Digital Communications I:Modulation and Coding Course

Spring - 2013Jeffrey N. Denenberg

Lecture 4: BandPass Modulation/Demodulation

Lecture 7 2

Last time we talked about:

Another source of error due to filtering effect of the system: Inter-symbol interference (ISI)

The techniques to reduce ISI Pulse shaping to achieve zero ISI at

the sampling time Equalization to combat the filtering

effect of the channel

Lecture 7 3

Today, we are going to talk about:

Some bandpass modulation schemes used in DCS for transmitting information over channel M-PAM, M-PSK, M-FSK, M-QAM

How to detect the transmitted information at the receiver Coherent detection Non-coherent detection

Lecture 7 4

Block diagram of a DCS

FormatSourceencode

FormatSourcedecode

Channelencode

Pulsemodulate

Bandpassmodulate

Channeldecode

Demod. Sample

Detect

Channel

Digital modulation

Digital demodulation

Lecture 7 5

Bandpass modulation

Bandpass modulation: The process of converting a data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, are varied in accordance with the transmitting data.

Bandpass signal:

where is the baseband pulse shape with energy . We assume here (otherwise will be stated):

is a rectangular pulse shape with unit energy. Gray coding is used for mapping bits to symbols. denotes average symbol energy given by

TtttitT

Etgts ic

iTi 0 )()1(cos

2)()(

)(tgT

)(tgT gE

sE

M

i is EM

E1

1

Lecture 7 6

Demodulation and detection

Demodulation: The receiver signal is converted to baseband, filtered and sampled.

Detection: Sampled values are used for detection using a decision rule such as the ML detection rule.

Nz

z

1

zT

0

)(1 t

T

0

)(tN)(tr

1z

Nz

z Decision circuits

(ML detector)m̂

Lecture 7 7

Coherent detection

Coherent detection requires carrier phase recovery at the

receiver and hence, circuits to perform phase estimation.

Sources of carrier-phase mismatch at the receiver: Propagation delay causes carrier-phase

offset in the received signal. The oscillators at the receiver which

generate the carrier signal, are not usually phased locked to the transmitted carrier.

Lecture 7 8

Coherent detection ..

Circuits such as Phase-Locked-Loop (PLL) are implemented at the receiver for carrier phase estimation ( ).

PLL

Oscillator 90 deg.

)()(cos2

)()( tnttT

Etgtr ii

iT ˆcos

2t

T c

ˆsin2

tT c

Used by correlators

ˆ

I branch

Q branch

Lecture 7 9

Bandpass Modulation Schemes

One dimensional waveforms Amplitude Shift Keying (ASK) M-ary Pulse Amplitude Modulation (M-

PAM) Two dimensional waveforms M-ary Phase Shift Keying (M-PSK) M-ary Quadrature Amplitude

Modulation (M-QAM) Multidimensional waveforms M-ary Frequency Shift Keying (M-FSK)

Lecture 7 10

One dimensional modulation, demodulation and detection

Amplitude Shift Keying (ASK) modulation:

tT

Ets c

ii cos

2)(

cos2

)(

,,1 )()(

1

1

ii

c

ii

Ea

tT

t

Mitats

)(1 t1s2s

0 1E

“0” “1”

On-off keying (M=2):

Lecture 7 11

One dimensional mod.,…

M-ary Pulse Amplitude modulation (M-PAM)

tT

ats cii cos2

)(

gs

gii

gi

c

ii

EM

E

MiEE

EMia

tT

t

Mitats

3

)1(

12

)12(

cos2

)(

,,1 )()(

2

22

1

1

s

4-PAM:

)(1 t2s1s

0gE3

“00” “01”

4s3s“11” “10”

gE gE gE3

Lecture 7 12

Example of bandpass modulation:Binary PAM

Lecture 7 13

Coherent detection of M-PAM

T

0

)(1 t

ML detector(Compare with M-1 thresholds)

)(tr 1zm̂

One dimensional mod.,...–cont’d

Lecture 7 14

Two dimensional modulation, demodulation and detection (M-

PSK) M-ary Phase Shift Keying (M-PSK)

M

it

T

Ets c

si

2cos

2)(

2

21

21

2211

2

sin 2

cos

sin2

)( cos2

)(

,,1 )( )()(

iis

sisi

cc

iii

EE

M

iEa

M

iEa

tT

ttT

t

Mitatats

s

Lecture 7 15

Two dimensional mod.,… (MPSK)

)(1 t

2s1s

bE

“0” “1”

bE

)(2 t

3s

7s

“110”)(1 t

4s 2ssE

“000”

)(2 t

6s 8s

1s

5s

“001”“011”

