherent ASK is given by:

Ed

oo N

EQ

N

dQeP

22)(

2

tfT

t c

b

2cos2

)(where 1

bc

b

TttfT

Ets 02cos

2)( then 1, isbit ed transmitt theIf

)()( 11 tEts

Binary Phase Shift Keying (BPSK)

• In PSK, the information is contained in the instantaneous phase of the modulated carrier.

• For binary PSK, phase states of 0 and 180 are used.

• There is no non-coherent PSK instead we have differentially coherent PSK.

Time domain representation:

1

0

Generation of BPSK

Coherent Detection of BPSK • There is no non-coherent detector for PSK.

• The coherent detector requires perfect knowledge of the carrier phase at the receiver.

S(t)

Coherent Detection of BPSK

)(ts

1x0bE bE

Thresholdb

b

c

bc

b

b

b

c

T

b

b

T

c

b

c

b

b

c

b

b

T

Ex

Ef

TfT

T

E

dttfT

E

dttfT

tfT

Ex

tfT

E

dtttsx

b

b

b

1

0

0

1

0

11

0, ngtransmittifor Similarly

4

)4sin(

)4(cos1(

)2cos(2

)2cos(2

)2cos(2

s(t)then

,dtransmitteis1Assume

)()(

0

Probability of Error of Coherent BPSK

• The distance between So and S1 is:

bEd 2

o

b

o N

EQ

N

dQeP

2

2)(

2

Differential PSK (DPSK)

Differential PSK (Cont.)

Detected bits at the receiver: 1 1 0 1 0

Receiver of Differential PSK

Receiver of DPSK (Cont.)

Probability of Error of DPSK

• The bit error probability of DPSK is given by:

Bandwidth of PSK:

• Null- to null bandwidth

Where is the bit rate

0

exp2

1

N

EP b

e

bRWB 2.

bR

Power spectral density of BPSK

Power spectral density of BPSK

SystemsionCommunicat

HaykinSimonPageExampleSee ,48,6.1

SystemsionCommunicat

HaykinSimonPageExampleSee ,48,6.1

Power spectral density of BPSK

fc+2Rb fc-2Rb

2Rb

Power Spectral Density of BPSK

Comparison of BER of Different Binary Digital Modulations