“010”

“101”

“111” “100”

)(1 t

2s 1s

sE

“00”

“11”

)(2 t

3s 4s“10”

“01”

QPSK (M=4)

BPSK (M=2)

8PSK (M=8)

Lecture 7 16

Two dimensional mod.,…(MPSK)

Coherent detection of MPSK

Compute Choose smallest

2

1arctanz

z ̂|ˆ| i

T

0

)(1 t

T

0

)(2 t)(tr

1z

2z

m̂

Lecture 7 17

Two dimensional mod.,… (M-QAM)

M-ary Quadrature Amplitude Mod. (M-QAM)

ici

i tT

Ets cos

2)(

3

)1(2 and symbols PAM are and where

sin2

)( cos2

)(

,,1 )( )()(

21

21

2211

MEaa

tT

ttT

t

Mitatats

sii

cc

iii

)1,1()1,3()1,1(

)3,1()3,3()3,1(

)1,1()1,3()1,1(

, 21

MMMMMM

MMMMMM

MMMMMM

aa ii

Lecture 7 18

Two dimensional mod.,… (M-QAM)

)(1 t

)(2 t

2s1s 3s 4s“0000” “0001” “0011” “0010”

6s5s 7s 8s

10s9s 11s 12s

14s13s 15s 16s

1 3-1-3

“1000” “1001” “1011” “1010”

“1100” “1101” “1111” “1110”

“0100” “0101” “0111” “0110”

1

3

-1

-3

16-QAM

Lecture 7 19

Two dimensional mod.,… (M-QAM)

Coherent detection of M-QAM

T

0

)(1 t

ML detector1z

T

0

)(2 t

ML detector

)(tr

2z

m̂Parallel-to-serialconverter

s) threshold1 with (Compare M

s) threshold1 with (Compare M

Lecture 7 20

Multi-dimensional modulation, demodulation & detection

M-ary Frequency Shift keying (M-FSK)

Tf

titT

Et

T

Ets c

si

si

2

1

2

)1(cos2

cos2

)(

2

1

0

cos

2)(

,,1 )()(

iis

sijii

M

jjiji

EE

ji

jiEat

Tt

Mitats

s

)(1 t

2s

1s

3s

)(3 t

)(2 tsE

sE

sE

Lecture 7 21

Multi-dimensional mod.,…(M-FSK)

Mz

z

1

zT

0

)(1 t

T

0

)(tM)(tr

1z

Mz

zML detector:

Choose the largest element

in the observed vector

m̂

Lecture 7 22

Non-coherent detection

Non-coherent detection: No need for a reference in phase with

the received carrier Less complexity compared to coherent

detection at the price of higher error rate.

Lecture 7 23

Non-coherent detection …

Differential coherent detection Differential encoding of the message

The symbol phase changes if the current bit is different from the previous bit.

,...,MiTtttT

Ets ii 1 ,0 ,)(cos

2)( 0

)())1(()( nTTnnT ikk

)(1 t

i

1s2s 0

0 1 2 3 4 5 6 7 1 1 0 1 0 1 11 1 1 0 0 1 1 1 0 0

Symbol index: Data bits:Diff. encoded bitsSymbol phase: k

kmk

Lecture 7 24

Non-coherent detection … Coherent detection for diff encoded mod.

assumes slow variation in carrier-phase mismatch during two symbol intervals.

correlates the received signal with basis functions uses the phase difference between the current

received vector and previously estimated symbol

TttnttT

Etr i 0 ),()(cos

2)( 0

)(1 t

)(2 t

),( 11 ba),( 22 ba

i

)())1(()())1(()( nTTnnTTnnT ijiji

Lecture 7 25

Non-coherent detection … Optimum differentially coherent detector

Sub-optimum differentially coherent detector

Performance degradation about 3 dB by using sub-optimal detector

T

0

)(1 t

)(tr m̂Decision

DelayT

T

0)(tr m̂Decision

DelayT

Lecture 7 26

Non-coherent detection … Energy detection

Non-coherent detection for orthogonal signals (e.g. M-FSK)

Carrier-phase offset causes partial correlation between I and Q branches for each candidate signal.

The received energy corresponding to each candidate signal is used for detection.

Lecture 7 27

Non-coherent detection …

Non-coherent detection of BFSK

T

0

)cos(/2 1tT

T

0)(tr

11z

12z

T

0

T

0

21z

22z

Decision stage:

)cos(/2 2tT

)sin(/2 2tT

)sin(/2 1tT

2

2

2

2 +

-

)(Tz

0ˆ ,0)( if

1ˆ ,0)( if

mTz

mTzm̂

212

211 zz

222

221 zz